01_08_2014_03_54_04_Mechanical.pdf

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Old GATE Questions along with Key from 1991-2014 in Mechanical Department

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Index

Sl.No. Name of the Subject Pg.No.s 1. Engineering Mathematics 1 -71 2. Strength of Materials 72 – 122 3. Theory of Machines 123 – 167 4. Fluid Mechanics 168- 209 5. Production Planning and Control 210 – 248 6. Machine Design 249-278 7. Theory of Machines 279-308 8. IM & OR 309 – 334 9. Heat-Transfer 335-352

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Index- Engineering Mathematics

Sl.No. Name of the Topic Pg.No.s 1. Linear Algebra 2-19 2. Calculus 20-23 3. Differential Equations 24-34 4. Complex variables 35-41 5. Numerical Methods 42-49 6. Probability and Statistics 50-62 7. Transform Theory 63-71









.

.

. 1 Marks GATE-CSE/IT-2000( )








1)The determinant of the matrix

is

[A]4 [B]0[C]15 [D]20

2)Consider the following set of equations:x + 2y = 54x + 8y = 123x + 6y + 3z = 15 This set

[A]has unique solution [B]has no solutions[C] has finite number of solutions [D]has infinite number of solutions

3)Let a= ( j ) be an n-rowed square matrix and be the matrix obtained by interchanging the first andsecond rows of the n-rowed Identify matrix. Then A is such that its first

[A] row is the same as its second row [B] row is the same as the second row of A[C]column is the same as the second column of A [D]row is all zero

4)Let Ax = b be a system of linear equations where A is an m × n matrix and b is a m × 1 column vector andX is a n × 1 column vector of unknows. Which of the following is false?

[A]The system has a solution if and only if, both Aand the augmented matrix [A b] have the samerank.

[B] If m <n and b is the zero vector, then the systemhas infinitely many solutions.

[C]If m = n and b is non-zero vector, then the systemhas a unique solution.

[D]The system will have only a trivial solution whenm = n, b is the zero vector and rank (A) = n.

5)The matrices and commute under multiplication

[A] if a = b or θ = nπ, is an integer [B]always[C]never [D]if a cos θ ≠ b sin θ

6)_The rank of the following (_n _+ _1)_× (_n _+ _1)_matrix, where a is a real number is

_

[A]1 [B]2[C]n [D]Depends on the value of a

7)A unit vector perpendicular to both the vectors a = 2i − 2 j + k and b = 1 + j − 2k is:

[A] (i+j+k) [B]1 / 3 (i+j-k)[C]1 /3 (i-j-k) [D] (i+j-k)

8)Let A and B be real symmetric matrices of size n × n . Then which one of the following is true?

[A] [B][C]AB = BA [D]

Linear Algebra

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. 2 Marks GATE-ECE/TCE-1993( )

. 2 Marks GATE-EEE-2011( )



9)

Therankof matrix is

[A]0 [B]1[C]2 [D]3

10)In a compact single dimensional array representation for lower triangular matrices (i.e all theelements above the diagonal are zero) of size n × n, non zero elements (i.e elements of the lower triangle)of each row are stored one after another, starting from the first row, the index of the (i, j )thtriangular matrix in this new representation is: element

[A] i+j [B] i+j-1[C]j+ i(i-1)/2 [D]i+j(j-1)/2

11)The eigen vector(s) of the matrix

, is (are)

[A] (0,0, ) [B] ( , 0 , 0)[C](0,0,1) [D](0, ,0)

12)Consider the following system of linear equations

Notice that the second and the third columns of the coefficient matrix are linearly dependent . For howmany values of , does this system of equations have infinity many solutions?

[A]0 [B]1[C]2 [D]Infinity many

13)

The eigen vector(s) of the matrix , is/are

[A] [B][C] [D]

14)The matrix is decomposed into a product of a lower triangular matrix [L] and an uppertriangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

[A] [B]

[C] [D]

15)A Matrix has eigenvalues -1 and -2. The corresponding eigenvectors are and respectively. Thematrix is

[A] [B]

[C] [D]

16)Roots of the algebraic equation are

[A] [B] ( -1, -j, +j)[C] [D]

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17) A cubic polynomial with real coefficients

[A]can possibly have no extrema and no zerocrossings

[B]may have up to three extrema and up to 2 zerocrossings

[C]cannot have more than two extrema and morethan three zero crossings

[D]will always have an equal number of extrema andzero crossings

18) The trace and determinant of a 2 ´ 2 matrix are known to be -2 and -35 respectively. Its eigen values are

[A] -30 and -5 [B] -37 and -1[C]-7 and 5 [D] 17.5 and -2

19)The determinant of the matrix

is

[A]100 [B]200[C]1 [D]300

20)A set of linear equations is represented by the matrix equation Ax=b. the necessary condition forthe existence of a solution for this system is:

[A]A must be invertible [B]b must be linearly depended on the columns of A[C]b must be linearly independent of the columns of

A [D]None of the above

21)

The vector is an eigen vector of .One of the given values A is

[A]1 [B]2[C]5 [D]-1

22)

sum of the eigen values of the matrix A is:

[A]10 [B] -10[C]24 [D]22

23)

. The inverse of A is:

[A] [B]

[C] [D]

24)A square matrix IS called singular, if its

[A]determinan t is unity [B]determinant is zero[C]determinantt is infinity [D]rank is unity

25)

The inverse of the matrix IS

[A] [B]

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[C] [D]

26)A matrix has all its entries equal to -a.the rank of the matrix is

[A]7 [B]5[C]1 [D]zero

27)The eigen values of the matrix are

[A] (a+1),0 [B]a,0[C](a-1),0 [D]0,0

28)The inverse of the matrix is

[A] [B]

[C] [D]

29)The eigenvalues of matrix are

[A] -2.42 and 6.86 [B]3.48 and 13.53[C]4.70 and 6.86 [D]6.86 and 9.50

30)[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sumand difference of these matrices are defined as [S] = [A] + [A]T and [D] = [A] - [A]T , respectively. Which ofthe following statements is TRUE?

[A]Both [S] and [D] are symmetric [B]Both [S] and [D] are skew-symmetric[C][S] is skew-symmetric and [D] is symmetric [D][S] is symmetric and [D] is skew-symmetric

31)If and are two arbitrary vectors. with magnitudes a and b, respectively, will be equal to

[A] [B][C] [D]

32)A square matrix B is skew-symmetric if

[A] [B][C] [D]

33)For a scalar function , the gradient at the point P (1, 2, -1) is

[A] [B][C] [D]

34)Solution for the system defined by the set of equations 4y+3z=8; 2x-z=2; and 3x+2y=5 is

[A]x=0; y=1; z=4/3 [B]x=0; y=1/2; z=2[C]x=1; y=1/2; z=2 [D]nonexistent

35)The product of matrices is

[A] [B][C] [D]

36)For a scalar function the directional derivative at the point P ( 1, 2, -1) in thedirection of a vector is

[A] -18 [B][C] [D]18

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37)For a given matrix , one of the eigenvalues is 3.The other two eigenvalues are

[A]2,- 5 [B]3, -5[C]2, 5 [D]3, 5

38)The directional derivative of f(x ,y, z) = at the point P: (2, 1, 3) in the direction of the vector a =i-2k is

[A] -2.785 [B] - 2.145[C]- 1.789 [D]1.000

39)The Eigen values of the matrix are

[A] -7 and 8 [B] -6 and 5[C]3 and 4 [D]1 and 2

40)Consider the matrices , and .The order of will be

[A] [B][C] [D]

41)Consider a non-homogeneous system of linear equations representing mathematically an overdetermined system. Such a system will be

[A]consistent having a unique solution [B]consistent having a many solutions[C]

inconsistent having a unique solution

[D]

inconsistent having no solution42)The following simultaneou s equations

x+yz=3x+2y+3z=4x+4y+kz=6will NOT have a uniqu e solution fork equal to

[A]0 [B]30[C]6 [D]7

43)The inner (dot) product of two vectors and is zero. The angle (degrees) between the two vectors is

[A]0 [B]5[C]90 [D]120

44)The minimum and the maximum eigen values of the matrix are -2 and 6, respectively. What is theother eigen value?

[A]5 [B]3[C]1 [D]-1

45)For what values of and the following simultaneous equations have an infinite number of solutions?

[A]2,7 [B]3,8[C]8,3 [D]72

46)A velocity vector is given as The divergence of this velocity vector at (1,1,1) is

[A]9 [B]10[C]14 [D]15

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47)The inverse of the 2 x 2 matrix is

[A] [B]

[C] [D]

48)Given that one root of the equation is 5, the other two roots are

[A]2 and 3 [B]2 and 4[C]3 and 4 [D]-2 and -3

49)If A and Bare two ma trices and if AB exists, then BA exists

[A] if A has as many rows as B has columns [B]only if both A and B are square matrices[C]only if A and B are skew matrices [D]only if both A and B are symmetric

50)If the determinant of the matrix is 26,then the determinant of the matrix is

[A] -26 [B]26[C]0 [D]52

51)Real matrix , , , , and are given. Matrices [B] and [E] are symmetric.Following statements are made with respect to these matrices.I. Matrix product is a scalarII. Matrix product is always symmetricWith reference to above statements, which of the following applies?

[A]Statement I is true but II is false [B]Statement I is false but II is true[C]Both the statements are true [D]Both the statements are false

52)The eigenvalues of the matrix

[A]are 1 and 4 [B]are -1 and 2[C]are 0 and 5 [D]cannot be determined

53)Consider the system of equations, where, 1is a scalar.

Let be an eigen-pair of an eigen value and its corresponding eigen vector for real matrix A. Let I bea (n' n) unit matrix. Which one of the following statement is NOT correct?

[A]For a homogeneous system of linearequations, (A-II) x= 0 having a nontrivial solution,the rank of (A-Il) is less than n.

[B]For matrix , m being a positive integer,will be the eigen-pair for all i

[C]If , then for all i [D]If , then is for all i54)

Given Matrix , the rank of the matrix is

[A]4 [B]3[C]2 [D]1

55)

Determinant of the following matrix is

[A] -76 [B] -28[C]+28 [D]+72

56)If,A, B, C are square matrices of the same order, is equal to

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. 2 Marks GATE-EIN/IN-2013( )

[A] [B][C] [D]

57)The product of the following two matrices [P] and [Q] is

;

[A] [B]

[C] [D]

58)The given values of the matrix are

[A] (5.13, 9.42) [B] (3.85, 2.93)[C](9.00, 5.00) [D](10.16, 3.84)

59)Consider the following two statements:I. The maximum number of linearly independent column vectors of a matrix A is called the rank of A.II. If A is an square matrix, it will be non singular is rank A = n.With reference to the above statements, which of the following applies ?

[A]Both the statements are false [B]Both the statements are true[C]I is true but II is false [D]I is false but II is true.

60)If A is any n x n matrix and k is a scalar, where is

[A] [B][C] [D]

61)

Inverse of matrix is

[A] [B]

[C] [D]

62)If A is a real square matrix,then is

[A]Unsymmetric [B]always symmetric[C]Skew-symmetric [D]Some times symmetric

63)In matrix algebra AS = AT (A, 5, T, a re matrices of appropriate order) implies S=T only if

[A]A is symmetric [B]A is singular[C]A is non singular [D]A is skew symmetric

64)The real symmetric matrix C corresponding to the Quadratic form

[A] [B]

[C] [D]

65)One pair of eigen vectors corresponding to the two eigenvalues of the matrix is

[A] [B]

[C] [D]

66)Given that and ,the value of is

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. 1 Marks GATE-ME-1999( )


[A]15A+12I [B]19A+30I[C]17A+15I [D]17A+21I

67)The eigen values of a (2x2) matrix X are -2 and -3. The eigenvalues of matrix (X+5I) are

[A] -3,-4 [B] -1,-2[C]-1,-3 [D]-2,-4

68)The matrix rotates a vector about the axis by an angle of

[A] [B][C] [D]

69)The rank of the matrix , is

[A]0 [B]1[C]2 [D]3

70)For a singular matrix.

[A]Atleast one eigen value would be at the origin [B]All eigen values would be at the origin[C]No eigen value would be at the origin. [D]None

71)Identify which one of the following is an eigenvector of the matrix

[A] [B][C] [D]

72)For a given matrix A, it is observed that

and Then matrix A is

[A] [B]

[C] [D]

73)Let , with and .Then the rank of A is

[A]0 [B]1[C]n-1 [D]n

74)Rank of the matrix given below is

[A]1 [B]2[C]3 [D]

75)Given the matrix , the eigen vector is

[A] [B]

[C] [D]

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76)Let . Then (a+b) =

[A]7/20 [B]3/20[C]19/20 [D]11/20

77)

Given an orthogonal matrix , then the value of is

[A] [B]

[C] [D]

78)

The rank of the matrix is

[A]0 [B]1[C]2 [D]3

79)The Eigen values and the corresponding Eigen vectors of a 2 x 2 matrix are given byEigen value Eigen vector

The matrix is

[A] [B]

[C] [D]

80)For the matrix the given value corresponding to the eigen vector is

[A]2 [B]4[C]6 [D]8

81)It is given that are M non-zero orthogonal vectors. The dimension of the vector space spannedby the 2M vectors is

[A]2M [B]M + 1[C]M [D]dependent on the choice of

82)All the four entries of the 2 x 2 matrix are nonzero, and one of its eigen values is zero.Which of the following statements is true?

[A] [B][C] [D]

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83)The system of linear equations4x+ 2y = 72x+y = 6has

[A] A unique solution [B]No solution[C]An infinite number of solutions [D]Exactly two distinct solutions

84)

Consider the matrix The value of is

[A] [B]

[C] [D]

85)

The eigen values of the following matrix are

[A]3, 3 + 5j, 6-j [B] -6, + 5j, 3 + j, 3-j[C]3 + j, 3-j, 5 + j [D]3, -1 + 3j, -1-3j

86)In the matrix equation Px = q, which of the following is a necessary condition for the existence of at leastone solution for the unknown vector x

[A]Augmented matrix [Pq] must have the same rankas matrix P [B]Vector q must have only non-zero elements

[C]Matrix P must be singular [D]Matrix P must be square87)

For the matrix P = one of the eigen values is equal to -2. which of the following is an eigenvector?

[A] [B]

[C] [D]

88)

If R = ,then top row of is

[A] [ 5 6 4 ] [B] [ 5 -3 1 ][C][ 2 0 -1 ] [D] [ 2 -1 1/2 ]

89) is an n-tuple nonzero vector. The n x n matrix

[A]Has rank zero [B]Has rank 1[C]Is orthogonal [D]Has rank n

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90)A loaded dice has following probability distribution of occurrences

If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on thethree dice is

[A]Same as that of occurrence of 3, 4, 5 [B]Same as that of occurrence of 1,2,5[C]1/128 [D]5/8

91)Let x and y be two vectors in a 3 dimensional space and <x,y> denote their dot product. Then thedeterminant

det

[A] Is zero when x and y are linearly independent [B] Is positive when x and y are linearly independent[C]Is non-zero for all non-zero x and y [D]Is zero only when either x or y is zero

92)The linear operation L(x) is defined by the cross product L(x) = b x X where and are three dimensional vectors. The 3 x 3 matrix M of this operation

satisfies

.Then the eigen value of M are

[A]0 + 1, -1 [B]1, -1, 1[C]i, -i, 1 [D]i, -i, 0

93)The characteristic equation of a (3 x3) matrix P is defined as

If I denotes identity matrix then the inverse of matrix P will be

[A] [B][C] [D]

94)If the rank of a (5 x 6) matrix Q is 4 then which one of the following statements is correct?

[A]Q will have four linearly independent rows andfour linearly independent columns

[B]Q will have for linearly independent rows and fivelinearly independent columns

[C] will be invertible [D] will be invertible95)A is m x n full rank matrix with m >n and I is an identity matrix. Let matrix . Then which one

of the following statement is False?

[A] [B][C] [D]

96) Let P be a 2 X 2 real orthogonal matrix and is a real vector with length . Thenwhich of one of the following statement is correct ?

[A] where at least one vectorsatisfies [B] for all vectors

[C] where at least one vector satisfies [D]No relationship can be established betweenand

97)The equation has

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. 2 Marks GATE-EEE-2012,GATE-ECE/TCE-2012( )




[A]no solution [B]only one solution

[C]non-zero unique solution [D]multiple solutions98)A polynomial with all coefficients positive has

[A]No real roots [B]No negative real root[C]Odd number of real roots [D]At least one positive and one negative real root

99)Let A be an matrix and B an matrix It is given that determinant = determinant ,where is the identity matrix . Using the above property, the determinant of the matrix of the givenbelow is

[A]2 [B]5[C]8 [D]16

100)

Which one of the following does NOT equal ?

[A] [B]

[C] [D]

101)Let A be the 2 x 2 matrix with elements = = = + 1 and =-1. Then = -1. Then the eigen valuesof the matrix are

[A]1024 and -1024 [B]1024 and -1024[C]4 and -4 [D]512 and -512

102)Given that and , the value of is

[A] [B][C] [D]

103)The two vectors [1,1,1] and , where , are

[A]Orthonormal [B]Orthogonal[C]Parallel [D]collinear

104)The eigen values of a skew-symmetric matrix are

[A]Always zero [B]Always pure imaginary[C]Either zero or pure imaginary [D]Always real

105)Consider the matrix as given below.

Which one of the following provides the CORRECT values of eigenvalues of the matrix?

[A]1,4,3 [B]3,7,3[C]7,3,2 [D]1,2,3

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106)An eigenvector of is

[A] [-1 1 1] [B] [1 2 1][C][1 -1 2] [D][2 1 -1]

107)For the set of equations, and .The following statement is true

[A]Only the trivial solution exists [B]There are no solutions[C]A unique non-trivial solution exists [D]Multiple non-trivial solutions exist

108)Consider the following matrix

A = If the eigenvalues of A are 4 and 8, then

[A]x = 4, y = 10 [B]x = 5, y = 8[C]x = -3, y = 9 [D]x = -4, y = 10

109)The system of equationsx + y + z = 6x + 4y + 6z = 20

has NO solution for values of given by

[A] [B][C] [D]

110)The elgen values of the matrix are

[A]1 , 1 [B] -1 , -1[C]j , -j [D]1 , -1

111)The rank of the matrix is

[A]4 [B]2[C]1 [D]0

112)Consider the following statements:S1: The sum of two singular n × n matrices may be non-singularS2: The sum of two n × n non-singular matrices may be singular.Which of the following statements is correct?

[A]S1 and S2 are both true [B] S1 is true, S2 is false[C]S1 is false, S2 is true [D] S1 and S2 are both false

113)Suppose the adjacency relation of vertices in a graph is represented in a table Adj (X,Y). Which of thefollowing queries cannot be expressed by a relational algebra expression of constant length?

[A]List of all vertices adjacent to a given vertex [B]List all vertices which have self loops[C]List all vertices which belong to cycles of less

than three vertices [D]List all vertices reachable from a given vertex

114)Among the following, the pair of vectors orthogonal to each other is

[A] [3,4,7], [3,4,7] [B] [1,0,0], [1,1,0][C][1,0,2], [0,5,0] [D][1,1,1], [-1,-1,-1]

115)In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leadsto

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[A]diagonal matrix [B] lower triangular matrix[C]upper triangular matrix [D]singular matrix

116)The eigen values of are

[A]0,0,0 [B]0,0,1[C]0,0,3 [D]1,1,1

117)The eigenvalues of a symmetric matrix are all

[A]complex with non-zero positive imaginary part. [B]complex with non-zero negative imaginary part.[C]real. [D]pure imaginary.

118)Choose the CORRECT set of functions, which are linearly dependent.

[A]sin x , and [B]cos x , sin x and tan x[C]cos 2x , and [D]cos 2x , sin x and cos x

119)The eigen values of the matrix are

[A]6 [B]5[C]-3 [D]-4

120)Consider the system of equations given below: x+y=2 2x+2y =5 This system has

[A]one solution [B]no solution[C]infinite solutions [D]four solutions

121)The following set of equations has 3x+2y+z = 4 x-y+z=2 -2x+2z=5

[A]no solution [B]a unique solution[C]multiple solutions [D]an inconsistency.

122)The rank of a 3 x 3 matrix C (=AB), found by multiplying a non-zero column matrix A of size 3 x 1 and anon-zero row matrix B of size 1x3 is

[A]0 [B]1[C]2 [D]3

123)For the matrix the eigen values are

[A]3 and -3 [B] -3 and -5[C]3 and 5 [D]5 and 0

124)The vector field. (where and are unit vectors) is

[A]divergence free, but not irrotational [B] irrotational, but not divergence free[C]divergence free and irrotational [D]neither divergence free nor irrotational.

125)One of the eigen vectors of the matrix A = is

[A] [B]

[C] [D]

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126)Eigenvalues of a real symmetric matrix are always

[A]positive [B]negative[C]real [D]complex

127)For the matrix , ONE of the normalized eigen vectors is given as

[A] [B]

[C] [D]

128)x+2y +z =42x+y+2x = 5x-y+z = 1The system of algebraic equations given above has

[A]a unique solution of x = 1, y = 1 and z = 1. [B]only the two solutions of (x = 1, y = 1, z = 1) and(x = 2, y = 1, z = 0).

[C]infinite number of solutions. [D]no feasible solution.129)

For a matrix , the transpose of the matrix is equal to the inverse of the matrix = Thevalue of x is given by

[A] [B][C] [D]

130)The sum of the eigen values of the given matrix

[A]5 [B]7[C]9 [D]18

131)For which value of r will the matrix given below become singular ?

[A]4 [B]6[C]8 [D]12

132)A is a 3 x 4 real matrix and Ax = b is an inconsistent system of equations. The highest possible rank ofA is

[A]1 [B]2[C]3 [D]4

133)

Which one of the following is an eigenvector of the matrix ?

[A] [B]

[C] [D]

Linear Algebra



____________________________________________________________________________________________________________________ Pg.No.16










134)Match the items in columns I and II.Column I Column IIP. Singular matrix 1. Determinant is notQ. Non-square matrix 2. Determinant is always oneR. Real symmetric matrix 3, Determinant is zeroS. Orthogonal matrix 4. Eigen values are always real 5, Eigen values are not defined

[A]P-3, Q-1, R-4, S-2 [B]P-2, Q-3, R-4, S-1[C]P-3, Q-2, R-5, S-4 [D]P-3, Q-4, R-2. S-1.

135)Multiplication of matrices E and F is G. Matrices.E and G are

and What is the matrix F?

[A] [B]

[C] [D]

136)The matrix has one eigenvalue equal to 3. The sum of the other two eigenvalues is

[A]p [B]p - 1[C]p - 2 [D]p - 3

137)lf a square matrix A is real and symmetric, then the Eigen values

[A]are always real [B]are always real and positive[C]are always real and non-negative [D]occur in complex conjugate pairs.

138)For what value of a, if any, will the following system of equations in x, y and. z have a solution ? 2x+3y= 4 x+Y+z=4 x+2y-z=a

[A]Any real number [B]0[C]1 [D]There is no such value.

139)The eigenvectors of the matrix are written in the form and . What is a+b ?

[A]0 [B]1/2[C]1 [D]2

140)The area of a triangle formed by the tips of vectors is

[A] [B][C] [D]

141)The number of linearly independent Eigen vectors of is

[A]0 [B]1[C]2 [D]infinite

Statement for Linked answer Q142 and Q143 is given below

Linear Algebra



____________________________________________________________________________________________________________________ Pg.No.17


. 2 Marks GATE-EEE-2006,GATE-EEE-2006( )


. 2 Marks GATE-EEE-2007,GATE-EEE-2007( )


.

142)

are three vectors An orthogonal set of vectors having a span that contains P, Q, R is

[A] [B]

[C] [D]

143)The following vector is linearly dependent upon the solution to the previous problem

[A] [B]

[C] [D]


144)Cayley- Hamilton Theorem states that a square matrix satisfies its own characteristic equation. Considermatrix

A satisfies the relation

[A] [B]A2 + 2A + 2I = 0[C](A+I) (A+2I) [D]exp (A) = 0

145) equals

[A]511 A + 510 I [B]309 A + 104 I[C]154 A + 155 I [D]exp (9A)

Linear Algebra



____________________________________________________________________________________________________________________ Pg.No.18


Key Paper

1. A 2. B 3. C 4. C 5. A

6. A 7. A 8. D 9. C 10. C

11. A 12. B 13. A 14. D 15. D

16. B 17. C 18. C 19. C 20. B

21. C 22. A 23. A 24. B 25. D

26. C 27. A 28. B 29. B 30. D

31. A 32. A 33. B 34. D 35. A

36. B 37. B 38. C 39. B 40. A

41. A 42. D 43. C 44. B 45. A

46. D 47. A 48. A 49. A 50. A

51. A 52. C 53. A 54. C 55. B

56. B 57. A 58. D 59. B 60. A

61. A 62. B 63. A 64. A 65. A

66. B 67. A 68. A 69. C 70. A

71. B 72. B 73. B 74. A 75. C

76. A 77. C 78. C 79. A 80. C

81. C 82. C 83. B 84. D 85. D

86. A 87. D 88. B 89. B 90. C

91. D 92. D 93. D 94. A 95. A

96. B 97. D 98. D 99. B 100. A

101. D 102. B 103. B 104. C 105. A

106. B 107. D 108. D 109. B 110. D

111. C 112. C 113. C 114. C 115. C

116. C 117. C 118. C 119. A 120. B

121. B 122. A 123. C 124. C 125. A

126. C 127. B 128. C 129. A 130. B

131. A 132. C 133. A 134. A 135. C

136. C 137. A 138. D 139. B 140. B

141. B 142. D 143. D 144. A 145. A

Linear Algebra



____________________________________________________________________________________________________________________ Pg.No.19


.

.







1)The function f(t) has the Fourier Transform g(ω). The Fourier Transform

is

[A] [B][C] [D]None of the above

2)Which of the following improper integrals is (are) convergent?

[A] [B]

[C] [D]

3)The following plot shows a function y which varies linearly with x . The value of the integral

[A]1.0 [B]2.5[C]4.0 [D]5.0

4)Three functions , and which are zero outside the interval [0, T] are shown in the figure.Which of the following statements is correct ?

[A] and are orthogonal [B] and are orthogonal[C] and are orthogonal [D] and are orthogonal

5)If then the value of is

[A] [B][C]x [D]1

6)The value of the integral

[A]1 [B][C]2 [D]2

Calculus



____________________________________________________________________________________________________________________ Pg.No.20










7)The derivative of the symmetric function drawn in given figure will look like

[A] [B]

[C] [D]

8) , where P is a vector is equal to

[A] [B][C] [D]

9) where P is a vector, is equal to

[A] [B][C] [D]

10)As x increased from - ∞ to ∞, the function f (x) =

[A]Monotonically increases [B]Monotonically decreases[C]Increases to a maximum value and then

decreases[D]Decreases to a minimum value and then

increases11)For |x| <<1, coth (x) can be approximated as

[A]x [B][C]1/x [D]1/

12)Which one of the following is strictly bounded?

[A] [B][C] [D]

13)For the function the linear approximation around x = 2 is

[A] [B][C] [D]

14)Consider the function (. The maximum value of f(x) in the closed interval [-4, 4] is

[A]18 [B]10[C]-2.25 [D]Indeterminate

15)For real values of x, the minimum value of the function f(x)= exp (x) + exp (-x) is

Calculus



____________________________________________________________________________________________________________________ Pg.No.21











.

[A]2 [B]1[C]0.5 [D]0

16)Which of the following functions would have only odd powers of x in its Taylor series expansion about thepoint x = 0?

[A] [B][C] [D]

17)In the Taylor series expansion of exp(x) + sin (x) about the point x = π, the coefficient of is

[A]exp (π) [B]0.5 exp (π)[C]exp (π) + 1 [D]exp (π) -1

18)The value of the integral of the function along the straight line segment from the point(0,0) to the point (1,2) in the x-y plane is

[A]33 [B]35[C]40 [D]56

19)Consider points P and Q in the x-y plane, with P = (1, 0) and Q= (0,1). The line integral along the semicircle with the line segment PQ as its diameter

[A] is-1 [B] is 0

[C]is 1 [D]depends on the direction (clockwise oranticlockwise) of the semicircle

20)The Taylor series expansion of at given by

[A] [B]

[C] [D]

21)The maximum value of until which the approximation holds to within 10% error is

[A] [B][C] [D]

22)The maximum value of in the interval [1 6] is

[A]21 [B]25[C]41 [D]46

23)If , then y has a

[A]Maximum at X = e [B]Minimum at X = e[C]Maximum at [D]Minimum at

Calculus



____________________________________________________________________________________________________________________ Pg.No.22


Key Paper

1. C 2. A 3. B 4. C 5. A

6. A 7. C 8. D 9. A 10. A

11. C 12. D 13. A 14. A 15. A

16. A 17. B 18. A 19. B 20. B

21. B 22. C 23. A

Calculus



____________________________________________________________________________________________________________________ Pg.No.23


.

.











1)The formula used to compute an approximation for the second derivative of a function f at a point is.

[A] [B][C] [D]

2)Thesolutionofdifferentialequation y_′' +3y_′ +2y=0isoftheform

[A] [B][C] [D]

3)Backward Euler method for solving the differential equation is specified by, (choose one ofthe following).

[A] [B][C] [D]

4)The differential equation

is

[A] linear [B]non-linear [C]homogeneous [D]of degree two

5)The differential equation,

[A] linear [B]non-linear[C]homogeneous [D]of degree two

6)With initial condition x(1)=0.5 the solution of the differential equation is

[A] [B][C] [D]

7)With K as a constant, the possible solution for the first order differential equation

[A] [B]

[C] [D]

8)The order and degree of the differential equation

are respectively

[A]3 and 2 [B]2 and 3[C]3 and 3 [D]3 and 1

9)The solution to the ordinary differential equation

[A] [B][C] [D]

10)The partial differential equation that can be formed from

z=ax + by + ab has the from (with and )

[A]z = px + qy [B]z = px + pq[C]z = px + qy + pq [D]z = qy + pq

11)Given a function

The optimal value of f(x, y)

Differential Equations



____________________________________________________________________________________________________________________ Pg.No.24














[A] Is a minimum equal to 10/3 [B] Is a maximum equal to 10/3[C]Is a minimum equal to 8/3 [D]Is a maximum equal to 8/3

12)The solution of the ordinary differential equation for the boundary condition, y = 5 at x=1

[A] [B][C] [D]

13)For an analytic function, f(x+iy)=u(x,y)+iv(x,y), u is given by u=3 -3 . The expression for v, consideringK to be a constant is

[A]3 - 3 + K [B]6x- 6y + K[C]6y - 6x + K [D]6xy + K

14)The solution of the differential equation , with the condition that y = 1 at x = 1, is

[A] [B][C] [D]

15)The differential equation is to be solved using the backward (implicit) Euler's method withboundary condition y=1 at x=0 and with a step size of 1. What would be the value of y at x=1

[A]1.33 [B]1.67[C]2.00 [D]2.33

16)The general solution is

[A] [B][C] [D]

17)Solution of the differential equation represents a family of

[A]ellipses [B]circles[C]parabolas [D]hyperbolas

18)The solution of the differential equation, , given that at x = 1 , y = 0 is

[A] [B][C] [D]

19)The equation can be transformed to by substiting

[A] [B]

[C] [D]

20)Solution of at x=1 and is

[A] [B][C] [D]

21)The solution of , in the range is given by

[A] [B]

[C] [D]

22)The degree of the differential equation is

[A]0 [B]1[C]2 [D]3




____________________________________________________________________________________________________________________ Pg.No.25












23)The solution for the differential equation with condition that y = 1 at x=0 is

[A] [B]

[C] [D]

24)A body originally at C cools down to C in 15minutes when kept in air at a temperature of C. Whatwill be the temperature of the body at the end of 30minutes?

[A] [B][C] [D]

25)For the differentia l equation,f(x,y) + g(x,y) = 0 to be exact,

[A]=

[B]=

[C]f = g [D]=

26)The differential equa tion + Py = Q, is a linear equation of first order only if

[A]P is a constant but Q is a function of y [B]P and Q are functions of y or constants[C]P is a function of y but Q is a constant [D]P and Q are functions of x or constants

27)Biotransformation of an organic compound having concentration (x) can be modeled using an ordinarydifferential equation , where k is the reaction rate constant. If x = a at t = 0, the solution of theequation is

[A] [B][C] [D]

28)The number of boundary conditions required to solve the differential equations is

[A]2 [B]0[C]4 [D]1

29)The solution for the following differential equation with boundary conditions y(0) = 2 and y'(1) = -3 is

[A] [B]

[C] [D]

30)Number of terms in the expansion of general determinant of order n is

[A] [B][C] [D]

31)If c is a constant , solution of the equation

[A]y=sin(x+c) [B]y=cos(x+c)[C]y=tan(x+c) [D]

32)

The equation =0 represents a parabola passing through the points

[A] (0, 1), (0, 2), (0, -1) [B] (0, 0), (-1, 1),(1, 2)[C](1, 1), (0, 0), (2, 2) [D](1, 2), (2i 1), (0, 0)

33)Consider the differential equation with boundary conditions y(0) =1 , y(1) = 0. The value ofy(2) is




____________________________________________________________________________________________________________________ Pg.No.26












[A] -1 [B][C] [D]

34)Consider the difference equation and suppose that . Assuming thecondition of initial of rest , the solution for y[n] , is

[A] [B]

[C] [D]

35)The type of the partial differential equation = is

[A]parabolic [B]Elliptic[C]Hyperbolic [D]Nonlinear

36)While numerically solving the differential equation , y(0) = 1, using Euler’s predictorcorrector(improved Euler-Cauchy) method with a step size of 0.2, the value of y after the first step is

[A]1.00 [B]1.03[C]0.97 [D]0.96

37)The maximum value of in the interval [1,6] is:

[A]21 [B]25[C]41 [D]46

38)Consider the Differential equation

with and

The numerical value of is :

[A] -2 [B] -1[C]0 [D]1

39)Given , the value of is equal to

[A]0 [B]4[C]12 [D]13

40)Consider the differential equation Which one of the following can be a particular solution of thisdifferential equation?

[A]y = tan(x+3) [B]y = tanx + 3[C]x=tan(y+3) [D]x = tany+3

41)Consider the function y = - 6x +9 The maximum value of y obtained when x varies over the interval 2 to 5is

[A]1 [B]3[C]4 [D]9

42)Consider differential equation with y (0) = 1 . The value of y(1) is

[A] [B][C] [D]

43)The differential equation with x(0)=0, and the constant >0 , is to be numerically integrated usingthe forward Euler method with a constant integration time step T. The maximum value of T such that thenumerical solution of x converges is




____________________________________________________________________________________________________________________ Pg.No.27











[A] / 4 [B] / 2[C] [D]2

44)The general solution of the differential equation , is of the form (given D=d/dx) and and are constants

[A] [B][C] [D]

45)The following differential equation has

[A]degree = 2, order = 1 [B]degree= 1, order = 2[C]degree= 4, order = 3 [D]degree= 2, order = 3

46)A solution of the following differential equation is given by

[A] [B][C] [D]

47)A solution for the differential equation with initial condition x(0-)= 0 is

[A] [B][C] [D]

48)For the differential equation the boundary conditions are(i) y = 0 for x = 0 and (ii) y = 0 for x = aThe form of non-zero solutions of y (where m varies over all integers) are

[A] [B]

[C] [D]

49)The solution of the differential equation under the boundary conditions

(i) y = at x= 0 and(ii) y = at x = , where k, and are constant is

[A] [B][C] [D]

50)Which of the following is a solution to the differential equation

[A] [B][C] [D]

51)The order of the differential equation is

[A]1 [B]2[C]3 [D]4




____________________________________________________________________________________________________________________ Pg.No.28








52)Match each differential equation in Group I to its family of solution curves from Group II

Group I Group II

A . 1 . Circles

B . 2 . Straight lines

C . 3 . Hyperbolas

D .

[A]A B C D2 3 3 1

[B]A B C D1 3 2 1

[C]A B C D2 1 3 3

[D]A B C D3 2 1 2

53)The solution of the first order differential equation , x ( 0 ) = is

[A] [B][C] [D]

54)Equation is required to be solved using Newton’s method with a initial guess . Then, afterone step of Newton’s method, estimate of the solution will be given by

[A]0.71828 [B]0.36784[C]0.20587 [D]0.00000

55)A system is described by the differential equation .Let x(t) be a rectangular pulsegiven by

Assuming that y(0) =0 and at t =0 , the Laplace transform of y(t) is

[A] [B]

[C] [D]

56)A system described by a linear, constant coefficient, ordinary, first order differential equation has an exactsolution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishesto modify the system so that the solution becomes -2y(t) for t>0, we need to

[A] change the initial condition to –y(0) and theforcing function to 2x(t)

[B]change the initial condition to 2y (0) and theforcing function to -x (t)

[C]Change the initial condition to and theforcing function to

[D]change the initial condition to 2y (0) and theforcing function to -2x (t)

57)Consider the differential equation

, with and

The numerical value of is

[A] -2 [B] -1[C]0 [D]1

58)A function n(x) satisfied the differential equation where L is a constant . The boundaryconditions are : n(0) = K and . The solution to this equation is




____________________________________________________________________________________________________________________ Pg.No.29













[A]n (x) = K exp(x/L) [B][C] [D]n(x) = K exp(-x/L)

59)Consider differential equation with the initial condition y(0)=0 . Using Euler's first ordermethod with a step of 0.1 , the value of y(0.3) is

[A]0.01 [B]0.031[C]0.0631 [D]0.1

60)For the differential equation with initial conditions X(0)=1 and , the solution is

[A] [B][C] [D]

61)The solution of the differential equation is

[A] [B][C] [D]

62)The value of in the mean value theorem of in (a,b) is

[A]b+a [B]b-a[C] [D]

63)For the differential equation with y(o)=1, the general solution is

[A] [B][C] [D]

64)The solution to the differential equation f''(x)+4f'(x)+4f(x) = 0 is

[A] [B][C] [D]

65)For the following set of simultaneous equations : 1.5x-0.5y=2 4x+2y+3z=9 7x+y+5z=10

[A] the solution is unique [B] infinitely many solutions exist[C]the equations are incompatible [D]finite number of multiple solutions exist.

66)The particular solution for the differential equation is

[A]0.5 cos x+1.5 sin x [B]1.5 cos x+0.5 sin x[C]1.5 sin x [D]0.5 cos x

67)If , then is

[A] [B][C]0 [D]1

68)The general solution of the differential equation is

[A] [B][C] [D]

69) represents the equation for




____________________________________________________________________________________________________________________ Pg.No.30












[A]Vibration of a stretched string [B]motion of a projectile in agravitational field[C]Heat flow in thin rod [D]Oscillation of a simple pendulum

70)The partial differential equation is a

[A] linear equation of order 2 [B]non-linear equation of order 1[C]linear equation of order 1 [D]non-linear equation of order 2

71)The function f (t ) satisfies the differential equation and the auxiliary conditions, f(o) = 0,

. The Laplace transform of f (t) is given by

[A] [B]

[C] [D]

72)The solution to the differential equation where k is a constant, subjected to the boundaryconditions u(0) = 0 and u(L) = U, is

[A] [B]

[C] [D]

73)lf z = f (x,y),then dz is equal to

[A] [B]

[C] [D]

74)The solution of the differential equation

[A] [B][C] [D]

75)

The above equation is a

[A]partial differential equation [B]non-linear differential equation[C]non-homogeneous differential equation [D]ordinary differential equation.

76)The maximum value of the directional derivative of the function at a point (1,1,-1) is

[A]10 [B] -4[C] [D]152

77)Consider the system of simultaneous equationsx+2y+z=62x +y +2z =6x+y+z=5This system has

[A]unique solution [B] infinite number of solutions[C]no solution [D]exactly two solutions.

78)The solution of the differential equation

[A] [B]

[C] [D]unsolvable as equation is non-linear.




____________________________________________________________________________________________________________________ Pg.No.31













79)The Blasius equation is a

[A]second order nonlinear ordinary differentialequation [B] third order nonlinear ordinary different equation

[C]third order linear ordinary differential equation [D]mixed order nonlinear ordinary differentialequation

80)Consider the differential equation with the boundary conditions of y (0)=0 and y (1)=1. The complete solution of the differential equation is

[A] [B][C] [D]

81)Consider the differential equation . The general solution with constant c is

[A] [B][C] [D]

82)The solution of with the condition is

[A] [B]

[C] [D]

83)If and , then will be equal to

[A] [B][C] [D]

84)The solution of the differential equation with y(0) = 1 is

[A] (1+x) [B] (1+x)[C](1-x) [D](1-x)

85)By a change of variables x(u,v) = u,v,y(u,v) = vlu. in a double integral, the integrand f(x, y) changes to f(uv, u/v) . Then is

[A]2v/u [B]2uv[C] [D]1

86)If , and y(1)=0 ,then what is y(e) ?

[A]e [B]1[C]1/e [D]

87)For , the particular integral is

[A] [B][C] [D]

88)Given that + 3x= 0, and x(0) = 1, (0) = 0, what is x (1) ?

[A] -0.99 [B] -0.16[C]0.16 [D]0.99

89)The minimum value of function in the interval [1, 5] is

[A]0 [B]1[C]25 [D]undefind




____________________________________________________________________________________________________________________ Pg.No.32







. 2 Marks GATE-ME-2005,GATE-ME-2005( )


.

90)The partial differential equation, has

[A]degree 1 order 2 [B]degree 1 order 1[C]degree 2 order 1 [D]degree 2 order 2

91)Let f= , What is at x=2, y=1 ?

[A]0 [B] In 2[C]1 [D]

92)It is given that + 2 + y = 0, y(0) = 0 y(1) = 0. What is y(0.5) ?

[A]0 [B]0.37[C]0.62 [D]1.13

93)If , then y(2)=

[A]4 or 1 [B] 4 only[C]1 only [D]undefined

94)The solution of with initial value y(0) =1 is bounded in the interval

[A] [B][C]x <1 , x >1 [D]


95)The complete solution of the ordinary differential equation is .

Q. Then p and q are

[A]p=3,q=3 [B]p=3,q=4[C]p=4 , q=3 [D]p=4 ,q=4

96)Which of the following is a solution of the differential equation ?

[A] [B][C] [D]




____________________________________________________________________________________________________________________ Pg.No.33


Key Paper

1. D 2. C 3. A 4. A 5. B

6. D 7. A 8. A 9. C 10. C

11. A 12. D 13. D 14. D 15. C

16. A 17. A 18. A 19. D 20. D

21. A 22. B 23. D 24. B 25. A

26. C 27. B 28. A 29. C 30. C

31. C 32. B 33. B 34. B 35. A

36. D 37. C 38. D 39. B 40. A

41. A 42. C 43. D 44. C 45. B

46. B 47. A 48. A 49. D 50. B

51. B 52. A 53. A 54. A 55. B

56. D 57. D 58. D 59. C 60. B

61. C 62. C 63. B 64. C 65. C

66. A 67. A 68. D 69. A 70. D

71. C 72. B 73. A 74. D 75. D

76. C 77. B 78. A 79. B 80. A

81. D 82. A 83. C 84. B 85. A

86. D 87. B 88. B 89. B 90. A

91. C 92. A 93. B 94. C 95. C

96. C




____________________________________________________________________________________________________________________ Pg.No.34


.

.







1) evaluated anticlockwise around the circle , where , is

[A] [B]0[C] [D]2+2i

2)Given If C is a counterclockwise path in the z-plane such that the value of is

[A] -2 [B] -1[C]1 [D]2

3)A point Z has been plotted in the complex plane, as shown in figure below.

The plot of the complex number is

[A] [B]

[C] [D]

4)The infinite series corresponds to

[A] [B][C] [D]

5)For the parallelogram OPQR shown in the sketch, and .The area of the parallelogram is

[A]ad-bc [B]ac+bd[C]ad+bc [D]ab-cd

6)The analytic function has singularities at

[A]1 and -1 [B]1 and i[C]1 and -i [D]i and -i

Complex Analysis



____________________________________________________________________________________________________________________ Pg.No.35













7)The value of the integral (where C is a closed curve given by ) is

[A] [B]

[C] [D]

8)What is the area common to the circles r = a and r = 2a cos ?

[A]0.524 [B]0.614 [C]1.047 [D]1.228

9)The velocity field for flow is given by and the densityvaries as exp (-21). ln order that the mass is conserved, the value of should be

[A] -12 [B] -10[C]-8 [D]10

10)Which one of the following is NOT true for complex number and ?

[A] [B]

[C] [D]11)For real values of x, can be written in one of the forms of a convergent series given below :

[A]cos (x) = 1 + .... [B]cos (x) = 1 - ....[C]cos (x) = x - .... [D]cos (x) = x - ....

12)The summation of series

[A]4.50 [B]6.0[C]6.75 [D]10.0

13)The value of the function is

[A]0 [B] -1/7[C]1/7 [D]

14)The function has its maxima at

[A]x = -2 only [B]x = 0 only[C]x = 3 only [D]both x = - 2 and x = 3

15)The following function has a local minim a at which value of x

[A] [B][C] [D]

16)The directional derivative of the following function at (1, 2) in the direction of (4i + 3j) is

[A]4/5 [B]4[C]2/5 [D]1

17) The function is

[A]Even [B]Odd[C]Neither even nor odd [D]None of the above

18)If , is equal to

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[A]Zero [B]1[C]2 [D]

19)The Taylor expansion of sin x about is given by

[A] [B][C] [D]

20)The limit of the function as is given by

[A]1 [B][C] [D]Zero

21)The maxima and minima of the function occur, respectively at

[A] X= 3 and x = 2 [B]x = 1and x = 3[C]x = 2 and x = 3 [D]x = 3 and x = 4

22)The curve given by the equation = 3 axy, is

[A]symmetrical about x - axis [B]symmetrical about y - axis[C]symmetrical about line y = x [D]tangential to x = y = a / 3

23) is periodic, with a period of

[A] [B][C] [D]

24)A discontinuous real function can be expressed as

[A]Tay lor's series and Fourier's series [B]Taylor's series and not by Fourier's series[C]neither Taylor's series nor Fourier's series [D]not by Taylor's series,bu t by Fourier's series

25)The Taylor's series expansion of is

[A] [B]

[C] [D]

26)The infinite series

[A]converges [B]diverges[C]oscillates [D]unstable

27)If , then the value of is :

[A] [B][C]X [D]1

28)The infinite series converges to

[A]cos(X) [B]Sin(x)[C]Sinh(x) [D]

29)Consider the function where x is real. Then the function f(x) at x = 0 is

[A]continuous but not differentiable [B]once differentiable but not twic[C]twice differentiable bnut not thrice [D]thrice differentiable

30)For the function of a complex variable W = In z (where, W = u + jv and Z = x + jy,the u = constant lines getmapped in Z-plane as

[A]set of radial straight lines [B]set of concentric circles[C]set of confocal hyperbolas [D]set of confocal ellipses

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31)The value of the contour integral dz in positive sense is

[A] [B][C] [D]

32)If the semi-circular contour D of radius 2 is as shown in the figure. Then the value of the integral

is

[A] j [B] -j [C] - [D]

33)The equation sin (z) = 10 has

[A]No real or complex solution [B]Exactly two distinct complex solutions[C]A unique solution [D]An infinite number of complex solutions

34) If , then is given by

[A] [B][C] [D]

35)The value of where C is the contour |z-i/2| =1 is

[A]2 π i [B]π[C] [D]

36)The function has

[A]a maxima at x = 1 and minimum at x = 5 [B]a maxima at x = 1 and minimum at x = -5[C]only maxima at x = 1 and [D]only a minimum at x = 5

37)The residues of a complex function at its poles are

[A] [B][C] [D]

38)The value of the integral where c is the circle |z| = 1 is given by

[A]0 [B]1/10[C]4/5 [D]1

39)Let f: A B be a function, and let E and F be subsets of A. Consider the following statements aboutimagesS1:f(E∪F) = f(E) ∪f(F)S2:f(E∩F) = f(E) ∩f(F)Which of the following is true about S1 and S2?

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[A]Only S1 is correct [B]Only S2 is correct[C]Both S1 and S2 are correct [D]None of S1 and S2 is correct

40)The residence of the function at z=2 is

[A] -1/32 [B] -1/16[C]1/16 [D]1/32

41)The function f(x) = on the interval [-2, 0] is

[A]continuous and differentiable [B]continuous on the integral but not differentiable atall points

[C]neither continuous nor differentiable [D]differentiable but not continuous42) , where ,is given by

[A]0 [B][C] [D]1

43)The magnitude of the gradient of function at (1,0,2) is

[A]0 [B]3[C]8 [D]

44)What is the derivative of f(x) = x at x = O ?

[A]1 [B] -1[C]0 [D]Does not exit

45)Which of the following functions is not differentiable in the domain [- 1, 1] ?

[A] f(x) = [B] f(x) = x-1[C]f(x) = 2 [D]f(x) = maximum (x, -x)

46)A regression model is used to express a variable Y as a function of another variable X.

[A] there is a causal relationship between Y and X [B]a value of X may be used to estimate a value of Y[C]values of X exactly determine values of Y [D]there is no causal relationship between Y and X.

47)The minimum point of the function is at

[A]x=1 [B]x= -1[C]x = 0 [D]

48)The function f(x, y) = has

[A]only one stationary point at (0, 0) [B] two stationary points at (0, 0) and and (1/6, -1/3)[C]two stationary points at (0, 0) and (1, - 1) [D]no stationary point.

49)The modulus of the complex number is

[A]5 [B][C]1/ [D]1/5

50)The function y =

[A] is continuous x R and differentiable x R [B] is continuous x R and differentiable x Rexcept at x = 3/2

[C]is continuous x R and differentiable x Rexcept at x = 2/3

[D]is continuous x R except at x = 3 anddifferentiable x R

51)A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a timewithout replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4bolts is

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.

[A]2/315 [B]1/630[C]1/1260 [D]1/2520

52)Consider the function f (x) = in the interval -1 x 1. At the point x = 0, f(x) is

[A]continuous and differentiable. [B]non-continuous and differentiable.[C]continuous and non-differentiable. [D]neither continuous nor differentiable.

53)A t x = 0, the function f (x) = +1 has

[A]a maximum value [B]a minimum value[C]a singularity [D]a point of inflection

54)A series expansion for the function is

[A] [B]

[C] [D]

55)The product of two complex numbers 1+ i and 2- 5i is

[A]7-3i [B]3-4i[C]-3-4i [D]7+3i

56)An analytic function of a complex variable z = x + iy is expressed as f (z) = u(x,y) + iv (x, y) where i = .If u = xy, the expression for v should be

[A] [B]

[C] [D]

57)The distance between the origin and the point nearest to it on the surface = 1 + xy is

[A]1 [B]

[C] [D]258)The volume of an object expressed in spherical co-ordinates is given by

The value of the integral is

[A] [B][C] [D]

59)The divergence of the vector field (x-y) + (y-x) + (x+y+z) ,is

[A]0 [B]1[C]2 [D]3

60)The integral evaluated around the unit circle on the complex plane for is

[A]2 i [B]4 i[C]-2 i [D]0

61)The length of the curve between x=0 and x=1 is

[A]0.27 [B]0.67[C]1 [D]1.22

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Key Paper

1. A 2. C 3. D 4. B 5. A

6. D 7. C 8. D 9. B 10. C

11. D 12. D 13. B 14. A 15. D

16. B 17. B 18. A 19. A 20. A

21. C 22. D 23. A 24. D 25. D

26. D 27. A 28. B 29. A 30. B

31. D 32. A 33. A 34. D 35. B

36. C 37. C 38. A 39. A 40. A

41. B 42. B 43. C 44. C 45. A

46. B 47. A 48. B 49. B 50. C

51. C 52. C 53. D 54. B 55. A

56. C 57. A 58. A 59. D 60. A

61. A

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1)The Newton-Raphson method is to be used to find the root of the equation f(x)=0 where is the initialapproximation and f ′ is the derivative of f. The method converges

[A]always [B]only if f is a polynomial[C]only if f( )<0 [D]None of the above

2)The Newton-Raphson method is used to find the root of the equation -2=0 If the iterations are startedform –1, the iterations will

[A]converge to -1 [B]converge to [C]converge to - [D]not converge

3)Using a forward Euler method to solve y'' (t) =f(t), y(0), y′' (0)=0 with a step size of h, we obtain thefollowing values of y in the first four iterations:

[A]0, hf (0), h(f(0) + f(h)) and h(f(0) + f(h) = f(2h)) [B]0, 0 h2 f(0) and 2h2f(0)+f(h)[C]0, 0, h2f(0) 3h2f(0) [D]0, 0, hf(0) + h2f(0) and hf (0) + h2f(0)+hf(h)

4)The trapezoidal method to numerically obtain∫ dx has an error E bounded by max f''(x) x ∈ [a,b]

where h is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure E ≤is computing in 7 using f = 1/x is

[A]60 [B]100[C]600 [D]10000

5)TheiterationformulatofindthesquarerootofapositiverealnumberbusingtheNewtonRaphsonmethodis


6)A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn toscale).

If we use the Newton-Raphson method to find the roots of f(x)=0 using x0 ,x1 , and x2 respectively asinitial guesses ,the obtained would be

[A]1.3 , 0.6 and 0.6 respectively [B]0.6 , 0.6 and 1.3 respectively[C]1.3 , 1.3 and 0.6 respectively [D]1.3 , 0.6 and 1.3 respectively

7)Simpson’s rule for integration gives exact result when f(x) is a polynomial of degree

[A]1 [B]2[C]3 [D]4

8)When the Newton-Raphson method is applied to solve the equation , the solution atthe end of the first iteration with the initial guess value as is

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[A] -0.82 [B]0.49[C]0.705 [D]1.69

9)Solution of the variables x1 and x2 for the following equations is to be obtained by employing the Newton-Raphson iterative method.equation(i) equation(ii) Assuming the initial valued and , the jacobian matrix is

[A] [B]

[C] [D]

10)The value of computed using Simpson's rule with a steps size of h=0.25 is:

[A]0.69430 [B]0.69385[C]0.69325 [D]0.69415

11)The estimate of obtained using Simpson’s rule with three-point function evaluation exceeds the exactvalues by

[A]0.235 [B]0.068[C]0.024 [D]0.012

12)The table below gives values of a function F(x) obtained for values of x at intervals of 0.25.

The value of the integral of the function between the limits 0 to 1 using Simpson’s rule is

[A]0.7854 [B]2.3562[C]3.1416 [D]7.5000

13)The square root of a number N is to be obtained by applying the Newton Raphson iterations to theequation - N = 0. If i denotes the iteration index, the correct iterative scheme will be

[A] [B]

[C] [D]

14)In the solution of the following set of linear equations by Gauss elimination using partial pivoting5x+y+2z=34; 4y-3z=12; and 10x-2y+z=-4;the pivots for elimination of x and y are

[A]10 and 4 [B]10 and 2[C]5 and 4 [D]5 and -4

15)A degree polynomial, f(x), has values of 1, 4, and 15 at x = O, 1, and 2, respectively. Theintegral is to be estimated by applying the trapezoidal rule to this data. What is the error (defined as"true value - approximate value") in the estimate?

[A] -4/3 [B] -2/3[C]0 [D]2/3

16)The following equation needs to be numerically solved using the Newton- Raphson method The iterative equation for this purpose is (k indicates the iteration level)

[A] [B]

[C] [D]

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17)Area bounded by the curve y = and lines x = 4 and y = 0 is given by

[A]64 [B]64/3[C]128/3 [D]128/4

18)The extremum (minimum or maximum ) point of a function f(x) is to be determined by solving

using the Newton - Raphson method . Let and be the initial guess of x . Thevalue of x after two iterations is

[A]0.0141 [B]1.4142[C]1.4167 [D]1.5000

19)For k = 0, 1, 2, .........,the steps of Newton-Raphson method for solving a non-linear equation is given as

Starting from a suitable initial choice as k tends to , the iterate tends.to

[A]1.7099 [B]2.2361[C]3.1251 [D]5.0000

20)Identify the Newton - Raphson iteration scheme for finding the square root of 2.

[A] [B]

[C] [D]

21)Using secant method , the first approximation to the root of the equation with the initialestimates = 9 and = 4 is ..........

[A]5.9563 [B]5.1111[C]5.5014 [D]5.6182

22)Using Newton- Raphson method the first approximation to a real root of the equation is .............(take initial approximation )

[A]1.1 [B]1.2[C]1.3 [D]1.4

23)Starting from = 1 one step of Newton- Raphson method , in solving the equation givesthe next value as

[A]0.5 [B]1.5[C]0.75 [D]1.25

24)Given that ; y(0) = 1 , Find y(0.02) using modified method of Euler . (Take step size h = 0.02)

[A]1.0424 [B]1.0204[C]1.0324 [D]1.0414

25)Given that . Using Taylor's Series method find y(0,1) by considering the Taylor'sSeries expansion upto term ( take h = 0.5)

[A]1.011 [B]1.115[C]1.015 [D]1.105

26)Given that . Using Taylor's Series method find y(0,1) by considering the Taylor'sSeries expansion upto term ( take h = 0.5)

[A]1.011 [B]1.115[C]1.015 [D]1.105

27)The first approximation of , which lies in [0, 1] by using Regula - falsi method is

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[A]0.7676 [B]0.7353[C]0.7962 [D]0.4632

28)The initial approximation of 3x = cos x + 1 is 1 , then the first approximation by using Newton- Raphson method is

[A]0.6338 [B]0.6200[C]0.6093 [D]0.6123

29)If ‘n’is the number of sub-intervals then which of the following is not a value for ‘n’ to use Simpson’s 3/8 rule

[A]6 [B]9[C]12 [D]16

30)Using the bisection method find the negative root of correct to the three decimal places

[A] - 2.506 [B] - 2.706[C]- 2.406 [D]None

31)Use Secant method to determine the root of the equation with initial approximation and . What is ?

[A]1 [B] - 2.178[C]0.3147 [D]0.4467

32)Match the following and choose the correct combinationGroup-I Group-IIE. Newton-Raphson method 1. Solving nonlinear equationsF. Rung-kutta method 2. Solving linear simultaneous equationsG. Simpson’s Rule 3. Solving ordinary differential equationsH. Gauss elimination 4. Numerical integration 5. Interpolation 6. Calculation of Eigen values

[A]E-6, F-1, G-5, H-3 [B]E-1, F-6, G-4, H-3[C]E-1, F-3, G-4, H-2 [D]E-5, F-3, G-4, H-1

33)The equation is to be solved using the Newton- Raphson method. If x = 2 is taken asthe initial approximation of the solution, then the next approximation using this method will be

[A]2/3 [B]4/3[C]1 [D]3/2

34)The recursion relation to solve x = using Newton Raphson method is

[A] [B][C] [D]

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35)Function f is known at the following points:

x 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0

f(x) 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00

The value of f(x)dx computed using the trapezoidal rule is

[A]8.983 [B]9.003[C]9.017 [D]9.045

36)Newton-Raphson method is used to compute a root of the equation - 13 = 0 with 3.5 as the initial value.The approximation after one iteration is

[A]3.575 [B]3.676[C]3.667 [D]3.607

37)A numerical solution of the equation can be obtained using Newton - Raphsonmethod. If the starting values is x = 2 for the iteration, the value of x that is to be used in the next step is

[A]0.306 [B]0.739[C]1.694 [D]2.306

38)Let . The iterative steps for the solution using Newton-Raphson's method is given by

[A] [B]

[C] [D]

39)The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree

[A]0 but not 1 [B]1 but not 0[C]0 or 1 [D]2

40) The Newton-Raphson iteration can be used to solve the equation

[A] = 3 [B] = 3[C] = 2 [D] = 2

41)Which of the following is useful for solving algebraic equations

[A]Euler's method [B]Coulombs method[C]Simpson's Rule [D]Newton Raphson method

42)The N-R method for finding roots of f(x)=0 converging to the root

[A] If f(x) is polynomial [B] If >0[C]Converges always [D]none of these

43)The N-R iteration formula for Square root of 'C' where c >0

[A] [B]

[C] [D]

44)N-R formula evaluates

[A]Square of R [B]Logarithm of R[C]Reciprocal of R [D]Square root of R

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45) has

[A]All complex roots [B]All real roots[C]1 real &4 complex roots [D]2 real roots &3 complex roots

46)

The value of the integral of the function between the limit 0 to 1 using simpson's rule is

[A]0.7854 [B]2.3562[C]3.1416 [D]7.5000

47)Newton-Raphson iteration formula for finding , where c >0 is

[A] [B]

[C] [D]

48)For given that y = 1 at x = 0. Using Euler method taking the step size 0.1, the y at x = 0.4 is

[A]1.0611 [B]2.4680[C]1.6321 [D]2.4189

49)The root of the equation using the bisection method in 4 stages

[A]2.4065 [B]2.6875[C]2.750 [D]None of the above

50)The Newton-Raphson iteration can be used to solve the equation

[A] [B][C] [D]

51)The 2’s complement representation of (− 539)10 is hexadecimal is

[A]ABE [B]DBC[C]DE5 [D]9E7

52)The decimal value of 0.2

[A] is equivalent to the binary value 0.1

[B] is equivalent to the binary value 0.01

[C] is equivalent to the binary value 0.00111..... [D]cannot be represented precisely in binary53)

Minimum number of equivalent sub intervals needed to approximate to an accuracy at least

using Trapezoidal rule

[A]1000 e [B]100[C]100 e [D]1000

54)The order of error is the Simpson's rule for numerical integration with a step size h is

[A]h [B][C] [D]

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. 2 Marks GATE-CE-2005,GATE-CE-2005( )


.

55)Following are the values of a function y(x) : y(-1)=5 , y(o) , at x=0 as per Newton's centraldifference is

[A]0 [B]1.5[C]2.0 [D]3.0

56)Match the CORRECT pairs.

[A]P-2, Q-1, R-3 [B]P-3, Q-2, R-1[C]P-1, Q-2, R-3 [D]P-3, Q-1, R-2

57)We wish to solve by Newton Raphson technique. Let the initial guess b . Subsequentestimate of x (i.e. ) will be

[A]1.414 [B]1.5[C]2.0 [D]none of these

58)The accuracy of Simpson's rule quadrature for a step size h is

[A] [B][C] [D]

59)The values of a function f(x) are tabulated below

Using Newton's forward difference formula, the cubic polynomial that can be fitted to the above data, is

[A]2 +7 -6x+2 [B]2 -7 -6x-2[C] -7 -6x+1 [D]2 -7 +6x+1

60)Starting from one step of Newton- Raphson method in solving the equation gives the nextvalue ( ) as

[A] =0.5 [B] =1.406[C] =1.5 [D] =2


61)Given a >0, we wish to calculate its reciprocal value by using Newton Raphson method for f(x) = 0

[A] [B]

[C] [D]62)For a = 7 and starting with xo= 0.2, the first two iterations will

[A]0.11, 0.1299 [B]0.12, 0.1392[C]0.12, 0.1416 [D]0.13, 0.1428

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Key Paper

1. D 2. C 3. D 4. C 5. A

6. B 7. C 8. C 9. B 10. C

11. D 12. A 13. A 14. A 15. A

16. A 17. B 18. B 19. A 20. A

21. B 22. D 23. B 24. B 25. D

26. D 27. B 28. B 29. D 30. B

31. B 32. C 33. B 34. C 35. D

36. D 37. C 38. A 39. C 40. A

41. D 42. D 43. B 44. D 45. C

46. A 47. C 48. A 49. B 50. A

51. C 52. D 53. A 54. B 55. B

56. D 57. D 58. D 59. D 60. C

61. C 62. B

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. 1 Marks IES-ECE/TCE-2013( )




1)Let P(E) denote the probability of the event E.Given P(A) = 1 , P(B) = 1/2 , the values of P(A|B) and P(B|A)respectively are

[A]1/4, 1/2 [B]1/2 , 1/4[C]1/2 , 1 [D]1 , 1/2

2)A polynomial p(r) is such that p(0) = 5, p(1) = 4, p(2) = 9 and P(3) =20 The minimum degree it can have is

[A]1 [B]2[C]3 [D]4

3)Two events A and B with probability 0.5 and 0.7 respectively, have joint probability of 0.4 . The probabilitythat neither A or B happens is

[A]0.2 [B]0.4[C]0.6 [D]0.8

4)There are two fair coins and a third biased coin where

and . One coin is picked at random and tossed once a Head is obtained . Theprobability that the coin tossed is one of the fair coins is

[A] [B]

[C] [D]

5)A probability density function is given by

The value of K should be

[A] [B]

[C] [D]

6)The function , has

[A]no local extremum [B]one local minimum but no local maximum[C]one local maximum but no local minimum [D]one local minimum but no local minimum

7)An event has two possible outcomes with probability = and = The rate of information with 16outcomes per second is:

[A] bits/sec [B] bits/sec[C] bits/sec [D] bits/sec

8)Two independent random variables X and y are uniformly distributed in the interval [-1 1]. The probabilitythat max[X y] is less than 1/2 is

[A]3/4 [B]9/16[C]1/4 [D]2/3

9)Two coins are simultaneously tossed.The probability of two heads simultaneously appearing is

[A]1/8 [B]1/6[C]1/4 [D]1/2

10)In an experiment, positive and negative values are equally likely to occur. The probability of obtaining atmost one negative value in five trials is

[A] [B]

[C] [D]

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. 2 Marks IES-CE-2002( )

11)There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3 Blueand 4 Green balls. One ball is drawn at random from each container. The probability that one of the balls isRed and the other is Blue will be

[A]1/7 [B]9/49[C]12/49 [D]3/7

12)A classof first year B.Tech. students is composed of four batches A, B, C and D, each consisting of 30students. It is found that the sessional marks of students in Engineering Drawing in batch C have a meanof 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are5.5 and 4.2, respectively. It is decided by the course instructor to normalize the marks of the students of allbatches to have the same mean and standard deviation as that of the entire class. Due to this, the marksof a student in batch C are changed from 8.5 to

[A]6.0 [B]7.0[C]8.0 [D]9.0

13)The standard normal probability function can be approximated as

where = standard normal deviate. If mean and standard deviation of annual precipitation are 102 emand 27 em respectively, the probability that the annual precipitation will be between 90 em and 102 em is

[A]66.7% [B]50.0%[C]33.3% [D]16.7%

14)If probability density function of a random variable X is and

= 0 for any other value of x Then, the percentage probability is

[A]0.247 [B]2.47[C]24.7 [D]247

15)A person on a trip has a choice between private car and public transport. The probability of using a privatecar is 0.45. While u s.ing the public transport, further choices available are bus and metro, out of which theprobability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals)of using a car, bu s and metro, respectively would be

[A]0.45, 0.30 and 0.25 [B]0.45, 0.25 and 0.30[C]0.45, 0.55 and 0.00 [D]0.45, 0.35 and 0.20

16)A hydraulic structure has four gates which operate independently. The probability of failure of each gate is0.2. Given that gate 1 has failed, the probability that both gates 2 and 3 will fail is

[A]0.240 [B]0.200[C]0.040 [D]0.008

17)A box contains 10 screws, 3 of which are defective. Two screws are drawn at random with replacement.The probability that none of the two screws is defective will be

[A]100% [B]50%[C]49% [D]None of these

18)The probability that the load on a scaffolding will exceed the design load of 3 tonnes is 0.15. At the sametime, the probability that the strength of the scaffolding will be more than 3tonnes is 0.85. The probabilitythat the scaffolding will fail is

[A]0.2775 [B]0.1275[C]0.0225 [D]0.0020

19)The probability that the load on a scaffolding will exceed 2t is 0.15. The probability that the strength of thescaffolding will be more than 2t is 0.8. The probability of failure of the scaffolding will be




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[A]0.68 [B]0.17[C]0.12 [D]0.03

20)From the probability equation it is found that the most probable values of a series of errors arising out ofobservations of equal weightage are those for which the sum of their squares is

[A]Zero [B] infinity[C]minimum [D]maximum

21)The box 1 contains chips numbered 3 , 6 , 9 , 12 and 15 . The box 2 contains chips numbered 6 , 11 , 16 ,21 and 26 . Two chips , one from each box , are drawn at random.The numbers . The numbers written onthese chips are multiplied . The probability for the to be even number is

[A]6/25 [B]2/5[C]3/5 [D]19/25

22)A continuous random variable X has a probability density function f (x) = , 0 <x < . Then P{X >1} is

[A]0.368 [B]0.5[C]0.632 [D]1.0

23)A fair coin is tossed till a head appears for the first time . The probability that the number of required tossesis odd , is :

[A]1/3 [B]1/2[C]2/3 [D]3/4

24)Two dices are rolled simultaneously. The probability that the sum of digits on the top surface of the twodices is even is

[A]0.5 [B]0.25[C]0.167 [D]0.125

25)A random variable X has & . Form a new random variable Y = 2x + 1 . The values of & are :

[A]0 &1 [B]1 &2[C]1 &4 [D]None of these

26)Person X can solve 80 % of the ISRO and person Y can solve 60 % . The probability that at least one ofthem will solve a problem from the question paper , selected at random is :

[A]0.48 [B]0.70[C]0.88 [D]0.92

27)A man with n keys wants to open a clock . He tries his keys at random . The expected number of attemptsfor this success is (keys are replaced after every attempt)

[A]n/2 [B]n[C] [D]None of the above

28)A husband and wife appear in an interview for two vacancies for same post . The probability of husbandgetting selected is 1/5 while the probability of wife getting selected is 1/7 . Then the probability thatanyone of them getting selected is

[A]11/35 [B]12/35[C]1/35 [D]34/35

29)A bag contains eight white and six red marbles . The probability of drawing two marbles of same colour is

[A] [B]

[C] [D]




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30)A box contains 5 black and 5 red balls . Two balls are randomly picked one after another from the box,without replacement . The probability for both balls being red is

[A]1/90 [B]1/5[C]19/90 [D]2/9

31)If A and B are two events and P(A / B) = 1 then is

[A] [B][C]0 [D]1

32)The regression equations are x + 2y = 3 ; 2x + 3y = 4 then E(X) , E(Y) are

[A] - 1 , -2 [B]1, -2[C]2, 1 [D]-1, 2

33)From 6 positive and 8 negative numbers , 4 numbers are chosen at random (without replacement) andmultiplied , the probability that the product is a positive number is

[A] [B]

[C] [D]55 / 1001

34)The probability of error on a single transmission in a digital communication system is . Then theprobability of more than three errors in 1000 transmissions is

[A] [B][C] [D]

35)The regression equations are 2x + 3y = 6 ; 4x + 3y = 6 then the correlation coefficient is .............

[A]1 / 2 [B]2[C]- 1/2 [D]

36)A problem is given to three students A, B and C ; whose chances of solving it are , and respectively .The probability that the problem will be solved by at least one of them is

[A] [B]

[C] [D]

37)A and B are two independent events with = 0.8 and P(A) = 0.5 then P(B) =

[A]0.3 [B]0.4[C]0.1 [D]0.6

38)A party of 'n' persons take their seats at random at a round table , then the probability that two specifiedpersons do not sit together is

[A] [B]

[C] [D]

39)A manufacturer knows that the condensers he makes contain on an average 1% defectives . He packsthem in boxes of 100 . What is the probability that a box picked up at random will contain 3 or more faultycondensers ?

[A] [B][C] [D]

40)In a series of independent trials with the result of each trial being classified either a success or failure , theprobability of a success in a trail is 1/3 . The probability that the fifth trail results in the third success is

[A]8/81 [B]40/243




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[C]1/27 [D]4/24341)A gambler has in his pocket a fair coin and a two headed coin . He selects one of the coins at random and

flips it and it shows head. The probability that it is the fair coin is

[A]1/4 [B]3/4[C]1/3 [D]2/3

42)A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that atthe end of 11 steps he is one step away from the starting point is

[A] [B]

[C] [D]

43)Out of 10,000 families with 4 children each the probable number of families , all of whose children aredaughters is

[A]1250 [B]625[C]2500 [D]9375

44)If A and B are mutually exclusive events, then

[A] [B][C] [D]

45)The variance of the two-point distribution

where p + q = 1 is

[A]ap + bq [B][C] [D]2pq

46)A fair dice is rolled twice. The probability that an odd number will follow an even number is

[A]1/2 [B]1/4[C]1/6 [D]1/3

47)A probability density function is of the form

The value of K is

[A]0.5 [B]1[C]0.5 [D]

48)An examination consists of two papers. Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is0.6. The probability of a student failing in both the papers is

[A]0.5 [B]0.18[C]0.12 [D]0.06

49)A fair coin is tossed 10 times. What is the probability that Only the first two tosses will yield heads?

[A] [B]

[C] [D]




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50)If P and Q are two random events, then the following is TRUE

[A] Independence of P and Q implies that probability(P ∩ Q) = 0

[B]Probability (P U Q) ≥ Probability (P) + Probability(Q)

[C]If P and Q are mutually exclusive, then they mustbe independent [D]Probability (P ∩ Q) ≤ Probability (P)

51)A fair coin is tossed three times in succession. If the first toss produces a head, then the probability ofgetting exactly two heads in three tosses is

[A]1/8 [B]1/2[C]3/8 [D]3/4

52)Two fair dice are rolled and the sum r of the numbers turned up is considered

[A]Pr (r >6)= [B]Pr (r/3 is an integer) = [C] Pr ( r= 8| r/4 is an integer) = [D]Pr (r= 6| r/5 is an integer) =

53)X is a uniformly distributed random variable that takes values between 0 and 1. The value of will be

[A]0 [B]1/8[C]1/4 [D]1/2

54)Consider an undirected random graph of eight vertices. The probability that there is an edge between apair of vertices is 1/2. What is the expected number of unordered cycles of length three?

[A]1/8 [B]1[C]7 [D]8

55)A continuous random variable X has a probability density function . Then P{X>1} is

[A]0.368 [B]0.5[C]0.632 [D]1.0

56)The minimum Eigen value of the following matrix is

[A]0 [B]1[C]2 [D]3

57)Suppose p is number of cars per minute passing through a certain road junction between 5 PM and 6PM,and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars duringany given minute in this interval?

[A]8/(2 ) [B]9/(2 )[C]17/(2 ) [D]26/(2 )

58)Consider a random variable X that takes values + 1 and -1 with probability 0.5 each. The values of thecumulative distribution function F(x) at x = -1 and +1 are

[A]0 and 0.5 [B]0 and 1[C]0.5 and 1 [D]0.25 and 0.75

59)If the difference between the expectation of the square of random variable and the square of theexpectation of the random variable is denoted by R then

[A]R = 0 [B]R<0 [C] [D]R>0




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60)If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probabilitythat both outcomes are heads?

[A]1/3 [B]1/4[C]1/2 [D]2/3

61)A fair coin is tossed independently four times. The probability of the event " the number of time headsshown up is more than the number of times tails shown up" is

[A] [B][C] [D]

62)Consider the methods used by processes P1 and P2 for accessing their critical sections wheneverneeded, as given below. The initial values of shared boolean variables S1 and S2 are randomly assigned.

Which one of the following statements describes the properties achieved?

[A]Mutual exclusion but not progress [B]Progress but not mutual exclusion[C]Neither mutual exclusion nor progress [D]Both mutual exclusion and progress

63)Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives thecorrect result for any computer with a probability of q. What is the probability of a computer beingdeclared faulty?

[A]pq + (1 - p) (1 - q) [B] (1-q)p[C](1-p)q [D]pq

64)What is the probability that divisor of is a multiple of ?

[A]1/625 [B]4/625[C]12/625 [D]16/625

65)A fair dice is tossed two times . The probability that the second toss results in a value that is higher thanthe first toss is

[A]2/36 [B]2/6[C]5/12 [D]1/2

66)Two dice are rolled once. The probability that the sum on the dice is neither 9 nor 11 is

[A]5/6 [B]1/3[C]2/3 [D]1/2

67)Let P(E) denotes the probability of the event E. Given P(A) = 1, P(B)=1/2. The values of P(A/B) and P(B/A)respectively are

[A]1/4 , 1/2 [B]1/2 , 1/4[C]1/2 , 1 [D]1, 1/2

68)A speaks truth in 75% and in 80% of cases. In what percentage of cases are they likely to contradict eachother narrating the same incident

[A]5% [B]45%[C]35% [D]15%

69)If 3 is the mean &3/2 is the standard deviation of a binomial distribution, then the distribution is




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70)If a fair coin is tossed four times. What is the probability that two heads and two tails will result ?

[A]3/8 [B]1/2[C]5/8 [D]3/4

71) The probability that a man who is 'x' years old will die in a year is P. Then amongst 'n' personseach 'x' years old now, the probability that will die in one year is

[A] [B][C] [D]

72)A can solve 90% of the problems given in a book and B can solve 70%. What isthe probability that at least one of them will solve a problem, selected at randomfrom the book?

[A]0.16 [B]0.63[C]0.97 [D]0.20

73)If the probabilities that A and B will die within a year are p and q respectively,then the probability that only one of them will be alive at the end of the year is

[A] pq [B] p(1 −q) [C] q(1 −p) [D] p+q−2pq

74)How many positive integers less than 100 are divisible by either 7 or 11

[A]2 [B]22[C]20 [D]23

75)Let a set A has a 4 elements then P(A) denotes the powerset of the set A. Now cardinality of P(A) is

[A]16 [B]81[C]256 [D]1

76)Which of the following statements is true in a year ?

[A]Among any group of 366 people there must be atleast one with the same birthday

[B]Among any group of 366 people there must be atleast two with the same birthday

[C]Among any group of 366 people there must be atmost one with the same birthday

[D]Among any group of 366 people there must be atmost none with the same birthday

77)What is the probability that a card selected from a deck is a king ?

[A]1/4 [B]1/52[C]4/52 [D]2/52

78)What is the probability that a positive integer less than 100 selected at random is divisible by 25 ?

[A]3 / 100 [B]4 / 100[C]2 / 100 [D]5 / 100

79)What is the probability that a positive integer selected at random from the set of positive integers notexceeding 21 is divisible by 5 or 3 ?

[A]11/ 20 [B]10 / 20[C]11 / 21 [D]10 / 21

80)X is uniformly distributed random variable that takes values between 0 and 1. The value of will be




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[A]1/4 [B]0[C]1/8 [D]1/2

81)In answering a question on multiple choice test , the students either knows the answer or guesses theanswer . Let ' P' be the probability that student knows the answer and i- p that of guessing the answer .Assume that the student guess the answer to a question will be correct with a probability 1/5 . What is theadditional probability that the students knows the answer to a question given that he answered correctly .

[A] [B]

[C] [D]

82)An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value isodd is 90% of the probability that the face value is even. The probability of getting any even numberedface is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one ofthe following options is closest to the probability that the face value exceeds 3 ?

[A]0.453 [B]0.468[C]0.485 [D]0.492

83)If 20 percent managers are technocrats, the probability that a random committee of 5 managers consistsof exactly 2 technocrats is:

[A]0.2048 [B]0.4000[C]0.4096 [D]0.9421

84)The manufactunng area of a plat is divided into four quadrants. Four machines have to be located, one ineach quandrant. The total number of possible layouts is

[A]4 [B]8[C]16 [D]24

85)A box contains 5 black balls and B red balls. A total of three balls are picked from the box one afteranother, without replacing them back. The probability of getting two black balls and one red ball is

[A]3/8 [B]2/15[C]15/28 [D]1/2

86)The probability of a defective piece being produced in a manufacturing process is 0.01. The probability thatout of 5 successive pieces, only one is defective is

[A] [B][C] [D]

87)The probability that two friends share the same birth-month is

[A]1/6 [B]1/12[C]1/144 [D]1/24

88)The probability that a student knows the correct answer to a multiple choice question is . If the studentdoes not know the answer, then the student guesses the answer. The probability of the guessed answer

being correct is . Given that the student has answered the question correctly, the conditional probabilitythat the student knows the correct answer is

[A] [B][C] [D]

89)In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standarddeviation of defective bolts in a total of 900 bolts are respectively





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90)Suppose X is a normal random variable with mean 0 and variance 4. Then the mean of the absolute valueof X is

[A] [B]

[C] [D]

91)Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight ?

[A]5/36 [B]5/18[C]1/4 [D]1/3

92)Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time ateither stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places.He can afford up to 13 minutes of total waiting time, if he is to arrive at D on time. What is the probabilitythat Manish will arrive late at D ?

[A]8/13 [B]13/64[C]119/128 [D]9/128

93)Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes betweensuccessive arrivals. The length of a phone call is distributed exponentially with mean 3 minutes. Theprobability that an arrival does not have to wait before service is

[A]0.3 [B]0.5[C]0.7 [D]0.9

94)An unbiased coin is tossed three times. The probability that the head turns up in exactly two cases is

[A]1/9 [B]1/8[C]2/3 [D]3/8

95)The area enclosed between the parabola y = and the straight line y = x is

[A]1/8 [B]1/6[C]1/3 [D]1/2

96)A box contains 5 black and 5 red balls. Two balls are.randomly picked one after another from the box,without replacement. The probability for both balls being red is

[A]1/90 [B]1/5[C]19/90 [D]2/9

97)A flexible rotor-shaft system comprises of a 10 kg rotor disc placed in the middle of a mass-less shaft ofdiameter 30 mm and length 500 mm between bearings (shaft is being taken mass-less as the equivalentmass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed tosimulate simply supported boundary conditions. the shaft is made of steel fo; which the value of E is 2.1x Pa. What is the critical speed of rotation of the shaft ?

[A]60 Hz [B]90 Hz[C]135 Hz [D]180 Hz

98)The parabolic are y = , 1 x 2 is revolved around the x-axis. The volume of the solid of revolution is

[A] /4 [B] /2[C]3 /4 [D]3 /2

99)25 persons are in a room.15 of them play hockey, 17 of them play football and 10 of them play bothhockey and football. Then the number of persons playing neither hockey nor football is :

[A]2 [B]17[C]13 [D]3

100)Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed ?




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[A]50 [B]51[C]52 [D]54

101)The area enclosed between the straight line y = x and the parabola y = in the x-y plane is

[A]1/6 [B]1/4[C]1/3 [D]1/2

102)A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one afteranother, without replacement. The probability that the selected set contains one red ball and two blackballs is

[A]1/20 [B]1/12[C]3/10 [D]1/2

103)If three coins are tossed simultaneously, the probability of getting at least one head

[A]1/8 [B]3/8[C]1/2 [D]7/8

104)An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. Theprobability of getting at least one head is

[A]1/32 [B]13/32[C]16/32 [D]31/32

105)From a pack of regular playing cards, two cards are drawn at random. What is the probability that bothcards will be Kings, if the first card is NOT replaced ?

[A]1/26 [B]1/52[C]1/169 [D]1/221

106)A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2of the chosen items are defective is

[A]0.0036 [B]0.1937[C]0.2234 [D]0.3874

107)A box contains 20 defective items and 80 non-defective items. If two items are selected at random withoutreplacement, what will be the probability that both items are defective ?

[A]1/5 [B]1/25[C]20/99 [D]19/495

108)A single die is thrown twice. What is the probability that the sum is neither 8 nor 9?

[A]1/9 [B]5/36[C]1/4 [D]3/4

109)Consider a continuous random variable with probability density functionf(t)=1+t for-1 t 0The standard deviation of the random variable is

[A] [B]

[C] [D]

110)A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

[A] [B][C] [D]

111)Let X and Y be two independent random variables. Which one of the relations between expectation (E),variance (Var) and covariance (Cov) given below is FALSE ?




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[A]E(XY)= E(X)E(Y) [B]Cov (X,Y) = 0[C]Var (X+Y) = Var (X)+Var(Y) [D]

112)Arrivals at a telephone booth are considered be Poisson with an average time of 10 minutes between onearrival and the next. The length of a phone call is assumed to be distributed exponentially with a mean of 3minutes. The probability that a person arriving at the booth will have to wait, is

[A]0.043 [B]0.300[C]0.429 [D]0.700


113)If A is a 3 x 3 matrix with entries from the set { - 1 , 0 , 1}Then the total number of different matrices of order '3' , which are neither symmetric nor skew-symmetricis

[A] [B][C] [D]

114)The probability that 'A' is neither symmetric nor skew symmetric is

[A] [B][C] [D]


115)Consider the experiment of tossing a pair of unbiased diceThe probability that the sum of the two numbers is a prime number is

[A]7/9 [B]5/12[C]4/9 [D]7/12

116)If the experiment is repeated 180 times then how many times we can expect the sum to be a primenumber

[A]140 [B]105[C]80 [D]75


117)The probability of a man hitting a target is 1/4 .If he fires 4 times , then the probability of his hitting the target at least twice is

[A]189/256 [B]196/256[C]67/256 [D]64/256

118)The least number of times he must fire so that the probability of his hitting the target at least once isgreater than 2/3 is

[A]3 [B]4[C]5 [D]6




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Key Paper

1. D 2. B 3. A 4. D 5. A

6. A 7. A 8. B 9. C 10. D

11. C 12. D 13. B 14. B 15. C

16. C 17. D 18. C 19. D 20. C

21. D 22. A 23. C 24. A 25. C

26. D 27. B 28. A 29. B 30. D

31. D 32. D 33. A 34. C 35. D

36. C 37. D 38. B 39. B 40. B

41. C 42. B 43. C 44. D 45. C

46. B 47. C 48. C 49. C 50. D

51. B 52. C 53. C 54. C 55. A

56. A 57. C 58. C 59. C 60. A

61. D 62. A 63. A 64. D 65. C

66. A 67. D 68. C 69. A 70. A

71. D 72. C 73. D 74. A 75. A

76. B 77. C 78. A 79. D 80. A

81. B 82. B 83. A 84. D 85. C

86. D 87. B 88. D 89. A 90. C

91. A 92. A 93. A 94. D 95. C

96. D 97. B 98. D 99. D 100. B

101. A 102. D 103. D 104. D 105. D

106. B 107. D 108. D 109. B 110. A

111. D 112. B 113. B 114. A 115. B

116. D 117. C 118. B




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1)If X(Z) is the z-transform of the ROC of X(z) is

[A] |z|>2 [B] |z|<2[C] [D]the entire z-plane

2)The two sided Laplace transform of

[A] [B]

[C] [D]

3)The z-transform X(z) of a sequence x[n] is given by

If X(z) converges for |z|=1 then x[-18] is

[A] [B][C] [D]

4)The z-transform X(z) of a real and right sided sequences x[n] has exactly two poles and one of them isat and there are two zeroes at the origin . If X(1) =1 , which one of the following is TRUE?

[A] [B]

[C] [D]

5)The Fourier Transform of cos (αt ) is equal to

[A] [B]

[C] [D]None of the above

6)The inverse Laplace transform of the is

[A] [B][C] [D]

7)Which of the following Derichlets conditions are correct for convergence of Fourier transform of thefunction x(t)?1. x(t) is square integrable2. x(t) must be periodic3. x(t) should have finite number of maxima and minima within any finite interval4. x(t) should have finite number of discontinuities within any finite interval

[A]1, 2, 3 and 4 only [B]1, 2 and 4 only[C]1, 3 and 4 only [D]2, 3 and 4 only

8)If f(t) is a real and odd function, then its Fourier transform F( ) will be

[A] real and even function of [B] real and odd function of [C]imaginary and odd function of [D]imaginary function of

9)For certain sequences which are neither absolutely summable nor square summable, it is possible to havea Fourier Transform (FT) representation if we

[A] take short time FT [B]evaluate FT only the real part of the sequence[C]allow DTFT to contain impulses [D]evaluate FT over a limited time span

Transforms



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10)A unit impulse function is defined by1. = 0 for all t except t = 0

2. =1The Fourier transform F( ) of is

[A]1 [B]1 / [C]0 [D]1 / j

11)if the z - transform of x(n) is x(z) = , then the is

[A]1 [B]2[C] [D]0

12)For the discrete signal x[n] = u[n] the z - transform is

[A]z / z+a [B]z-a / z[C]z / a [D]z / z-a

13)If the power spectral density is and the auto correlation function is defined by dfThe integral on the right represents the Fourier transform of

[A]Delta function [B]Step function[C]Ramp function [D]Sinusoidal function

14)Laplace transform for the function f(x) = cosh(ax) is

[A] [B][C] [D]

15)Transformation to linear form by substituting of the equation will be

[A] [B]

[C] [D]

16)If L defines the Laplace Transform of a function, L [sin (at)] will be equal to

[A] [B][C] [D]

17)The Fourier series expansion of a symmetric and even function, f(x) where

will be

[A] [B]

[C] [D]

18)List of the following series as x approaches is

[A] [B][C] [D]1

19)The Laplace Transform of the following function is

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. 1 Marks IES-EEE-2000( )



[A] [B]

[C] [D]

20)The inverse Laplace Transform of is

[A] [B]

[C] [D]

21)A function with a period is shown below.

The Fourier series for this function is given by

[A] [B]

[C] [D]

22)The Laplace transform of the functionf(t) = k, 0 <t <c = 0,c <t < is

[A] [B]

[C] [D]

23)Let denote the Laplac transform of the function f(t). Which of the following statements iscorrect ?

[A];

[B];

[C];

[D];

24)The Laplace Transform of a unit step function , defined as

[A] [B][C] [D]

25)If the unilateral Laplace transform X(s) of a signal x(t) is , then the initial and final values of the signalwould be respectively.

[A]3.5 and 5 [B]zero and 7[C]5 and zero [D]7 and 5

26)The Fourier transform of a signal is

[A] [B][C] [D]

27)

The region of the z plane for which is

[A]x-axis [B]y-axis[C]The straight line z = | a| [D]None of the above

Transforms



____________________________________________________________________________________________________________________ Pg.No.65



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28)Laplace transform of is

[A] [B]

[C] [D]

29)The constant term in the Fourier expansion of f(x) if f(x) = 2 + x , -2 <x <0 = 2 - x , 0 <x <2

[A]2 [B] - 2[C]1 [D]1/2

30)If Fourier Transform of F(x) is f(s) then the Fourier Transform of F(x - a) is

[A] [B][C]1/a f(s/a) [D]1/a f(a/s)

31)The Fourier Series of f(x) if f(x) = 1 0 <x < = 0 <x <2 is

[A] [B]

[C] [D]

32)The Laplace Transform of is

[A] [B]

[C] [D]

33)The Z-transform of is

[A] [B]

[C] [D]

34)The Laplace Transform of t sint is

[A] [B]

[C] [D]

35)Z-Transform of is ............

[A] [B]

[C] [D]

36)The half range cosine series of f(x) = x in the interval (0,2) is given by then=

[A]0 [B][C] [D]

37)The Inverse Laplace Transform of is ............

[A] [B][C] [D]

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____________________________________________________________________________________________________________________ Pg.No.66


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38)

[A] [B][C] [D]

39)If F{ f(x) } = g(s) then F { f(x-1) } = ...............

[A] [B][C] [D]

40)

[A] (t - a) H(t - a) [B][C] [D]

41)The Fourier series of the periodic function at x = converges to

[A] [B]2[C] [D] +

42)

[A] [B][C] [D]

43)If the Fourier transform of f(x) = F(s) then the Fourier transform of f(x) cos ax is

[A] [B][C] [D]

44)If Then L { F(t) } =

[A] [B][C] [D]

45)If then the Fourier cosine transform of f(x) in (0, ) is

[A] [B]

[C] [D]

46)The Z-transform of is

[A] [B]

[C] [D]

47)In what range should Re(s) remain so that the Laplace transform of the function exits.

[A]Re (s) >a+2 [B]Re (s) >a+7[C]Re (s) <2 [D]Re (s) >a + 5

48)For the equation , the solution x (t) approaches which of the following values att → ?

[A]0 [B]5/2[C]5 [D]10

Transforms



____________________________________________________________________________________________________________________ Pg.No.67






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49)The differential equation dx/dt = (1-x)/τ is discretised using Euler’s numerical integration method with atime step ∆ T >0. What is the maximum permissible value of ∆ T to ensure stability of the solution of thecorresponding discrete time equation?

[A]1 [B] τ/2[C]τ [D]2 τ

50)The bisection method is applied to compute a zero of the function f(x) = in the interval[1,9]. The method converges to a solution after_______ iterations.

[A]1 [B]3[C]5 [D]7

51)If , then the value of

[A]Cannot be dertermined [B] is zero[C]is unity [D]is infinite

52)The trigonometric Fourier series of a periodic time function can have only

[A]cosine terms [B]sine terms[C]cosine and sine terms [D]d.c. and cosine terms

53)The following of Laplace transform is

[A] [B]

[C] [D]

54)F.S.T of

[A] [B]

[C] [D]

55)If for , then is

[A]1 [B]0[C]3 [D]2

56)If ; n <0 ; , then ROC is

[A] [B][C] [D]Does not exist

57)Apply the transform to is

[A] [B]

[C] [D]

58)

if then find f(x) ?

[A] [B]

[C] [D]

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____________________________________________________________________________________________________________________ Pg.No.68


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59)What is answer of this equation is

[A] [B]

[C] [D]

60) is____

[A]u(n) [B][C]nu(n) [D]

61)Solve the following function

[A] [B]

[C] [D]

62) = _____

[A] (n+1)u(n) [B][C] [D]u(n)

63)

[A] [B][C] [D]

64)What is inverse Fourier transform of is

[A] [B][C] [D]

65)The voltage across an impedance in a network is V (s) = z (s) I (s) , where V(s) , Z(s) are the Laplacetransforms of the corresponding time function v (t ) , z (t ) and i (t ). The voltage v (t ) is:

[A] [B][C] [D]

66) is the Laplace transform of

[A] [B][C] [D]

67)Laplace transform of where 'a' and 'b' are constants is given by

[A] [B]

[C] [D]

68)The Laplace transform of the function , is

[A] [B]

[C] [D]

69)Laplace transform of the function sin t is

[A] [B][C] [D]

70)The Laplace transform of a function f(t) is . The function f(t) is

Transforms



____________________________________________________________________________________________________________________ Pg.No.69








. 2 Marks ( )

. 1 Marks GATE-ECE/TCE-2012,GATE-EEE-2012( )

.

[A] t - 1 + [B] t + 1 + [C]-1 + [D]2t +

71)The inverse Laplace transform of the function is given by

[A] f(t) = sin t [B] f(t) = sin t[C]f(t) = [D]f(t) 1-

72)The inverse Laplace transform of is

[A]1 + [B]1 - [C]1 - [D]1 +

73)A delayed unit step function is defined as

.Its Laplace transform is

[A] [B][C] [D]

74)Eigenvalues of a matrix are 5 and 1. What are the eigenvalues of the matrix =SS?


75)If F(s) is the Laplace transform of function f (t), then Laplace transform of is

[A]1/s F(s) [B]1/s F(s) - f(0)[C]sF(s) -f(0) [D]

76)Given If then value of "K" is

[A]4 [B]2[C]3 [D]1

77)If , then the region of convergence (ROC) of its Z-transform in the Z-plane willbe

[A] [B]

[C] [D]

Transforms



____________________________________________________________________________________________________________________ Pg.No.70


Key Paper

1. C 2. A 3. B 4. D 5. A

6. A 7. C 8. C 9. C 10. A

11. A 12. D 13. A 14. B 15. A

16. B 17. B 18. D 19. C 20. D

21. A 22. D 23. D 24. A 25. D

26. A 27. B 28. C 29. C 30. B

31. A 32. A 33. B 34. B 35. A

36. D 37. B 38. C 39. A 40. A

41. D 42. B 43. A 44. B 45. A

46. A 47. A 48. B 49. D 50. B

51. A 52. D 53. A 54. B 55. B

56. D 57. B 58. B 59. C 60. C

61. A 62. B 63. D 64. A 65. A

66. D 67. C 68. A 69. B 70. A

71. D 72. C 73. B 74. A 75. A

76. A 77. C

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____________________________________________________________________________________________________________________ Pg.No.71






Index- Strength of Materials

Sl.No. Name of the Topic Pg.No.s 1. Simple Stress 73-77 2. Complex Stress 78-80 3. Shear Force & Bending Diagram 81-90 4. Centroids & Moment Of Inertia 91-92 5. Pure Bending 93-95 6. Springs 96-97 7. Torsion 98-100 8. Slopes Deflection 101-104 9. Thin Cylinders 105-106 10. Columns & Struts 107-110 11. Propped & Fixed Beams 111-113 12. Strain Energy 114-115 13. Engineering Mechanics 116-122









.

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1)The Poisson’s ratio is defined as

[A] [B][C] [D]

2)The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

[A]4 [B]3[C]2 [D]1

3)A mild steel specimen is under uni-axial tensile stress. Young's modulus and yield stress for mild steelare MPa and 250 MPa respectively. The maximum amount of strain energy per unit volume that canbe stored in this specimen without permanent set is

[A] [B][C] [D]

4)Consider the beam AB shown in the figure below. Part AC of the beam is rigid while Part CB has theflexural rigidity El. ldentify the correct combination of deflection at end B and bending moment at end A,respectively.

[A] [B]

[C] [D]

5)A vertical PQ of length Lis fixed at its top end P and has a flange to the bottom end Q. A weight W isdropped vertically from a height h (

[A] increasing the length of the rod [B]decreasing the length of the rod

[C]decreasing the area of cross-section of the rod [D]increasing the modulus of elasticity of thematerial

6)The maximum tensile stress at the section X-X shown in the figure below is

[A] [B][C] [D]

7)A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by. If the coefficient of thermal expansion is and the Young’s modulus is , the stress in

the bar is

[A]zero [B]12 MPa[C]24 MPa [D]2400 MPa

Simple stress



____________________________________________________________________________________________________________________ Pg.No.73







8)A homogeneous, simply supported prismatic beam of width B, depth D and span L is subjected to aconcentrated load of magnitude P. The load can be placed anywhere along the span of the beam. Themaximum flexura stress developed in beam is

[A] [B][C] [D]

9)A rigid bar is suspended by three rods made of the same material as shown in the figure. The area andlength of the central rod are 3A and L, respectively while that of the two outer rods are 2A and 2Lrespectively. If a downward force of 50kN is applied to the rigid bar, the forces in the central and each ofthe outer rods will be

[A]16.67 kN each [B]10MPa and 80 Mpa[C]118 Mpa and 160 MPa [D]200 MPa 160 MPa

10)A bar of varying square cross-section is loaded symmetrically as shown in the figure. Loads shown areplaced on one of the axes of symmetry of cross section. Ignoring self weight, the maximum tensile stressin anywhere is

[A]16.0 [B]20.0[C]25.0 [D]30.0

11)Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise inthe bar BD alone in the plane truss shown below:

[A]No reactions develop at supports A and D. [B]The bar BD will be subject to a tensile force.[C]The bar AC will be subject to a compressive force [D]The bar BC will be subject to a tensile force

12)The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio (v) of a material are related as,

[A] [B][C] [D]

13)Fig. 1 shows a rigid bar hinged at A and supported in a horizontal position by two vertical identical steelwires. Neglect the weight of the beam. The tension

and induced in these wires by a vertical load P applied as shown are

Simple stress



____________________________________________________________________________________________________________________ Pg.No.74








[A] [B][C] [D]

14)A free bar of length I is uniformly heated from to a temperature . is the coefficient of linearexpansion and E is the modulus of elasticity. The stress in the bar is

[A] tE [B] tE /2[C]zero [D]none of the above

15)A rod of length 1 m is sliding in a corner as shown in Fig. At an instant when the rod makes an angle of 60degrees with the horizontal plane, the velocity of point A on the rod is 1 m/s. The angular velocity of therod at this instant.

[A]2 rad/s [B]1.5 rad/s[C]0.5 rad/s [D]0.75 rad/s

16)A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in thefigure below. If the Young’s modulus of the material varies linearly from to along the length of the rod,the normal stress developed at the section-SS is

[A] [B]

[C] [D]

17)A 1.5 mm thick sheet is subject to unequal biaxial stretching and the true strains in the directionsofstretching are 0.05 and 0.09. The frnal thickness of the sheet in mm is

[A]1.414 [B]1.304[C]1.362 [D]289

18)A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by . Ifthe thermal coefficient of the material is , Young’s modulus is E and the Poisson’s ratio is , the thermalstress developed in the cube due to heating is

[A] [B]

[C] [D]

Simple stress



____________________________________________________________________________________________________________________ Pg.No.75









19)A solid shaft of diameter, d and length L is fixed at both the ends. A torque, is applied at a distance, L/4from the left end as shown in the figure given below

The maximum shear stress in the shaft is

[A] [B][C] [D]

20)In terms of Poisson's ratio (v) the ratio of Young's Modulus (E) to Shear Modulus (G) of elastic materials is

[A]2(1+v) [B]2(1-v)[C] [D]

21)The Figure below shows a steel rod of 25 m cross sectional area. It is loaded at four points, K, L, M andN. Assume = 200 GPa. The total change in length of the rod due to loading is

[A]1 [B] -10 [C]16 [D]-20

22)A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on africtionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses arerepresented by and , respectively, then

[A] [B][C] [D]

23)A steel bar of 40 mm x 40 mm square cross-section is subjected to an axial compressive load of 200 kN. Ifthe length of the bar is 2 m and E = 200 GPa, the elongation of the bar will be

[A]1.25 mm [B]2.70 mm[C]4.05 mm [D]5.40 mm

24)A bar having a crose-sectional area of 700mm is subjected to axial loads at the positions indicated. Thevalue of stress in the segment QR is (See Figure)

[A]40 MPa [B]50 MPa[C]70 Mpa [D]120 MPa

25)A rod of length t and diameter D is subjected to a tensile load P. Which of the following is sufficient tocalculate the resulting change in diameter ?

[A]Young's modulus [B]Shear modulus[C]Poisson's ratio [D]Both Young's modulus and shear modulus.

Simple stress



____________________________________________________________________________________________________________________ Pg.No.76


Key Paper

1. B 2. C 3. D 4. A 5. A

6. A 7. D 8. D 9. C 10. C

11. B 12. C 13. C 14. C 15. A

16. A 17. B 18. A 19. B 20. A

21. B 22. A 23. A 24. A 25. D

Simple stress



____________________________________________________________________________________________________________________ Pg.No.77


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1)The major and minor principal stresses at a point are 3MPa and -3MPa respectively. The maximum shearstress at the point is

[A]Zero [B]3MPa[C]6MPa [D]9MPa

2)Mohr's circle for the state of stress defined by M Pa is a circle with

[A]center at (0, 0) and radius 30 M Pa [B]center at (0,0) and radius 60 M Pa[C]center at (30, 0) and radius 30 M Pa [D]center at (30, 0) and zero radius

3)Consider the following statements:I. On a principal plane, only normal stress acts.II. On a principal plane, both normal and shear stresses act.III. On a principal plane, only shear stress acts.IV. Isotropic state of stress is independent of frame of reference.The TRUE statements are

[A] I and IV [B] II[C]II and IV [D]II and III

4)The symmetry of stress tensor at a point in the body under equilibrium is obtained from

[A]conservation of mass [B] force equilibrium equations[C]moment equilibrium equations [D]conservation of energy

5)The components of strain tensor at a point in the plane strain case can be obtained by measuringlongitudinal strain in following directions

[A]along any two arbitrary directions [B]along any three arbitrary directions[C]along two mutually orthogonal directions [D]along any arbitrary direction

6)If principal stresses in a two-dimensional case are - 10MPa and 20 MPa respectively,then maximum shearstress at the point is

[A]10 MPa [B]15 MPa[C]20 MPa [D]30 MPa

7)For an isotropic material, the relationship between the Young’s modulus (E), shear modulus (G) andPoisson’s ratio ( ) is given by

[A] [B]

[C] [D]

8)In a two dimensional stress analysis, the state of stress at a point is shown below.If s = 120 MPa and t = 70 MPa, then and are respectively

[A]26.7 MPa and 172.5 MPa [B]54 MPa and 128 MPa[C]67.5 MPa and 213.3 MPa [D]16 MPa and 138 MPa

Complex stress



____________________________________________________________________________________________________________________ Pg.No.78








.

9)Pick the incorrect statement from the following four statements :

[A]On the plane which carries maximun1 normalstress, the shear stress is zero [B]Principal planes are mutually orthogonal.

[C]On the plane which carries maximum shearstress, the normal stress is zero.

[D]The principal stress axes and principal strainaxes coincide for an isotropic material.

10)Two perpendicular axes x and y of a section are called principal axes when

[A]Moments of inertia about the axes are equal [B]Product moment of inertia is zero

[C]Product moment of inertia is zero [D]Moment of inertia about one of the axes isgreater than the other

11)If an element of a stressed body is in a state of pure shear with a magnitude of ,the magnitudeof maximum principal stress at that location is

[A] [B][C] [D]

12)The maximum principal strain in a thin cylindrical tank, having a radius of25 cm and wall thickness of 5 mmwhen subjected to an internal pressure of 1 MPa, is (taking Young's midulus as 200 GPa and Poisson'sratio as 0.2)

[A] [B]2.25[C] [D]22.5

13)A torque of 10 Nm is transmitted through a stepped shaft as shown in Figure. The torsional stiffnesses ofindividual sections of lengths MN, NO and OP are 20 Nm/rad, 30 Nm/rad and 60 Nm/rad respectively. Theangular deflection between the ends M and P of the shaft is

[A]0.5 rad [B]1.0 rad[C]5.0 rad [D]10.0 rad

14)A two dimensional fluid element rotates like a rigid body. At a point within the element, the pressure is 1unit. Radius of the Mohr's circle, characterizing the state of stress at that point, is

[A]0.5 unit [B]0 unit[C]1 unit [D]2 unit

Complex stress



____________________________________________________________________________________________________________________ Pg.No.79


Key Paper

1. B 2. D 3. A 4. C 5. B

6. B 7. A 8. A 9. C 10. C

11. B 12. A 13. B 14. B

Complex stress



____________________________________________________________________________________________________________________ Pg.No.80


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Common Data for Q1 and Q2 is given below

A three-span continuous beam has an internal hinge at B. Section B is at the mid-span of AC. Section E isat the mid-span of CG. The 20 kN load is applied at section 8 whereas 10 kN loads are applied at sectionsD and F as shown in the figure. Span GH is subjected to uniformly distributed load of magnitudes 5 kN/m.For the loading shown, shear force immediate to the right of section E is 9.84 kN upwards and the saggingmoment at section E is 10.31 kN-m

1)The magnitude of the shear force inlmediate to the left and immediat to the right of section B are,respectively

[A]0 and 20 kN [B]10 kN and 10 kN[C]20 kN and 0 [D]9.84 kN and 10.16 kN

2)The vertical reaction at support H is

[A]15 kN upward [B]9.84 kN upward[C]15 kN downward [D]9.84 kn downward

3)The bending moment (in kNm units) at the mid-span location X in the beam with overhangs shown belowis equal

[A]0 [B] -10[C]-15 [D]-20

4)For the loading given in the figure below, two statements (I and II) are made.

I .Member AB ca rries shea r force and bending momentII.Member BC carries axial load and shear force. Which of the followjng is true?

[A]Statement I is true but II is false [B] Statement I is false but II is tme[C]Both statements I and II are true [D] Both statements I and II are false

Shear force & Bending diagram



____________________________________________________________________________________________________________________ Pg.No.81





5)Group 1 shows different loads acting on a beam and Group 2 shows different bending momentdtstrobutions. Match the toad with the corresponding bendin g moment diagram Group-1 Group-2

P. 1.

Q. 2.

R. 3.

S. 4.

5. Codes: P Q R S

[A]4 2 1 3 [B]5 4 1 3[C]2 5 3 1 [D]2 4 1 3

6)A linear time-invariant discrete-time system is described by the vector matrix difference equation

Where is the state vector, F is an n × n constant matrix, G is a (n × r ) constant matrix and is thecontrol vector. The state transition matrix of the system is given by inverse Z-transform of

[A]ZI-F [B] (ZI-F)Z[C] [D]

7)A block of steel is loaded by a tangential force on its top surface while the bottom surface is held rigidly.The deformation of the block is due to

[A]shear only [B]bending only[C]shear and bending [D]torsion




____________________________________________________________________________________________________________________ Pg.No.82







8)A spring scale indicates a tension T in the right hand cable of the pulley system shown in Figure. Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass m is


9)The ratio of average shear stress to the maximum shear stress in a beam with a square cross-section is

[A]1 [B]2/3[C]3/2 [D]2

10)A concentrated force, F is applied (perpendicular to the plane of the figure) on the tip of the bent barshown in Fig. The equivalent load at a section close to the fixed end is

[A]Force F [B]Force F and bending moment FL

[C]Force F and twisting moment FL [D]Force F, bending Moment FL, and twistingmoment FL

11)A simply supported beam of length L is subjected to a varying distributed load sin (3p x/L) N , where thedistance x is measured from the left support. The magnitude of the vertical reaction force in N at the leftsupport is

[A]zero [B]L/3[C]L/ [D]2L/

12)The shapes of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributedload over its length is

[A]a suraight line [B]a hyperbola[C]an elipse [D]a parabola




____________________________________________________________________________________________________________________ Pg.No.83






13)A simply supported beam carries a load 'P' through a bracket, as shown in Figure. The maximum bendingmoment in the beam is

[A]Pl/2 [B]Pl/2 + ap/2[C]Pl/2 +aP [D]Pl/2 -aP

14)Bars AB and BC, each of negligible mass, support load P as shown in the Fig. In this arrangement

[A]bar AB is subjected to bending but bar BC is notsubjected to bending

[B]bar AB is not subjected to bending but bar BC issubjected to bending

[C]neither bar AB nor bar BC is subjected to bending [D]both bars AB and BC are subjected to bending.15)A simply supported beam PQ is loaded by a moment of 1 k.N-m at the mid-span of the beam as shown in

the figure. The reaction forces Rp and RQ at supports P and Q respectively are

[A] 1 kN downward, 1 kN upward [B] 0.5 kN upward, 0.5 kN downward[C]0.5 kN downward, 0.5 kN upward [D]1 kN upward, 1 kN upward

16)A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force Pis applied at a distance of 2L/3 from the hinge so that the rod swings to the right. The reaction at the hingeis

[A] -P [B]0[C]P/3 [D]2P/3




____________________________________________________________________________________________________________________ Pg.No.84







17)Two identical cantilever beams are supported as shown in Fig with their free ends in contact through arigid roller. After the load P is applied, the free ends will have

[A]equal deflections but not equal slopes [B]equal slopes but not equal deflections[C]equal slopes as well as equal deflections [D]neither equal slopes nor equal deflections.

18)A beam is made up of two identical bars AB and BC,by hinging them together at B. The end A is built-in(cantilevered) and the end C is simply-supported. With the load P acting as shown in Fig. the bendingmoment at A is

[A]zero [B]PL/2[C]3PL/2 [D]indeterminate

19)A cantilever beam has the square cross- section 10 mm x 10 mm. It carries a transverse load of 10 N.Considering only the bottom fibres of the beam, the correct representation of the longitudinal variation ofthe bending stress is

[A] [B]

[C] [D]

20)The transverse shear stress acting in a beam of rectangular cross-section, subjected to a transverse shearload, is

[A]variable with maximum at the bottom of the beam [B]variable with maximum at the top of the beam[C]uniform [D]variable with maximum at the neutral axis.

21)In a simply-supported beam loaded as shown below, the maximum bending moment in Nm is

[A]25 [B]30[C]35 [D]60

22)The following statements are related to bending of beams:1.The slope of the bending moment diagram is equal to the shear force.2. The slope of the shear force diagram is equal to the load intensity.3. The slope of the curvature is equal to the flexural rotation.4. The second derivative of the deflection is equal to the curvature.The only FALSE statement is




____________________________________________________________________________________________________________________ Pg.No.85








[A]1 [B]2[C]3 [D]4

23)The people weighing W each are sitting are on a plank of length L floating on water at from eitherend.Neglecting the weight of plank , the bending moment at the center of the plank is

[A]WL/8 [B]WL / 16[C]WL / 32 [D]Zero

24)For the simply supported beam of length L, subjected to a uniformly distributed moment M kN-m per unitlength as shown in the figure, the bending moment (in kN-m) at the mid-span of the beam is

[A]Zero [B]M[C]ML [D]M/L

25)A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on halfof the span from one end. The length of the span and the flexural stiffness are denoted as l and EI,respectively. The deflection at mid-span of the beam is

[A] [B]

[C] [D]

26)The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force Pand a moment M at mid-height. The reaction(s) at R is/are

[A]a vertical force equal to P [B]a vertical force equal to P/2[C]a vertical force equal to P and a horizontal force

equal to M/h[D]a vertical force equal to P/2 and a horizontal force

equal to M/h27)A symmetric frame PQR consists of two inclined members PQ and QR, connected at ‘Q’ with a rigid joint,

and hinged at ‘P’ and ‘R’. The horizontal length PR is l. If a weight W is suspended at ‘Q’, the bendingmoment at ‘Q’ is

[A] [B]

[C] [D]




____________________________________________________________________________________________________________________ Pg.No.86




28)Consider a simply supported beam with a uniformly distributed load having a neutral axis (NA) as shown.For points P (on the neutral axis) and Q (at the bottom of the beam) the state of stress is best representedby which of the following pairs?

[A] [B]

[C] [D]

29)Group I gives the shear force diagrams and Group II gives the diagrams of beams with supports andloading. Match the Group I with Group II. Group I List-II

P. 1.

Q. 2.

R. 3.

S. 4.

[A]P-3,Q-1,R-2,S-4 [B]P-3,Q-4,R-2,S-1[C]P-2,Q-1,R-4,S-3 [D]P-2,Q-4,R-3,S-4




____________________________________________________________________________________________________________________ Pg.No.87





30)A simply supported beam AB has the bending moment diagram as shown in the following figure

.The beam is possibly under the action of following loads:

[A]Couples or M at C and 2M at D [B]Couples or 2M at C and M at D

[C]Concentrated loads of M/L at C and 2M/L at D [D]Concentrated loads of M/L at C and couple of 2Mat D

31)A beam with the cross-section given below is subjected to a positive bending moment (causingcompression at the top) of 16kN-m acting a round the horizontal axis.The tensile force acting on thehatched area of the cross-section is

[A]zero [B]5.9 kN[C]8.9 kN [D]17.8 kN

32)Vertical reaction developed at B in the frame below due to the applied load of 100 kN (with 150000 cross-sectional area and , moment of inertia for both members) is

[A]5.9 kN [B]302 kN[C]66.3 kN [D]94.1 kN




____________________________________________________________________________________________________________________ Pg.No.88





.

33)A curved member with a straight vertical leg is carrying a vertical load at Z, as shown in the figure. Thestress resultants in the XY segment are

[A]bending moment shear force and axial force [B]bending moment and axial force only[C]bending moment and shear force only [D]axial force only


34)A two span continuous beam having equal spans each of length L is subjected to a uniformly distributedload per unit length. The beam has constant flexural rigidity.

The reaction at the middle support is

[A] [B]

[C] [D]

35) The being moment at the middle support is

[A] [B]

[C] [D]




____________________________________________________________________________________________________________________ Pg.No.89


Key Paper

1. A 2. B 3. C 4. C 5. D

6. A 7. C 8. C 9. B 10. D

11. B 12. D 13. C 14. A 15. A

16. A 17. D 18. B 19. A 20. D

21. B 22. C 23. C 24. B 25. B

26. C 27. D 28. A 29. A 30. A

31. C 32. A 33. B 34. C 35. B




____________________________________________________________________________________________________________________ Pg.No.90


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.





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1)A disc of radius r has a hole of radius r 2 cut-out as shown. The centroid of the remaining disc (shadedportion) at a radial distance from the centre “O” is

[A] r/2 [B] r/3[C]r/6 [D]r/8

2)The square root of the ratio of moment of inertia of the cross section to its cross sectional area is called

[A]second moment of area [B]section modulus[C]slenderness ratio [D]radius of gyration

3)For the section shown below, second moment of the area about an axis d/4 distance above the bottom ofthe area

[A] [B]

[C] [D]

4)ln section, shear centre is a point through which,if the result ant load passes, the section will not besubjected to any

[A]Bending [B]Tension[C]Comp ression [D]Torsion

Centroids & Moment of inertia



____________________________________________________________________________________________________________________ Pg.No.91


Key Paper

1. B 2. D 3. C 4. D

Centroids & Moment of inertia



____________________________________________________________________________________________________________________ Pg.No.92


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1)The ‘plane section remains plane’ assumption in bending theory implies

[A]strain profile is linear [B]stress profile is linear[C]both strain and stress profiles are linear [D]shear deformations are neglected

2)The shape of the cross-section, which has a largest shape factor, is

[A] rectangular [B] I-section[C]diamond [D]solid circular

3)T-section of a beam is formed by gluing wooden planks as shown in the figure below. lf th1s beamtransmits a constant vertical shear force of 3000 N, the glue at any of the four joints will be subjected to ashear force (in kN per meter length) of

[A]3.0 [B]4.0[C]8.0 [D]10.7

4)If a beam of rectangular cross-section is subjected to a vertical shear force V, the shear force carried bythe upper one-third of the cross-section is

[A]zero [B]7V/27[C]8V/27 [D]V/3

5)The maximum shear stress in a solid shaft of circular cross-section having diameter subjected to atorque T is .If the torque is increased by four times and the diameter of the shaft is increased by twotimes, the maximum shear stress in the shaft will be

[A]2 [B] /2[C] /4 [D]

6)An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is

[A]75 MPa [B]86.5 MPa[C]100 MPa [D]122.3 MPa

7)The shear stress at the neutral axis in a beam of triangular section with a base of 40mm and height of20mm, subjected to a shear force of 3kN is

[A]3MPa [B]6MPa[C]10MPa [D]20MPa

8)The dimensions for.the flexural rigidity of a beam element in mass (M), length (LJ and time (T) is given by

[A] [B][C] [D]

Pure bending



____________________________________________________________________________________________________________________ Pg.No.93







.

9)A cantilever beam carries the anti-symmetric load shown in Fig. 11, where is the peak intensity of thedistributed load. Qualitatively, the correct bending moment diagram for this beam is

[A] [B]

[C] [D]


10)A massless beam has a loading pattern as shown in the Fig. 6. The beam is ofrectangular cross-sectionwith a width of 30 mm and height of 100 mm

Fig. 6The maximum bending moment occurs at

[A]Location B [B]2675 mm to the right of A[C]2500 mm to the right of A [D]3225 mm to the right of A.

11)The maximum magnitude of bending stress (in MPa) is given by

[A]60.0 [B]67.5[C]200.0 [D]225.0


12)A simply supported beam of span length 6 m and 75 mm diameter carries a uniformly distributed load of1.5 kN/m

What is the maximum value of bending

[A]9 kNm [B]6.75 kNm[C]81 kNm [D]125 kNm

13)What is the maximum value of bending stress ?

[A]162.98 MPa [B]325.95 MPa[C]625.95 MPa [D]651.90 MPa

Pure bending



____________________________________________________________________________________________________________________ Pg.No.94


Key Paper

1. A 2. C 3. B 4. B 5. C

6. B 7. C 8. B 9. C 10. C

11. B 12. B 13. A

Pure bending



____________________________________________________________________________________________________________________ Pg.No.95


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.





.

1)If the wire diameter of a closed coil helical spring subjected to compressive load is increased from 1 cm to2 cm, other parameters , remaining same, then deflection will decrease by a factor of

[A]16 [B]8[C]4 [D]2

2)A forged steel link with uniform diameter of 30mm at the centre is subjected to an axial force that variesfrom 40kN in compression to 160kN in tension. The tensile( ), yield ( ) and corrected endurance ( ) strengths of the steel material are 600MPa, 420MPa and240MPa respectively. The factor of safety against fatigue endurance as per Soderberg’s criterion is

[A]1.26 [B]1.37[C]1.45 [D]2.00


3)A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of 'k') atpoints' 1' and '2', and an inclined load acts at '2', as shown.

Which of the following options represents the deflections and at points '1' and '2'?

[A] [B][C] [D]

4)If the load P equals 100 kN, which of the following options represents forces and in the springs atpoints '1' and '2'?

[A] = 20 kN and = 40 kN [B] = 50 kN and = 50 kN[C] = 30 kN and = 60 kN [D] = 40 kN and = 80 kN

Springs



____________________________________________________________________________________________________________________ Pg.No.96


Key Paper

1. A 2. A 3. B 4. D

Springs



____________________________________________________________________________________________________________________ Pg.No.97


.

.









1)A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque t isapplied at the free end. The shear modulus of the material is G. The angle of twist at three free ends is

[A] [B][C] [D]

2)A long shaft of diameter d is subjected to twisting moment T at its ends.The maximum normal stress actingat its cross-section is equal to

[A]zero [B]16T/[C]32T/ [D]64T/

3)A hollow circular shaft has an outer diameter of 100 mm and a wall thickness of 25 rnm. The allowableshear stress in the shaft is 125 MPa . The maximum torque the shaft can transmit is

[A]46 kN m [B]24.5 kN m[C]23 kN m [D]11.5 kN m

4)A circular shaft shown in the figure is subjected to torsion T at two points A and B.The torsional rigidity ofportions CA and BD is and that of portion AB is The rotations of shaft at point A and Bare and .The rotation is

[A] [B]

[C] [D]

5)The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20mm andthickness 2mm, subjected to a torque of 92.7 N.m will be

[A]59 MPa and 47.2 MPa [B]10MPa and 80MPa[C]118 MPa and 160 MPa [D]200 MPa and 160 MPa

6)A circular solid shaft of span L = 5m is fixed at one end and free at the other end. A twisting moment T =100 kN-m is applied at the free end. The torsional rigidity GJ is 50000 kN- /red.Following statements are made for this shaft.(I) The maximum rotation is 0.01 rad(II) The torsional strain energy is 1kN-mWith reference to the above statements, which of the following applies?

[A]Both statements are true [B]Statement I is true but n is false[C]Statement II is true but I is false [D]Both the statements are false

7)The outside diameter of a hollow shaft is twice its inside diameter. The ratio of its torque carrying capacityto that of a solid shaft of the same material and the same outside diameter is:

[A] [B][C] [D]

8)Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. Theratio of power which can be transmitted by shaft A to that of shaft B is

[A] [B][C] [D]

9)A steel shaft 'A' of diameter 'd' and length 'l' is subjected to a torque 'T' . Another shaft 'B' made ofaluminium of the same diameter 'd' and, length 0.5 l is also subjected to the same torque 'T'. The shearmodulus of steel is 2.5 times the shear modulus of aluminium. The shear stress in the steel shaft is 100MPa. The shear stress in the aluminium shaft, in MPa, is

Tortion



____________________________________________________________________________________________________________________ Pg.No.98









.

[A]40 [B]50[C]100 [D]250

10)A column has a rectangular cross-section of 10 mm x 20 mm and a length of 1m. The slenderness ratioof the column is close to

[A]200 [B]346[C]477 [D]1000

11)A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. Theshear modulus of the material of the rod is G. The expression for d to produce an angular twist at thefree end is

[A] [B][C] [D]

12)In . terms of theoretical stress concentration factor ( ) and fatigue stress concentration factor ( ), thennotch sensitivity 'q' is expressed is

[A] [B][C] [D]

13)A solid circular shaft of 60 mm diameter transmits a torque of 1600 N.m. The value of maximum shearstress developed is

[A]37.72 MPa [B]47.72 MPa[C]57.72 MPa [D]67.72 MPa

14)For a circular shaft of diameter d subjected to torque T, the maximum value of the shear stress is

[A] [B][C] [D]

15) The two shafts AB and BC, of equal length and diameters d and 2d, are made of the same material.They are joined at B through a shaft coupling, while the ends.A and C are built-in (cantilevered). A twistingmoment T is applied to the coupling. If and represent the twisting moments at the ends A and C,respectively, then

[A] = [B] = 8[C] = 16 [D] =16

Tortion



____________________________________________________________________________________________________________________ Pg.No.99


Key Paper

1. C 2. B 3. C 4. A 5. B

6. B 7. A 8. C 9. C 10. B

11. B 12. A 13. A 14. C 15. C

Tortion



____________________________________________________________________________________________________________________ Pg.No.100


.

.







A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the Figure. Assume = 200GPa.

1)fire beam is subjected to a maximum bending moment of

[A]3375 kNm [B]4750 kNm[C]6750 kNm [D]8750 kNm.

2)The value of maximum deflection of the beam is

[A]93.75 mm [B]83.75 mm[C]73.75 mm [D]63.75 mm.

3)A cantilever type gate hinged at Q is shown in the Figure. P and R are the centres of gravity of thecantilever part and the counterweight respectively. The mass of the cantilever part is 75 kg. The mass ofthe counterweight, for static balance, is

[A]75 kg [B]150 kg[C]225 kg [D]300 kg

4)Identify the correct deflection diagram corresponding to the loading in the plan e frame shown below:

[A] [B]

[C] [D]

5)The slope of the elastic curve at the free end of a cantilever beam of span L, and with flexural rigidity EI ,subjected to uniformly distributed load of intensity w is

Slopes & Deflection



____________________________________________________________________________________________________________________ Pg.No.101






[A] [B]

[C] [D]

6)A lean elastic beam of given flexural rigidity,.EI, is loaded by a single force F as show.n in Fig. How manyboundary conditions are necessary to determine thedeflected centre line of the beam ?

[A]5 [B]4[C]3 [D]2

7)A simply supported laterally loaded beam was found to deflect more than 4 specified value. Which of thefollowing measures will reduce the deflection ?

[A] Increase the area moment of inertia [B] Increase the span of the beam[C]Select a different material having lesser modulus

of elasticity [D]Magnitude of the load to be increased.

8)A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of thebeam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of themaximum deflection is

[A] [B]

[C] [D]

9)A frame of two arms of equal length L is shown in the adjacent figure. The flexural rigidity of each arm ofthe frame is EI. The vertical deflection at the point of application of load P is

[A] [B][C] [D]


Slopes & Deflection



____________________________________________________________________________________________________________________ Pg.No.102






.

10)Beam GHI is supported by these pontoons as shown in the figure below. the horizontal cross-sectionalarea of each pontoon is 8 , the flexural rigidity of the beam is 10000 kN- and the unit weight of water is1OkN-

When the middle pontoon is removed, the deflection at H will be

[A]0.2 m [B]0.4 m[C]0.6 m [D]0.8 m

11)When the middle pontoon is brought back to its position as shown in the figure above, the reaction at H willbe

[A]8.6 kN [B]15.7 kN[C]19.2 kN [D]24.2 kN


12)A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus ofthe material of the beam is E. A concentrated load P is applied at the free end of the beam.

Q. The area moment of inertia about the neutral axis of a cross-section at a distance x measured fromthe free end is

[A] [B][C] [D]

13) The maximum deflection of the beam is

[A] [B][C] [D]

Slopes & Deflection



____________________________________________________________________________________________________________________ Pg.No.103


Key Paper

1. A 2. A 3. D 4. D 5. A

6. D 7. A 8. A 9. D 10. B

11. C 12. B 13. D

Slopes & Deflection



____________________________________________________________________________________________________________________ Pg.No.104


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.









.

1)If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on allfaces of the cube is p, then the maximum shear stress developed inside the cube is

[A] [B][C] [D]

2)A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjectedto an internal pressure of 700 kPa. The hoop stress developed is

[A]14MPa [B]1.4MPa[C]0.14MPa [D]0.014MPa

3)A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure pand axial compressive force F at its ends. In order to produce 'pure shear' state of stress in the wall of thecylinder, F should be equal to

[A] [B][C] [D]

4)A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratioof the hoop stress (circumferential stress) to longitudinal stress developed in the shell is

[A]0.5 [B]1.0[C]2.0 [D]4.0

5)A thin walled cylindrical vessel of wall thickness t and diameter d is filled with gas to a gauge pressure of p.The maximum shear stress on the vessel wall will then be

[A]pd/t [B]pd/2t[C]pd/4t [D]pd/8t

6)A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentagechange in the circumferential (hoop) stress is

[A]0 [B]1[C]1.08 [D]1.02

7)A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa.The average circumferential (hoop) stress in MPa is

[A]100 [B]250[C]500 [D]1000

8)The strain energy stored in the beam with flexural rigidity .FL and loaded as shown in the Figure is

[A] [B]

[C] [D]

Thin cylinders



____________________________________________________________________________________________________________________ Pg.No.105


Key Paper

1. A 2. A 3. C 4. C 5. C

6. D 7. B 8. C

Thin cylinders



____________________________________________________________________________________________________________________ Pg.No.106


.

.








1)The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column withthe same dimensions and material, but with pinned ends, is equal to

[A]0.5 [B]1.0[C]2.0 [D]4.0

2)The effective length of a column of length L fixed against rotation and translation at one end and free at theother end is

[A]0.5 L [B]0.7 L[C]1.414 L [D]2 L

3)Two steel columns P (length L and yield strength ) and Q (length 2L and yield strength) have the same cross-sections and end-conditions. The ratio of buckling load of column P to

that of column Q is:

[A]0.5 [B]1.0[C]2.0 [D]4.0

4)The state of 2D-stress at a point is given by the following matrix of stresses:

What is the magnitude of maximum shear stress in MPa?

[A]50 [B]75[C]100 [D]110

5)The buckling load P = for the column AB m the figure, as approaches infinity, become , where isequal to

[A]0.25 [B]1.00[C]2.05 [D]4.00

6)Consider the following statements for a compression member :I. The elastic critical stress in compression increases with decrease in slenderness ratio.II. The effective length depends on the boundary conditions at its ends.II. The elastic critical stress in compression is independent of the slenderness ratio.IV. The ratio of the effective length to its radius of gyration is called as slenderness ratio.The TRUE statements are

[A] II and III [B] III and IV[C]II,III, and IV [D]I, II and IV

7)Cross-section of a column consisting of two steel strips, each of thickness t and width b is shown in thefigure below. The critical loads of the column with perfect bond and without bond between the strips are Pand Po respectively. The ration is

[A]2 [B]4[C]6 [D]8

Columns & Struts



____________________________________________________________________________________________________________________ Pg.No.107








8)A rigid bar GH of length L is supported by a hinge and a spring of stiffness K as shown in the figure below.The bu ckling load , for the bar will be

[A]0.5 KL [B]0.8 KL[C]1.0 KL [D]1.2 KL

9)A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained againstlateral movement at its mid-height, its buckling load will be

[A]200 kN [B]283 kN[C]400 kN [D]800 kN

10)A long structural column'(length = L) with both ends hinged is acted upon by an axial compressive load, P.The differential equation governing the bending of column is give by where y is thestructural lateral deflection and E1 is the flexural rigidity. The first critical load on column responsible for itsbuckling is given by

[A] [B][C] [D]

11)Four column of the same material and having identical geometric properties are supported in differentways as shown below :

It is required to order these four beams in the increasing order of their respective first buckling loads. Thecorrect ordr is given by

[A] I, II, III, IV [B] III, IV, I, II[C]II, I, IV, III [D]I, II, IV, III

12)Effective length of a rafter member between two nodes at a distance L, perpendicular to the plane of thetruss is

[A]2.00 L [B]0.85[C]1.50 [D]1.00 L

13)For the case of a slender column of length l and flexural rigidity EI built-in at its base and free at the top,the Euler's critical buckling load is

[A] [B]

[C] [D]

Columns & Struts



____________________________________________________________________________________________________________________ Pg.No.108








.

14)The buckling load for a column pinned at both ends is 10 kN. If the ends are fixed, the buckling loadchanges to

[A]40 kN [B]2.5 kN[C]5kN [D]20 kN

15)The ratio of Euler's buckling loads of columns with the same parameters having (i) both ends fixed, and (ii)both ends hinged is

[A]2 [B]4[C]6 [D]8

16)Two beams, one having square crosssection and another circular cross section, are subjected to the sameamount of bending moment. If the cross sectional area as well as the material of both the beams are thesame then

[A]maximum bending stress developed in both thebeams is the same

[B] the circular beam experiences more bendingstress than the square one

[C]the square beam experiences more bendingstress than the circular one

[D]as the material is same both the beams willexperience same deformation.

17)For a long slender column of uniform cross section, the ratio of critical buckling load for the case with bothends clamped to the case with both ends hinged is

[A]1 [B]2[C]4 [D]8

18)A pin-ended column of length L, modulus of elasticity E and second moment of the cross-sectional area Iis loaded centrically by a compressive load P. The critical buckling load ( ) is given by

[A] [B]

[C] [D]

19)The rod PQ of length L and with flexural rigidity EI is hinged at both ends. For what minimum force F is itexpected to buckle ? (See Figure)

[A] [B]

[C] [D]

Columns & Struts



____________________________________________________________________________________________________________________ Pg.No.109


Key Paper

1. D 2. C 3. D 4. A 5. D

6. D 7. B 8. C 9. D 10. A

11. D 12. B 13. D 14. A 15. B

16. B 17. C 18. D 19. B

Columns & Struts



____________________________________________________________________________________________________________________ Pg.No.110


.

.






1)The point within the cross sectional plane of a beam through which the resultant of the external loading onthe beam has to pass through to ensure pure bending without twisting of the cross-section of the beam iscalled

[A]moment center [B]shear center[C]centroid [D]elastic center

2)In the propped cantilever beam carrying a uniformly distributed load of w N/m, shown in the followingfigure, the reaction at the support B

[A] [B][C] [D]

3)The shape factor of the section shown in the figure 1 is

[A]1.5 [B]1.12[C]2 [D]1.7


4)In the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity EI and thesegment QR has infinite flexuaral rigidity.

The deflection and slope of the beam at ‘Q’ are respectively

[A] [B]

[C] [D]

5)The deflection of the beam at ‘R’ is

[A] [B]

[C] [D]


Propped & Fixed beams



____________________________________________________________________________________________________________________ Pg.No.111




.

6)Consider a propped cantilever beam ABC under two loads of magnitude P each as shown in the figurebelow. Flexural rigidity of the beam is EI.

The reaction at C is

[A] [B][C] [D]

7)The rotation at B is

[A] [B][C] [D]




____________________________________________________________________________________________________________________ Pg.No.112


Key Paper

1. C 2. B 3. C 4. A 5. C

6. C 7. A




____________________________________________________________________________________________________________________ Pg.No.113


.

.






.

1) and are the strain energies stored in a prismatic bar due to axial tensile forces and respectively.The strain energy stored in the same bar due to combined action of and will be

[A] [B][C] [D]

2) is the deflection under the load P of a cantilever beam [length L, modulus of elasticity E, moment ofinertia I]. The strain energy due to bending is

[A] [B]

[C] [D]

3)A square bar ofside 4 cm and length 100 cm is subjected to an axial load P. The same bar is then used asa cantilever beam and subjected to an end load P. The ratio of the strain energies, stored in the bar in thesecond case to that stored in the first case is

[A]16 [B]400[C]1000 [D]2500

4)For a ductile material, toughness is a measure of

[A] resistance to scratching [B]ability to absorb energy up to fracture[C]ability to absorb energy till elastic limit [D]resistance to indentation

5)For a mechanism shown below, the mechanical advantage for the given configuration is

[A]0 [B]0.5[C]1.0 [D]

Strain energy



____________________________________________________________________________________________________________________ Pg.No.114


Key Paper

1. D 2. B 3. D 4. B 5. D

Strain energy



____________________________________________________________________________________________________________________ Pg.No.115


.

.







Two steel truss members, AC and BC, each having cross sectional area of 100 m , are subjected to ahorizontal force F as shown in figure. All the joints are hinged.

1)If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is

[A]0.63 [B]0.32[C]1.26 [D]1.46

2)The maximum force F in kN that can be applied at C such that the axial stress in any of the truss membersDOES NOT exceed 100 MPa is

[A]8.17 [B]11.15[C]14.14 [D]22.30


A reel of mass "m" and radius of gyration "k" is rolling down smoothly from rest with one end of the threadwound on it held in the ceiling as depicted iu the Fig. Consider the thickness of the thread and its massnegligible in comparison with the radius "r" of the hub and the reel mass "m". Symbol "g" represents theacceleration due to gravity.

3)The linear acceleration of the reel is

[A] [B]

[C] [D]

4)The tension in the thread is

[A] [B]

[C] [D]

5)A shell is fired from a cannon with a speed v at an angle with the horizontal direction. At the highestpoint in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to thecannon. The speed of other piece immediately after explosion is

[A] [B][C] [D]

Engineering Mechanics



____________________________________________________________________________________________________________________ Pg.No.116







6)A wheel of mass m and, radius r is in accelerated rolling motion without slip under a steady axle torque T.If the coefficient of kinetic friction is , the friction force from the ground on the wheel is

[A] [B][C]zero [D]none of the above

7)A ball falls from a height of 1m, hits the ground and rebounds with half its velocity just before impact. Thenafter rising it falls and hits the ground and again rebounds with half its velocity just before impact, and soon. The total distance travelled by the ball till it comes to rest on the ground is

[A]2 m [B]5/3 m[C]2/3 m [D]5/4 m

8)A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficientof rolling resistance is 0.3. The force in N, necessary to roll the wheel along the rail is

[A]0.5 [B]5[C]15 [D]150

9)An automobile of weight W is shown in Fig. 2. A pull'P is applied as shown. The reaction at the frontwheels (location A) is

[A]W/2 - pb/2a [B]W/2 + pb/2a[C]W/2 - pa/2b [D]W/2

10)For the loading on truss shown in the Fig. the force in member CD is

[A]0 kN [B]1 kN[C] [D]

11)Bodies 1 and 2 shown in the Fig. have equal mass m. All surfaces are smooth. The value of force Prequired to prevent sliding of body 2 on body 1. is




____________________________________________________________________________________________________________________ Pg.No.117







[A]p = 2mg [B][C] [D]p = mg

12)A truss consists of horizontal members (AC, CD, DB and EF) and vertical members (CE and DE) havinglength l each. The members AE, DE and BF are inclined at to the horizontal. For the uniformlydistributed load P per unit length on the member EF of the truss shown in Figure given below, the force inthe member CD is

[A] [B]pl[C]0 [D]

13)A bullet of mass "m" travels at a very high velocity v (as shown in the Figure) and gets embedded insidethe block of mass "If initially at rest on a rough horizontal floor. The block with the bullet is seen to move adistance "s" along the floor. Assuming to be the coefficient of kinetic friction between the block and thefloor and "g" the acceleration due to gravity what is the velocity u of the bullet ?

[A] [B][C] [D]

14)The coefficient of restitution of a perfectly plastic impact is

[A]0 [B]1[C]2 [D]

15)A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force Fx (in N) exerted by therubber band as a function of distance x (in m) is given by .If the stone is displaced by 0.1 mfrom the on-stretched position (x = 0) of the rubber band , the energy stored in the rubber band is

[A]0.01 J [B]0.1 J[C]1 J [D]10 J




____________________________________________________________________________________________________________________ Pg.No.118






16)A block weighing 981N is resting on a horizontal surface. The coefficient of friction between the block andthe horizontal surface is = 0.2A vertical cable attached to the block provides partial support as shown. Aman can pull horizontally with a force of 100N. What will be the tension, T (in N) in the cable if the man isjust able to move the block to the right?

[A]176.2 [B]196.0[C]481.0 [D]981.0

17)A 1 kg block is resting on a surface with coefficient of friction force of 0.8 N is applied to the blockas shown in the figure. The friction force is

[A]0 [B]0.8 N[C]0.98 kN [D]1.2 N

18)The Figure shows a pin-jointed plane truss loaded at the point M by hanging a mass of 100 kg. Themember LN of the truss is subjected to a load of

[A]0 Newton [B]490 Newtons in compression[C]981 Newtons in compression [D]981 Newtons in tension.

19)The Figure shows a pair of pin-jointed gripper-tongs holding an object weighing 2000 N. The co-efficient offriction ( ) at the gripping surface is 0.1XX is the line of action of the input force and YY is the line ofapplication of gripping force. If the pin-joint is assumed to be frictionless, then magnitude of force Frequired to hold the weight is

[A]1000 N [B]2000 N[C]2500 N [D]5000 N




____________________________________________________________________________________________________________________ Pg.No.119






20)Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on everypair of contacting surfaces is 0.3. The lower book is pulled with a horizontal force F. The minimum value ofF for which slip occurs between the two books is

[A]zero [B]1.06N[C]5.74 N [D]8.83 N

21)An elevator (lift) shown in Fig. consists of the elevator cage and a counter weight, of mass m each. Thecage and the counter weight are connected by a chain that passes over a pulley. The pulley is coupled toa motor. It is desired that the elevator should have a maximum stopping time of f seconds from a peakspeed v. If the inertias of the pulley and the chain are neglected, the minimum power that the motor musthave is

[A] [B][C] [D]

22)If point A is in equilibrium under the action of the applied forces, the values of tension T* and fo" arerespectively (Figure)

[A]520 N and 300 N [B]300 N and 520 N[C]450 N and 150 N [D]150 N and 450 N

23)A straight rod of length L(t), hinged at one end and freely extensible at the other end, rotates through anangle (t) about the hinge. At time t, L(t) = 1 m, (t) = 1 m/s, rad and rad/s. The magnitude ofthe velocity at the other end of the rod is

[A]1 m/s [B] m/s[C] m/s [D]2 m/s

24)Consider a truss PQE loaded at P with a force F as shown in the Figure. The tension in the member QB is




____________________________________________________________________________________________________________________ Pg.No.120






.

[A]0.5 F [B]0.63 F[C]0.73 F [D]0.87 F

25)During inelastic collision of two particles, which one of the following is conserved ?

[A] total Iinear momentum only [B] total kinetic energy only[C]both linear momentum and kinetic energy [D]neither linear momentum nor kinetic energy.

26)A block of mass M is released from point P on a rough inclined plane with inclination angle , shown in theFig. 3 below. The co-efficient of friction is . If then the time taken by the block to reach anotherpoint Q on the inclined plane, where PQ = s, is

[A] [B][C] [D]

27)A mass m1 of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary massm2 of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficientof restitution is

[A]0.6 [B]0.1[C]0.01 [D]0




____________________________________________________________________________________________________________________ Pg.No.121


Key Paper

1. A 2. B 3. A 4. C 5. A

6. A 7. B 8. D 9. C 10. A

11. D 12. A 13. A 14. A 15. B

16. C 17. B 18. A 19. D 20. D

21. C 22. A 23. B 24. B 25. A

26. A 27. D




____________________________________________________________________________________________________________________ Pg.No.122






Index- Thermodynamics

Sl.No. Name of the Topic Pg.No.s 1. Zeroth Law & Basics Concepts 124-125 2. Work/Heat 126-128 3. 1st Law of Thermodynamics 129-132 4. 2nd Law Of Thermodynamics 133-135 5. Entropy 136-139 6. Properties of Pure Substance 140-141 7. Availability 142-143 8. Air Cycles 144-148 9. Psychrometry 149-152 10. Rankine Cycle 153-157 11. Gas Turbines 158-160 12. Refrigeration 161-163 13. Internal Combustion Engines 164-167









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1)The definition of 1 K as per the internationally accepted temperature scale is

[A] th times the difference between normal boilingpoint and normal freezing point of water. [B] th times the normal freezing point of water.

[C]100 times the difference between the triple pointof water and the normal freezing point of water [D] th of the triple point of water

2)The specifrc heats of an ideal gas depend on its

[A] temperature [B]pressure[C]volume [D]molecular weight and structure

3)For a given heat flow and for the same thickness, the temperature drop across the material will bemaximum for

[A]copper [B]steel[C]glass-wool [D]refractory brick

4)An isolated thermodynamic system executes a process. Choose the correct statement (s) from thefollowing

[A]No heat is transferred [B]No work is done[C]No mass flows across the boundary of the

system[D]No chemical reaction takes place with in the

system5)Match items from groups I, II, III, IV and V.

[A]F-G-J-K-ME-G-J-K-N

[B]E-G-I-K-MF-H-I-K-N

[C]F-H-J-L-NE-H-I-L-M

[D]E-G-J-K-NF-H-J-K-M


6)A football was inflated to a gauge pressure of 1 bar when the ambient temperature was C.When the game started next day, the air temperature at the stadium was C.Assume that the volume of the football remains constant at 2500 c .

The amount of heat lost by the air in the football and the gauge pressure of air in the football at thestadium respectively equal

[A]30.6 J, 1.94 bar [B]21.8 J, 0.93 bar[C]61.1 J, 1.94 bar [D]43.7 J, 0.93 bar

7)Gauge pressure of air to which the ball must have been originally inflated so that it would equal 1 bargauge at the stadium is

[A]2.23 bar [B]1.94 bar[C]1.07 bar [D]1.00 bar

Zeroth law/basic concepts



____________________________________________________________________________________________________________________ Pg.No.124


Key Paper

1. D 2. D 3. C 4. A 5. D

6. D 7. C

Zeroth law/basic concepts



____________________________________________________________________________________________________________________ Pg.No.125


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Nitrogen gas (molecular weight 28) is enclosed in a cylinder by a piston, at the initial condition of 2bar 298K and . In a particular process, the gas slowly expands under isothermal condition, until the volumebecomes . Heat exchange occurs with the atmosphere at 298 K during this process.

1)The work interaction for the Nitrogen gas is

[A]200 kJ [B]138.6 kJ[C]2 kJ [D]-200 kJ

2)The entropy change for the Universe during the process in kJ/K is

[A]0.4652 [B]0.0067[C]0 [D]-0.6711

3)A mono-atomic ideal gas(y = 1.67, molecular weight = 40)is compressed adiabatically from 0.1 MPa, 300K to 0.2 MPa. The universal gas constant is 8.314 kJ kmo . The work of compression of the gas (inkJ k ) is

[A]29.7 [B]19.9[C]13.3 [D]0

4) Heat and work are

[A] intensive properties[B]extensive properties

[C]point functions [D] path functions5)The contents of a well-insulated tank are heated by a resistor of 23 Q in which 10 A current is flowing.

Consider the tank along with its contents as a thermodynamic system. The work done by the system andthe heat transfer to the system are positive. The rates of heat (Q), work (W) and change in internalenergy during the process in kW are

[A]Q = 0 , w = -2.3 , = +2.3 [B]Q = +2.3 , w = 0 , = +2.3[C]Q = -2.3 , w = 0 , = -2.3 [D]Q = 0 , w = +2.3 , = -2.3

6)A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressoris designated as state 1 and state 2 respectively. Potential and kinetic energy changes are to be ignored.The following notations are used:v= specific volume and P=pressure of the gas.The specific work required to be supplied to the compressor for this gas compression process is

[A] [B]

[C] [D]7)In a condenser, water enters at C and flows at the rate 1500 kg/hr. The condensing steam is at a

temperature of C and cooling water leaves the condenser at C. Specific heat of water is 4.187 kJ/kgK. If the overall heat transfer coefficient is 2000 W/ K , then heat transfer area is

[A]0.707 [B]7.07 [C]70.7 [D]141.4

8)Nitrogen at an initial state of 10 bar, and 300 K is expanded isothermally to a final volume of . The p-v-T relation is ,Where a >o.The final pressure.

[A]will be slightly less than 5 bar [B]will be slightly more than 5 bar

[C]will be exactly 5 bar [D]cannot be ascertained in the absence of thevalue of a.

Work / Heat



____________________________________________________________________________________________________________________ Pg.No.126




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9)In a steady state steady flow process taking place in a device with a single inlet and a single outlet, the

work done per unit mass flow rate is given by where is the specific volume and p is thepressure. The expression for given above

[A] is valid only if the process is both reversible andadiabatic

[B] is valid only if the process is both reversible andisothermal

[C]is valid for any reversible process [D]is incorrect ; it must be10)A cylinder contains 5 of an ideal gas at a pressure of 1 bar. This gas is compressed in a reversible

isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is

[A]804.7 [B]953.2[C]981.7 [D]1012.2

Work / Heat



____________________________________________________________________________________________________________________ Pg.No.127


Key Paper

1. B 2. A 3. A 4. D 5. A

6. B 7. A 8. B 9. C 10. A

Work / Heat



____________________________________________________________________________________________________________________ Pg.No.128


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1)For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is

[A] [B][C] [D]

2)Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, areas given below:

Specific enthalpy (kJ/kg) Velocity (m/s)Inlet steam condition 3250 180Exit steam condition 2360 5The rate of heat loss from the turbine per kg of steam flow rate is 5 kW. Neglecting changes in potentialenergy of steam, the power developed in kW by the steam turbine per kg of steam flow rate, is

[A]901.2 [B]911.2[C]17072.5 [D]17082.5

3)A steam turbine receives steam steadily at 10 bar with an enthalpy of 3000 kJ/kg and discharges at 1 barwith an enthalpy of 2700 kJ/kg. The work output is 250 kJ/ kg. The changes in kinetic and potentialenergies are negligible. The heat transfer from the turbine casing to the surroundings is equal to

[A]0 kJ [B]50 kj[C]150 kJ [D]250 kJ

4)When an ideal gas with constant specific heats is throttled adiabatically, with negligible changes in kineticand potential energieswhere h, T and. S represent respectively, enthalpy, temperature and entropy.

[A] = 0, = 0 [B] >0 , = 0[C] >0, >0 [D] = 0, >0

5)A small steam whistle (perfectly insulated and doing no shaft wbrk) causes a drop of 0.8 kJ/g in theenthalpy of steam from entry to exit. If the kinetic energy of the steam at entry is negligible, the velocity ofthe steam at exit is

[A]4 m/s [B]40 m/s[C]80 m/s [D]120m/s

6)A 2 kW, 40 litre water heater is switched on for 20 minutes. The heat capacity for water is 4.2 kJ/kg K.Assuming all the electrical energy has gone into heating the water, increase of the water temperature indegree centrgrade is

[A]2.7 [B]4.0[C]14.3 [D]25.25

7)The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 2800kJ/kg and 1800 kJ/kg respectively. Neglecting pump work, the specific steam consumption in kg/kW -houris

[A]3.60 [B]0.36[C]0.06 [D]0.01

8)A frictionless piston-cylinder device contains a gas initially at 0.8MPa and 0.015 . It expands quasi-statically at constant temperature to a final volume of 0.030 . The work output (in kJ) during this processwill be

[A]8.32 [B]12.00[C]554.67 [D]8320.00

9)A gas contained in a cylinder is compressed, the work required for compression being 5000 kJ. During theprocess, heat interaction of 2000 kJ causes the surroundings to the heated. The change in internal energyof the gas during the process is

[A] -7000 kJ [B] -3000 kJ[C]+3000 kJ [D]+7000 kJ

1st law of thermodynamics



____________________________________________________________________________________________________________________ Pg.No.129






10)A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon rupturesand the gas fills up the entire room. Which one of the following statements is TRUE at the end of aboveprocess ?

[A]The internal energy of the gas decreases from itsinitial value, but the enthalpy remains constant

[B]The internal energy of the gas increases from itsinitial value, but the enthalpy remains constant

[C]Both internal energy and enthalpy of the gasremain constant

[D]Both internal energy and enthalpy of the gasincrease.

11)A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air(assumed to be ideal gas with constant specific heats) passes at 1 MPa, C. A value connected withthe supply line is opened and the tank is charged with air until the final pressure inside the tank reaches 1MPa. The final temperature inside the tank (Figure)

[A] is greater than C [B] is less than C

[C]is equal to C [D]may be greater than, less than, or equal to C,depending on the volume of the tank.


12)Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPawith a velocity of 180 m/s. The inlet area is 80 c . The specific heat of air is 1008 J/kg.K.

Q. T he exit temperature of the air is

[A]516 K [B]532 K[C]484 K [D]468 K

13)Air enters an adiabatic nozzle at 300 kPa, 500 K with a velocity of 10 m/s. It leaves the nozzle at 100 kPawith a velocity of 180 m/s. The inlet area is 80 c . The specific heat of air is 1008 J/kg.K.

The exit area of the nozzle in c is

[A]90.1 [B]56.3[C]4.4 [D]12.9





____________________________________________________________________________________________________________________ Pg.No.130




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14)The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A convergingdiverging nozzle of exit area is fitted to the wall of the reservoir as shown in the figure. The staticpressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gasconstant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively .

Q. The density of air in at the nozzle exit is

[A]0.560 [B]0.600[C]0.727 [D]0.800

15)Q.The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A convergingdiverging nozzle of exit area is fitted to the wall of the reservoir as shown in the figure. The staticpressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gasconstant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively .

The mass flow rate of air through the nozzle in kg/s is

[A]1.30 [B]1.77[C]1.85 [D]2.06




____________________________________________________________________________________________________________________ Pg.No.131


Key Paper

1. B 2. A 3. B 4. A 5. B

6. C 7. A 8. A 9. C 10. C

11. A 12. C 13. D 14. C 15. D




____________________________________________________________________________________________________________________ Pg.No.132


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1)A condenser of a refrigeration system rejects heat at a rate f 120kW,while its compressor consumes apower of 30 kW. The coefficient of performance of the system would be:

[A] [B]4[C] [D]3

2)Round the clock cooling of an apartment having a load of 300 MT/day requires an air-conditioning plant ofcapacity about

[A]1 ton [B]5 tons[C]10 tons [D]100 tons

3)Consider a refrigerator and a heat pump working on the reversed Carnot cycle between the sametemperature limits. Which of the following is correct.(o)

[A]COP of refrigerator = COP of heat pump [B]COP of refrigerator = COP of heat pump + L[C]COP of refrigerator = COP of heat pump - 1 [D]COP of refrigerator = inverse COP of heat pump.

4)A solar energy based heat engine which receives 80 kJ of heat at 100 degree C and rejects 70 kJ of heatto the ambient at 30 degree C is to be designed. The thermal efficiency of the heat engine is

[A]70% [B]1.88%[C]12.5% [D]indeterminate

5)For two cycles coupled in series, the topping cycle has an efficiency of 30% and, the bottoming cycle hasan effrciency of 20%. The overall combined cycle efficiency is

[A]50% [B]44%[C]38% [D]55%

6)A Stirling cycle and a Carnot cycle operate between and . Their efficiencies are and respectively. In this case which of the following statements is true ?

[A] [B]

[C] [D]The sign of depends on the working fluidsused.

7)A Carnot cycle refrigerator operates between 250 K and 300 K. Its coefficient of performance is

[A]6.0 [B]5.0[C]1.2 [D]0.8

8)A cyclic heat engine does 50 kJ of work per cycle. If the efficiency of the heat engine is 75% the heatrejected per cycle is

[A] [B][C] [D]

9)A Carnot cycle is having an efficiency of 0.75. If the temperature of the high temperature reservoir is ,what is the temperature of low temperature reservoir ?

[A] [B][C] [D]

10)An industrial heat pump operates between the temperatures of and - . The rates of heat additionand heat rejection are 750 W and 1000 W, respectively. The COP for the heat pump is

[A]7.5 [B]6.5[C]4.0 [D]3.0

11)Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and leaves asa saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the saturated liquid andvapor at 15 kPa are = 225.94 kJ/kg and = 2598.3 kJ/kg respectively. The mass flow rate of steam is 10kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine in MW is

2nd law of thermodynamics



____________________________________________________________________________________________________________________ Pg.No.133








.

[A]6.5 [B]8.9[C]9.1 [D]27.0

12)An irreversible heat engine extracts heat from a high temperature source at a rate of 100kW and rejectsheat to a sink at a rate of 50kW. The entire work output of the heat engine is used to drive a reversibleheat pump operating between a set of independent isothermal heat reservoirs at and . The rate (inkW) at which the heat pump delivers heat to its high temperature sink is

[A]50 [B]250[C]300 [D]360

13)A heat engine having an efficiency of 70% is used to drive a refrigerator having a coefficient ofperformance of 5. The energy absorbed from low temperature reservoir by the refrigerator for each kJ ofenergy absorbed from high temperature source by the engine is

[A]0.14 kJ [B]0.71 kJ[C]3.5 kJ [D]7.1 kJ

14)A solar collector receiving solar radiation at the rate of 0.6 kW/ transforms it to the internal energy of afluid at an overall efficiency of 50%. The fluid heated to 350 K is used to run a heat engine which rejectsheat at 313 K If the heat engine is to deliver 2.5 kW power, then minimum area of the solar collectorrequired would be

[A]8.33 [B]16.66 [C]39.68 [D]79.36

15)The following four figures shown in Fig. have been drawn to represent a fictitious thermod5mamic cycle,on the p-v and T-s planes.

According to the first law of thermodynamics, equal areas are enclosed by

[A] figures 1 and 2 [B] figures 1 and 3[C]figures 1 and 4 [D]figures 2 and 3

16)A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediatetemperature, to a high temperature reservoir while rejecting the remaining part to a low temperature heatsink. In such a heat transformer, 100 kJ of heat is supplied at 350 K. The maximum amount of heat in kJthat can be transferred to 400 K, when the rest is rejected to a heat sink at 300 K is

[A]12.50 [B]14.29[C]33.33 [D]57.14




____________________________________________________________________________________________________________________ Pg.No.134


Key Paper

1. D 2. A 3. C 4. C 5. B

6. C 7. B 8. A 9. B 10. C

11. B 12. C 13. C 14. D 15. A

16. D




____________________________________________________________________________________________________________________ Pg.No.135


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. 2 Marks GATE-ME-2008,GATE-ME-2008,GATE-ME-2008( )



Common Data for Q1 Q2 and Q3 is given below

In the Figure shown, the system is a pure substance kept in a piston-cylinder arrangement. The system isinitially a two-phase mixture containing 1 kg of liquid and 0.03 kg of vapour at a pressure of 100 kPa.Initially, the pieton rests on a eet of stops, as shown in the figure. A pressure of 200 kPa is required toexactly balance the weight of the piston and the outside atmospheric pressure. Heat transfer takes placeinto the system until its volume increases by 50%. Heat transfer to the system occurs in each a mannerthat the piston, when allowed to move, does so in a very slow (quasi. static/quasi-equilibrium) process.The thermal reservoir from which heat is transferred to the system has a temperature of C. Averagetemperature of the system boundary can be taken as C. The heat transfer to the system is 1 kJ, duringwhich its entropy increases by 10 J/K

Specific volume of liquid ( ) and vapour ( ) phases, as well as values of saturation temperatures, aregiven in the table below.

1)At the end of the process, which one of the following situations will be true ?

[A]superheated vapour will be left in the system [B]no vapour will be left in the system

[C]a liquid + vapour mixture will be left in the system [D]the mixture will exist at a dry saturate vapourstate.

2)The work done by the system during the process is

[A] 0.1 kJ [B]0.2 kJ[C]0.3 kJ [D]0.4 kJ

3)The net entropy generation (considering the system and the thermal reservoir together) during the processis closest to

[A]7.5 J/K [B]7.7 J/K[C]8.5 J/K [D]10 J/K


In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flowdepends on the pressure and temperature conditions maintained at P and Q. The conditions at stationPare 150 kPa and 350 K. The temperature at station Q is 300 K.The following are the properties andrelations pertaining to air:Specific heat at constant pressure, Specific heat at constant volume , ;Characteristic gas constant, R = 0.287 kJ/kgK.Enthalpy, .Internal energy, .

Entropy



____________________________________________________________________________________________________________________ Pg.No.136







4)If the air has to flow from station P to station Q, the maximum possible value of pressure in kPa at stationQ is close to

[A]50 [B]87[C]128 [D]150

5)If the pressure at station Q is 50 kPa, the change in entropy in kJ/kgK is

[A] -0.155 [B]0[C]0.160 [D]0.355

6)A vapour absorption refrigeration system is a heat pump with three thermal reservoirs as shown in the Fig.A refrigeration effect of 100 W is required at 250 K when the heat source available is at 400 K Heatrejection occurs at 300 K The minimum value of heat required (in W) is

[A]167 [B]100[C]80 [D]20

7)2 moles of oxygen are mixed adiabatically with another 2 moles of oxygen in mixing chamber, so that thefinal total pressure and temperature of the mixture become same as those of the individual constituents attheir initial states. The universal gas constant is given as R. The change in entropy due to mixing, per moleof oxygen, is given by

[A] - R in 2 [B]0[C]R in 2 [D]R in 4

8)A cyclic device operates between three thermal reservoirs, as shown in the Figure. Heat is transferredto/from the cyclic device. It is assumed that heat transfer between each thermal reservoir and the cyclicdevice takes place across negligible temperature difference. Interactions between the cyclic device andthe respective thermal reservoirs that are shown in the figure are all in the form of heat transfer.

The cyclic device can be

[A]a reversible heat engine [B]a reversible heat pump or a reversible refrigerator

[C]an irreversible heat engine [D]an irreversible heat pump or an irreversiblerefrigerator.

9)Which combination of the following statements is correct ?P: A gas cools upon expansion only when its Joule-Thomson co-efficient is positive in the temperaturerange of expansion.Q: For a system undergoing a process, its entropy remains constant only when the process is reversible.R:The work done by a closed system in an adiabatic process is a point function. S:A liquid expands upon freezing when the slope of its fusion curve on Pressure-Temperature diagram isnegative

Entropy



____________________________________________________________________________________________________________________ Pg.No.137












[A]R and S [B]P and Q[C]Q,R and S [D]P,Q and R

10)Constant pressure lines in the superheated region of the Mollier diagram will have a

[A]a positive slope [B]a negative slope[C]zero slope [D]both positive and negative slope

11)One kilomole of an ideal gas is throttled from an initial pressure of 0.5 MPa to 0.1 MPa. The initialtemperature is 300 K. The entropy change of the universe is

[A]13.38 kJ/K [B]401.3 kJ/K[C]0.0446 kJ/K [D]- 0.0446 kJ/K

12)For an ideal gas the expression

is always equal to

[A]zero [B][C]R [D]RT

13)A system undergoes a state change from 1 to 2. According to the second law of thermodynamics for theprocess to be feasible, the entropy change, of the system

[A] is positive or zero [B] is negative or zero[C]is zero [D]can be positive, negative or zero.

14)Considering the relationship TdS = dU + pdV between the entropy (S), internal energy (U), pressure (p),temperature (T) and volume (V), which of the following statements is correct ?

[A] It is applicable only for a reversible process [B]For an irreversible process, TdS >dU + pdV[C]It is valid only for an ideal gas [D]It is equivalent to 1 law, for a reversible process.

15)One kilogram of water at room temperature is brought into contact with a high temperature thermalreservoir. The entropy change of the universe is

[A]equal to entropy change of the reservoir. [B]equal to entropy change of water.[C]equal to zero. [D]always positive.

16)Consider the following two processes : I. A heat source at 1200 K loses 2500 kJ of heat to asink at 800 KII. A heat source at 800 K loses 2000 kJ of heat to a sink at 500 KWhich of the following statements is true?

[A]Process I s more irreversible than Process II [B]Process II is more irreversible than Process I[C]Irreversibility associated in both the processes

are equal [D]Both the processes are reversible.

17)An ideal gas of mass m and temperature undergoes a reversible isothermal process from an initialpressure to final pressure . The heat loss during the process is Q. The entropy change of the gas is

[A] [B]

[C] [D]zero

18)If a closed system is undergoing an irreversible process, the entropy of the system

[A]Must increase [B]Always remains constant[C]Must decrease [D]Can increase, decrease or remain constant

Entropy



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Key Paper

1. A 2. B 3. D 4. B 5. C

6. C 7. B 8. A 9. C 10. A

11. A 12. C 13. D 14. D 15. D

16. B 17. B 18. D

Entropy



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1)Water has a critical specific volume of . A closed and rigid steel tank of volume containsa mixture of water and steam at 0.1 MPa. fire mass of the mixture is 10 kg. The tank is now slowly heated.The liquid level inside the tank

[A]will rise [B]will fall

[C]will remain constant [D]may rise or fall depending on the amount of heattransferred.


2)The following table of properties was printed out for saturated liquid and saturated vapour of ammonia.The titles for only the first two columns are available. All that we know is that the other columns (columns 3to 8) contain data on specific properties, namely, internal energy (kJ/kg), enthalpy (kJ/kg) and entropy(kJ/kg.K).

The specific enthalpy data are in columns


3)When saturated liquid at is throttled to the quality at exit will be

[A]0.189 [B]0.212[C]0.231 [D]0.788

Properties of pure substance



____________________________________________________________________________________________________________________ Pg.No.140


Key Paper

1. A 2. D 3. B

Properties of pure substance



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In two air standard cycles-oue operating on the Otto and the other on the Brayton cycle- air isisentropically compressed from 300 to 450 k. Heat is added to raise the temperature to 600 K in the Ottocycle and to 550k in the Brayton cycle.

1)If and are the efficiencies of the Otto an Brayton cycles, then

[A] = 0.25 , = 0.18 [B] = = 0.33

[C] = 0.5 , = 0.45[D]it is not possible to calculate the efficiencies

unless the temperature after the expansion isgiven

2)If and are work outputs per unit mass,then

[A] > [B] <

[C] = [D]it is not possible to calculate the work outputsunless the temperature after expansion is given.

3)A gas expands in a frictionless pistoncylinder arrangement. The expansion process is very slow, and isresisted by an ambient pressure of 100 kPa. During the expansion process, the pressure of the system(gas) remains constant at 300 kPa. The change in volume of the gas is 0.01 . The maximum amount ofwork that could be utilized from the above process is

[A]0 kJ [B]1 kJ[C]2 kJ [D]3 kJ

4)A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During thisperiod 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process rs

[A]18000 KJ [B]9000 KJ[C]6000 KJ [D]None of the above

5)The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s, respectively.The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK,respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and300 K, respectively, the available energy in kJ/kg of the air stream is

[A]170 [B]187[C]191 [D]213

6)Availability ofa system at any given state is

[A]a property of the system [B] the maximum work obtainable as the systemgoes to dead state

[C]the total energy of the system [D]the maximum useful work obtainable as thesystem goes to dead state.

7)A steel billet of 2000 kg mass is to be cooled from 1250 K to 450 K. The heat released during this processis to be used as a source of energy. The ambient temperature is 303 K and specific heat of steel is 0.5kJ/kg K. The available energy of this billet is

[A]490.44 MJ [B]30.95 MJ[C]10.35 MJ [D]0.10 MJ

Availability



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Key Paper

1. B 2. A 3. C 4. D 5. B

6. D 7. A

Availability



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A thermodynamic cycle with an ideal gas as working fluid is shown below

1)The above cycle is represented on T-S plane by

[A] [B]

[C] [D]

2)lf the specific heats of the working fluid are constant and the value of specific heat ratio is 1.4, thethermal efficiency (%) of the cycle is

[A]21 [B]40.9[C]42.6 [D]59.7

3)Consider a two stage reciprocating air compressor with a perfect intercooler operating at the bestintermediate pressure. Air enters the low pressure cylinder at 1 bar, and leaves the high pressurecylinder at 9 bar. Assume the index of compression and expansion in each stage is 1.4, and that for air R= 286.7 J/kg K, the work done per kg air in the high pressure cylinder is

[A]111 kJ [B]222 kJ[C]37 kJ [D]74 kJ

4)Air enters a compressor at a temperature of . The compressor pressure ratio is 4. Assuming anefficiency of 8O%, the compressor work required in kJ/kg is

[A]160 [B]172[C]182 [D]225

5)Pertaining to a steam boiler, pick the correct statement among the following

[A]Primary boiler heat surfaces include evaporatorsection, economizer and air preheater

[B]Primary boiler heat transfer surfaces includeevaporator section, super heater section andeconomizer

[C]Secondary boiler heat transfer surfaces includesuper heater, economizer and air preheater

[D]Primary boiler heat transfer surfaces includeevaporator section, super heater section andreheat section.

6)Which of the following statements does not apply to the volumetric efficiency of a reciprocating aircompressor ?

Air cycles



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[A] It decreases with increase in inlet temperature [B] It increases with decrease in pressure ratio

[C]It increases with decrease in clearance ratio [D]It decreases with increases in clearance to strokeratio.

7)Consider air standard Otto and Diesel cycles, both having the same state of air at the start of compression.If the maximum pressure in both the cycles is the same, then compression ratio 'r'and the efficiency' ' arerelated by

[A] [B][C] [D]

8)A fuel represented by the formula is used in an I.C. Engine. Given that the molecular weight of air is29 and that 4.76 kmols of air contain 1 kmol of oxygen and 3.76 kmols of nitrogen, the Air/Fuel ratio bymass is

[A]11.47 [B]12.78[C]14.79 [D]19.52

9)For the following "Matching' exercise, choose the correct one from among the alternatives A, B, C and DGroup I Group 21. Marine Diesel Engine (A) Two stroke engine2. Air conditioning (B) Four stroke engine3. Steam Power Plant (C) Rotary engine4. Gas Turbine Power Plant (D) Cooling and dehumidifrcation

(E) Cooling tower(F) Brayton cycle

(G) Rankine cycle(F)D-slide valve

[A]1-B, 2-E, 3-F, 4-H [B]1-C, 2-F, 3-E, 4-G[C]1-C, 2-F,3-G, 4-E [D]1-A, 2-D, 3-G, 4-F

10)A single-acting two-stage compressor with complete intercooling delivers air at 16 bar. Assuming an intakestate of 1 bar at the pressure ratio per stage is

[A]16 [B]8[C]4 [D]2

11)An ideal air standard Otto cycle has a compression ratio of 8.5. If the ratio of the specific heats of ( ) is1.4, then what is the thermal efficiency (in percentage) of the Otto cycle ?

[A]57.5 [B]45.7[C]52.5 [D]95

12)In a spark ignition engine working on the ideal Otto cycle, the compression ratio is 5.5. The work outputper cycle (i.e., area of the P-V diagram) is equal to where is the clearance volume in m3.The indicated mean effective pressure is


13)For an engine operating on air standard Otto cycle, the clearance volume is 10% of the swept volume. Thespecific heat ratio of air is 1.4. The air standard cycle efficiency is

[A]38.3% [B]39.8%[C]60.2% [D]61.7%

14)A turbo-charged four-stroke direct injection diesel engine has a displacement volume of 0.0259 (25.9litres). The engine has an output of 950 kW at 2200 rpm.The mean effective pressure (in MPa) is closestto

[A]2 [B]1[C]0.2 [D]0.1

Air cycles



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15)In an air-standard Otto cycle, the compression ratio is 10. The condition at the beginning of thecompression process is 100kPa and . Heat added at constant volume is 1500kJ/kg, while 700kJ/kg ofheat is rejected during the other constant volume process in the cycle. Specific gas constant for air=0.287kJ/kgK. The mean effective pressure (in kPa) of the cycle is

[A]103 [B]310[C]515 [D]1032

16)The crank radius of a single-cylinder I. C. engine is 60 mm and the diameter of the ·cylinder is 80 mm.Theswept volume of the cylinder in is

[A]48 [B]96[C]302 [D]603

17)An engine working on air standard Otto cycle has a cylinder diameter of 10 cm and stroke length of 15 cm.The ratio of specific heats for air is 1.4. If the clearance volume is 196.3 cc and the heat supplied per kg ofair per cycle is 1800 kJ/kg, then work output per cycle per kg of air is

[A]879.1 kJ [B]890.2 kJ[C]895.3 kJ [D]973.5 kJ

18)A p-v diagram has been obtained from a test on a reciprocating compressor. Which of the followingrepresent that diagram?

[A] [B]

[C] [D]

19)A reversible thermodynamic cycle containing only three processes and producing work is to beconstructed. The constraints are (i) there must be one isothermal process,(ii) there must be one isentropic process,(iii) the maximum and minimum cycle pressures and the clearance volume are fixed, and(iv) polytropic processes are not allowed. Then the number of possible cycles are

[A]1 [B]2[C]3 [D]4

20)Given below is an extract from steam tables.

Specific enthalpy of water in kJ/kg at 150 bar and C is

[A]203.60 [B]200.53[C]196.38 [D]188.45

Air cycles



____________________________________________________________________________________________________________________ Pg.No.146





.

21)Group I shows different heat addition processes in power cycles. Likewise,Group II shows different heat removal processes. Group III lists power cycles. Match items from Groups I,IIand III.

[A]P-S-5R-U.3P-S-1Q-T-2

[B]P-s-1R-U-3P-S-4P-T-2

[C]R-T-3P-S-1P-T-4Q-S-5

[D]

P-T-4R-S-3P-S-1P-S-5

22)Which one of the following is NOT a necessary assumption for the air-standard Otto cycle ?

[A]All processes are both internally as well asexternally reversible.

[B] Intake and exhaust processes are constantvolume heat rejection processes.

[C]The combustion process is a constant volumeheat addition process.

[D]The working fluid is an ideal gas with constantspecific heats.

23)The stroke and bore of a four stroke spark ignition engine are 250 mm and 200 mm respectively. Theclearance volume is . If the specific heat ratio , the air-standard cycle efficiency of the engineis

[A]46.40 % [B]56.10 %[C]58.20 % [D]62.80 %

Air cycles



____________________________________________________________________________________________________________________ Pg.No.147


Key Paper

1. C 2. A 3. A 4. C 5. C

6. A 7. B 8. C 9. B 10. C

11. A 12. B 13. D 14. B 15. D

16. D 17. D 18. D 19. B 20. D

21. A 22. B 23. C

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1)The pressure, dry bulb temperature and relative humidity of air in a room are 1 bar, and 70%,respectively. If the saturated steam pressure at is 4.25 kPa, the specific humidity of the room air in kgwater vapour/kg dry air is

[A]0.0083 [B]0.0101[C]0.0191 [D]0.0232

2)Ambient air dry-bulb temperature is and wet bulb temperature is . Select the lowest possiblecondensing temperature from the following for an evaporatively cooled condenser.

[A] [B][C] [D]

3)When atmospheric air is heated at constant pressure, its

[A]humidity ratio does not change [B] relative humidity increases[C]dew point temperature does not change [D]wet bulb temperature increases.

4)A gas having a negative Joule-Thompson coefficient when throtteled will

[A]become cooler [B]become warmer

[C]remain at the same temperature [D]either be cooler or warmer depending on the typeof gas

5)A positive value to Joule-Thomson coefficient of a fluid means

[A] temperature drops during throttling [B] temperature remains constant during throttling[C]temperature rises during throttling [D]none of these.

6)For air with a relative humidity of 80%

[A] the dry bulb temperature is less than the wet bulbtemperature

[B] the dew point temperature is less than the wetbulb temperature

[C]the dew point and wet bulb temperatures areequal

[D]the dry bulb and dew point temperatures areequal.

7)A moist air sample has dry bulb temperature of 30°C and specific humidity of 11.5 g water vapour per kgdry air. Assume molecular weight of air pressure of water at 30°C is 4.24 kPa and the total pressure is 90kPa, then the relative humidity (in %) of air sample is

[A]50.5 [B]38.5[C]56.5 [D]68.5

8)If a mass of moist air in an airtight vessel is heated to a higher temperature then

[A]specific humidityof the air increases [B]specific humidity of the air decreases[C]relative humidity of the air increases [D]relative humidity of the air decreases

9)A room contains 35 kg of dry air and 0.5 kg of water vapor. The total pressure and temperature of air in theroom are 100 kPa and C respectively. Given that the saturation pressure for water at C is 3.17 kPa,the relative humidity of the air in the room is

[A]67% [B]55%[C]83% [D]71%

10)During chemical dehumidification process of air

[A]dry bulb temperature and specific humiditydecrease

[B]dry bulb temperature increases and specifichurnidity decreases

[C]dry bulb temperature decreases and specifichumidity increases

[D]dry bulb temperature and specific humidityincrease.

Psychometry



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11)Dew point temperature of air at one atmospheric pressure (1.013 bar) is C. The air dry bulb temperatureis C. The saturation pressure of water at C and C are 0.02062 bar and 0.04241 bar respectively.fire specific heat of air and water vapour respectively are 1.005 and 1.88 kJ/kg K and the latent heat ofvaporization of water at C is 2500 kJ/ kg. The specific humidity (kJ/kg of dry air) and enthalpy (kJ/kg ofdry air) of this moist air respectively, are

[A]0.01051, 52.64 [B]0.01291, 63.15[C]0.01421, 78.60 [D]0.01532, 81.40

12)For a typical sample of ambient air (at 35°C, 75% relative humidity and standard atmospheric pressure),the amount of moisture in kg per kg of dry air will be approximately

[A]0.002 [B]0.027[C]0.25 [D]0.75

13) Water at 42°C is sprayed into a stream of air at atmospheric pressure, dry bulb temperature of 40°C and awet bulb temperature of 20°C. The air leaving the spray humidifier is not saturated. Which of the followingstatements is true?

[A]Air gets cooled and humidified [B]Air gets heated and humidified[C]Air gets heated and dehumidified [D]Air gets cooled and dehumidified.

14)Dew point temperature is the temperature at which condensation begins when the air is cooled at constant

[A]volume [B]entropy[C]pressure [D]enthalpy

15)The statements concern psychrometric chart.1. Constant relative humidity lines are uphill straight lines to the right2. Constant wet bulb temperature lines are downhill straight lines to the right3. Constant specific volume lines are downhill straight lines to the right4. Constant enthalpy lines are coincident with constant wet bulb temperature linesWhich of the statements are correct ?


16)A thin layer of water in a field is formed after a farmer has watered it. The ambient air conditions are :temperature C and relative humidity 5%.An extract of steam tables is given below.

Neglecting the heat transfer between the water and the ground, the water temperature in the field afterphase equilibrium is reached equals

[A]10.3 [B] -10.3[C]-14.5 [D]14.5

Psychometry



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17)Various psychrometric process shown in the Fig. below.

Process in Figure Name of the processp. 0-1 1.chemical dehumidificationQ. 0-2 2. sensibile heatingR.0-3 3. cooling and dehumidifications. 0-4 4.humidification with steam injectionT. 0-5 5.humidification with water injection.The matching pairs are

[A]P-1,Q-2,R-3,S-4,T-5 [B]P-2,Q-1,R-3,S-5,T-4[C]P-2,Q-1,R-3,S-4,T-5 [D]P-3,Q-4,R-5,S-1,T-2

18)Moist air at a pressure of 100 kPa is compressed to 500 kPa and then cooled to C in an aftercooler. Theair at the entry to the aftercooler is unsaturated and becomes just saturated at the exit of the aftercooler.The saturation pressure of water at C is 5.628 kPa. The partial pressure of water vapour (in kPa) in themoist air entering the compressor is closest to

[A]0.57 [B]1.13[C]2.26 [D]4.52

19)Air (at atmospheric pressure) at a dry bulb temperature of C and wet bulb temperature of C ishumidified in an air washer operating with continuous water recirculation. The wet bulb depression (i.e.thedifference between the dry and wet bulb temperatures) at the exit is 25% of that at the inlet. The dry bulbtemperature at the exit of the air washer is closest to

[A] [B][C] [D]

20)Atmospheric air at a flow rate of 3 kg/s (on dry basis) enters a cooling and dehumidifying coil with anenthalpy of 85 kJ/kg of dry air and a humidity ratio of 19 grams/kg of dry air. The air leaves the coil with anenthalpy of 43 kJ/kg of dry air and a humidity ratio of 8 grams/kg of dry air. If the condensate water leavesthe coil with an enthalpy of 67 kJ/kg, the required cooling capacity of the coil in kW

[A]75.0 [B]123.8[C]128.2 [D]159.0

Psychometry



____________________________________________________________________________________________________________________ Pg.No.151


Key Paper

1. C 2. D 3. D 4. B 5. A

6. B 7. B 8. D 9. D 10. B

11. B 12. B 13. B 14. C 15. A

16. C 17. B 18. B 19. C 20. B

Psychometry



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Consider a steam power plant using a reheat cycle as shown in Figure. Steam leaves the boiler and entersthe turbine at 4 MPa, C ( = 3995 kJ/kg). After expansion in the turbine to 400 kPa ( = 2609 kJ/kg),the steam is reheated to C ( = 3170 kJ/kg), and then expanded in a low pressure turbine to 10 kPa( = 2165 kJ/kg). The specific volume of liquid handled by the pump can be assumed to be negligible.

1)The thermal efficiency of the plant neglecting pump work is

[A]15.8 % [B]41.1 %[C]48.5 % [D]58.6 %

2)The enthalpy at the pump discharge ( ) is

[A]0.33 kJ/kg [B]3.33 kJ/kg[C]4.0 kJ/K [D]33.3 kJ/kg


The inlet and the outlet conditions of stream for an adiabatic steam turbine are as indicated in thenotations are as usually followed

3)If mass flow rate of steam through the turbine is 20kg/s, the power output of the turbine (in MW) is

[A]12.157 [B]12.941[C]168.001 [D]168.785

4)Assume the above turbine to be part of a simple Rankine cycle. The density of water at the inlet to thepump is 1000kg/ . Ignoring kinetic and potential energy effects, the specific work (in kJ/kg) supplied to thepump is

[A]0.293 [B]0.351[C]2.930 [D]3.510


Rankine cycle



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In a steam power plant operating on the Rankine cycle, steam enters the turbine at 4 MPa, 350°C andexists at a pressure of 15 kPa. Then it enters the condenser and exits as saturated water. Next, a pumpfeeds back the water to the boiler. The adiabatic efficiency of the turbine is 90%. The thermodynamicstates of water and steam are given in the table.

State h(kJ k ) s(kJ k ) v( k ) Steam: 3092.5 6.5821 0.06645 4 MPa, 350°CWater 15 kPa 225.94 2599.1 0.7549 8.0085 0.001014 10.02 h is specific enthalpy, s is specific entropy and the specific volume ; subscripts f and g denote saturatedliquid state and saturated vapour state.

5)The net work output (kJ k ) of the cycle is

[A]498 [B]775[C]860 [D]957

6)Heat supplied (kJ k ) to the cycle is

[A]2375 [B]2576[C]2863 [D]3092

7)Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].Assertion [a] : In a power plant working on a Rankine cycle, the regenerative feed water heating improvesthe efficiency of the steam turbine.Reason [r] : The regenerative feed water heating raises the average temperature of heat addition in theRankine cycle.

[A]Both [a] and [r] are true and [r] is the correctreason for [a]

[B]Both [a] and [r] are true but [r] is NOT the correctreason for [a]

[C]Both [o] and [r] are false [D][a] is false but [r] is true.8)Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

Assertion [a] : Condenser is an essential equipment in a steam power plant.Reason [r] : For the same mass flow rate and the same pressure rise, a water pump requires substantiallyless power than a steam compressor.

[A]Both [a] and [r] are true and [r] is the correctreason for [a]

[B]Both [a] and [r] are true but [r] is NOT the correctreason for [a]

[C][a] is true but [r] is false [D][a] is false but [r] is true.

Rankine cycle



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9)A thermal power plant operates on a regenerative cycle with a single open feedwater heater, as shown inthe Figure. For the state points shown, the specific enthalpies are : = 2800 kJ/kg and = 200 kJ/kg. Thebleed to the feedwater

heater is 20% of the boiler steam generation rate. The specific enthalpy at state 3 is

[A]720 kJ/kg [B]2280 kJ/kg[C]1500 kJ/kg [D]3000 kJ/kg

10)Which combination of the following statements is correct ?The incorporation ofreheater in a steam power plant :P: Always increases the thermal efficiency of the plantQ: Always increases the dryness fraction of steam at condenser inlet.R : Always increases the mean temperature of heat additionS: Always increases the specific work output

[A] P and S [B]Q and S[C]P,R and S [D]P,Q,R and S

11)Boiler rating is usually defined in terms of

[A]maximum temperature of steam in Kelvin [B]heat transfer rate in KJ/hr[C]heat transfer area in [D]steam output in kg/hr

12)In stream and other vapour cycles, the process of removing non-condensables is called

[A]scavenging process [B]deaeration process[C]exhaust process [D]condensation process

13)The equivalent evaporation (kg/hr) of a boiler producing 2000 kg/hr of steam with enthalpy content of 2426kJ/kg from feed water at temperature 40°C (liquid enthalpy = 168 kJ/kg, enthalpy of vaporization of waterat 100°C = 2258 kJ/kg) is:

[A]2000 [B]2149[C]1682 [D]1649

14)Which among the following is the boiler mounting ?

[A]Blow off cock [B]Feed pump[C]Economiser [D]Superheater.

15)A steam plant has the boiler efficiency of 92% , turbirre efficiency (mechanical) of 94%, generatorefficiency of 95% and, cycle efficiency of 44%. If 6% of the generated power is used to run the auxiliaries,the overall plant efficiency is

[A]34% [B]39%[C]45% [D]30%

Rankine cycle



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.

16)The following data pertain to a single stage impulse stream turbine :Nozzle angle = ,Blade velocity = 200 m/sRelative stream velocity at entry = 350 m/sBlade inlet = Blade exit angle = .If blade friction is neglected, the work done per kg steam is

[A]124 kJ [B]164 kJ[C]169 kJ [D]174 kJ

17)Consider an actual regenerative Rankine cycle with one open feed water heater. For each kg steamentering the turbine, if m kg steam with a specific enthalpy of , is bled from the turbine, and the specificenthalpy of liquid water entering the heater is , then , specific enthalpy of saturated liquid leaving theheater is equal to

[A]m - ( - ) [B] -m( - )[C] -m( - ) [D]m -( - )

18)The isentropic heat drop in the nozzle of an impulse steam turbine with a nozzle efficiency 0.9, bladevelocity ratio 0.5, and mean blade velocity 150 m/s in kJ/kg is

[A]50 [B]40[C]60 [D]75

19)A gas turbine power plant has a specific output of 350 kJ/kg and an efficiency of 34%. A regenerator isinstalled and the efficiency increases to 51%. The specificoutput will be closest to

[A]350 KJ/kg [B]468 KJ/kg[C]525 KJ/kg [D]700 KJ/kg

20)A correctly designed convergent-divergent nozzle working at a designed load is

[A]always isentropic [B]always choked[C]never choked [D]never isentropic.

21)The efficiency of superheat Rankine cycle is higher than that of simple Rankine cycle because

[A] the enthalpy of main steam is higher forsuperheat cycle

[B] the mean temperature of heat addition is higherfor superheat cycle

[C]the temperature of steam in the condenser is high [D]the quality of stem in the condenser is low.22)In a Rankine cycle, regeneration results in higher efficiency because

[A]pressure inside the boiler increases [B]heat is added before steam enters the lowpressure turbine

[C]average temperature of heat addition in the boilerincreases [D]total work delivered by the turbine increases.

23)Considering the variation of static pressure and absolute velocity in an impulse stream turbine, across onerow or moving blades

[A]both pressure and velocity decrease [B]pressure decreases but velocity increases[C]pressure remains constant, while velocity

increases[D]pressure remains constant, while velocity

decreases.

Rankine cycle



____________________________________________________________________________________________________________________ Pg.No.156


Key Paper

1. B 2. D 3. A 4. C 5. C

6. C 7. A 8. B 9. A 10. B

11. D 12. B 13. D 14. A 15. A

16. A 17. C 18. A 19. A 20. B

21. B 22. C 23. D

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1)A gas turbine cycle with heat exchanger and reheating improves

[A]only the thermal efficiency [B]only the specific power output

[C]both thermal efficiency and specific power output [D]neither thermal efficiency nor specific poweroutput

2)A gas turbine cycle with infinitely large number of stages during compression and expansion leads to

[A]stirling cycle [B]atkinson cycle[C]Ericsson cycle [D]Brayton cycle

3)A Curtis stage, Rateau stage and a 5O% reaction stage in a steam turbine are examples of

[A]different types of impulse stages [B]different types of reaction stages[C]a simple impulse stage, a velocity compounded

impulse stage and reaction stage[D]a velocity compounded impulse stage, a simple

impulse stage and a reaction stage.4)What is the speed of sound in Neon gas at a temperature of 500 K (Gas constant of Neon is 0.4210 kJ/kg-

K) ?

[A]492 m/s [B]460 m/s[C]592 m/s [D]543 m/s

5)In a gas turbine, hot combustion products with the specific heats co = 0.98 kJ/kg K and = 0.7538 kJ/kgK enter the turbine at 20 bar, 1500 K and exit at 1 bar. The isoentropic efficiency of the turbine is 0.94. Thework developed by the turbine per kg of gas flow is

[A]689.64 kJ/kg [B]794.66 kJ/kg[C]1009.72 kJ/kg [D]1312.00 kJ/kg

6)An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum andmaximum temperatures of 300 K and 1500 K. The ratio of specific heats of the working fluid is 1.4. Theapproximate final temperatures in Kelvin at the end of the compression and expansion processes arerespectively


7)The compression ratio of a gas power plant cycle corresponding to maximum work output for the giventemperature limits of and will be

[A] [B]

[C] [D]


8)In a simple Brayton cycle, the pressure ratio is 8 and temperatures at the entrance of compressor andturbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficienciesequal to 0.8. For the gas, assume a constant value of (specific heat at constant pressure) equal to 1kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

Q. The power required by the compressor in kW/kg of gas flow rate is

[A]194.7 [B]243.4[C]304.3 [D]378.5

9)In a simple Brayton cycle, the pressure ratio is 8 and temperatures at the entrance of compressor andturbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficienciesequal to 0.8. For the gas, assume a constant value of (specific heat at constant pressure) equal to 1kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

Q: The thermal efficiency of the cycle in percentage (%) is

Gas turbines



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[A]24.8 [B]38.6[C]44.8 [D]53.1

Gas turbines



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Key Paper

1. C 2. C 3. D 4. C 5. A

6. A 7. A 8. A 9. A

Gas turbines



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A refrigerator operates between 120 kPa and 800 kPa in an ideal vapor compression cycle with R-134a asthe refrigerant. The refrigerant enters the compressor as saturated vapor and leaves the condenser assaturated liquid. The mass flow rate of the refrigerant is 0.2 kg/s. Properties for R-134a are as follows:

1)The rate at which heat is extracted, in kJ/s from the refrigerated space is

[A]28.3 [B]42.9[C]34.4 [D]14.6

2)The power required for the compressor in kW is

[A]5.94 [B]1.83[C]7.9 [D]39.5


A refrigerator based on ideal vapour compression cycle operates between the temperature c limits of and c. The refrigerant enters the condenser as saturated vapour and leaves as saturated liquid. Theenthalpy and entropy values for saturated liquid and vapour at these temperatures are given in the tablebelow.

3)If refrigerant circulation rate is 0.025 kg/s, the refrigeration effect is equal to

[A]2.1 kW [B]2.5 kW[C]3.0 kW [D]4.0 kW

4)The COP of the refrigerator is

[A]2.0 [B]2.33[C]5.0 [D]6.0

5)The use of Refrigerant-22 (R-22) for temperatures below -30°C is not recommended due to its

[A]good miscibility with lubricating oil [B]poor miscibility with lubricating oil[C]low evaporating pressure [D]high compressor discharge temperature

6)In a vapour compression refrigeration system, liquid to suction heat exchanger is used to

[A]keep the COP constant [B]prevent the liquid refrigerant from entering thecompressor

[C]subcool the liquid refrigerant leaving thecondenser

[D]subcool the vapour refrigerant from theevaporator.

7)In the window air conditioner, the expansion device used is

[A]capillary tube [B] thermostatic expansion valve[C]automatic expansion valve [D]float valve.

Refrigeration



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8)Environment friendly refrigerant R13 is used in the new generation domestic refrigerators. Its chemicalformula is

[A] [B][C] [D]

9)The vapour compression refrigeration cycle is represented as shown in the Fig. below, with state 1beingthe exit of the evaporator. The coordinate system used in this figure is

[A]p-h [B]T-s[C]p-s [D]T-h

Refrigeration



____________________________________________________________________________________________________________________ Pg.No.162


Key Paper

1. A 2. C 3. A 4. B 5. B

6. C 7. A 8. D 9. D

Refrigeration



____________________________________________________________________________________________________________________ Pg.No.163


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1)Alcohols are unsuitable as diesel engine fuels because

[A] the cetane number of alcohol fuels is very lowwhich prevents their ignition by compression

[B] the cetane number of alcohol fuels is very highwhich prevents their ignition by compression

[C]the cetane number of alcohol fuels is constantwhich prevents their ignition by compression [D]None of the above

2)Brake thermal efficiency of the three types of reciprocating engines commonly used in road vehicles aregiven in the increasing order as

[A]2 stroke SI engine, 4 stroke SI engine, 4 stroke CIengine

[B]2 stroke SI engine, 4 stroke CI engine, 4 stroke SIengine

[C]4 stroke SI engine, 2 stroke SI engine, 4 stroke CIengine

[D]4 stroke CI engine, 4 stroke SI engine, 2 strokeCI engine

3)Knocking tendency in a S.I engine reduces with increasing

[A]compression [B]wall temperature[C]supercharging [D]engine speed

4)In order to burn 1 kilogram of completely, the minimum number of kilograms of oxygen needed is (takeatomic weights of H, C and O as 1, 12 and 16 respectively).

[A]3 [B]4[C]5 [D]6

5)Clearance volume of a reciprocating compressor is 100 ml, and the volume of the cylinder at bottom deadcentre is 1.0 litre. The clearance ratio of the compressor is

[A] [B]

[C] [D]

6)With increasing temperature of intake air, IC engine efficiency

[A]decreases [B] increases[C]remains same [D]depends on other factors

7)An IC engine has a bore and stroke of 2 units each. The area to calculate heat loss can be taken as

[A] [B][C] [D]

8)An air breathing aircraft is flying at an altitude where the air density is half the value at ground level. Withreference to the ground level, the air-fuel ratio at this altitude will be

[A] [B][C]2 [D]4

9)The silencer of an internal combustion engine

[A] reduces noise [B]decreases brake specific fuelconsumption(BSFC)

[C]increases BSFC [D]has no effect its efficiency10)For a spark ignition engine, the equivalence ratio ( ) of mixture entering the combustion chamber has

values

[A] <L for idling and >1for peak power conditions [B] >I for both idling and peak power conditions[C] >I for idling and <1 for peak power conditions [D] <1 for both idling and peak power conditions.

11)A diesel engine is usually more efficient than a spark ignition engine because

[A]diesel being a heavier hydrocarbon, releasesmore heat per kg than gasoline

[B] the air standard efficiency of diesel cycle is higherthan the Otto cycle, at a fixed compression ratio

Internal combustion engines



____________________________________________________________________________________________________________________ Pg.No.164







[C]the compression ratio of a diesel engine is higherthan that of an SI engine

[D]self ignition temperature of diesel is higher thanthat of gasoline.

12)An automobile engine operates at a fuel air ratio of 0.05, volumetric efficiency of 90% and. indicatedthermal efficiency of 30%. Given that the calorific value of the fuel is 45 MJ/kg and the density of air atintake is L kg/ , the identical mean effective pressure for the engine is

[A]6.075 bar [B]6.75 bar[C]67.5 bar [D]243 bar

13)In an ideal vapour compression refrigeration cycle, the specific enthalpy of refrigerant (in kJ/kg) at thefollowing states is given as:Inlet of condenser: 283Exit of condenser: 116Exit of evaporator: 232The COP of this cycle is

[A]2.27 [B]2.75[C]3.27 [D]3.75

14)At the time of starting, idling and low speed operation, the carburettor supplies a mixture which can betermed as

[A] lean [B]slightly leaner than stoichiometric[C]stoichiometric [D]rich.

15)During a Morse test on a 4 cylinder engine, the following measurements of brake power were taken atconstant speed.All cylinders firing 3037 kWNumber l cylinder not firing 2102 kWNumber 2 cylinder not firing 2102 kWNumber 3 cylinder not firing 2100 kWNumber 4 cylinder not firing 2098 kWThe mechanical efficiency of the engine is

[A]91.53 % [B]85.07 %[C]81.07 % [D]61.22 %

16)A R-12 refrigerant reciprocating compressor operates between the condensing temperature of C andevaporator temperature of - C. The clearance volume ratio of the compressor is 0.03. Specific heat ratioof the vapour is 1.15 and the specific volume at the suction is 0.1089 /Kg. Other properties at variousstates are given in the Figure. To realize 2 Tons of refrigeration, the actual volume displacement rateconsidering the effect of clearance is

[A]6.35 x /s [B]63.5 x /s[C]635 x /s [D]4.88 x /s





____________________________________________________________________________________________________________________ Pg.No.165




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17)In a machining experiment, tool life was found to vary with the cutting speed in the following manner:

The exponent (n) and constant (k) of the Taylor’s tool life equation are

[A]n = 0.5 and k = 540 [B]n = 1 and k = 4860[C]n = −1 and k = 0.74 [D]n = −0.5 and k = 1.155

18)What is the percentage increase in tool life when the cutting speed is halved?

[A]50% [B]200%[C]300% [D]400%




____________________________________________________________________________________________________________________ Pg.No.166


Key Paper

1. D 2. A 3. D 4. B 5. C

6. A 7. C 8. B 9. A 10. B

11. C 12. A 13. A 14. D 15. C

16. A 17. A 18. C




____________________________________________________________________________________________________________________ Pg.No.167






Index- Fluid Mechanics and Thermal Sciences

Sl.No. Name of the Topic Pg.No.s 1. Property of Fluids 168-171 2. Fluid Statics 172-176 3. Fluid Kinematics 177-181 4. Fluid Dynamics 182-186 5. Laminar Flow 187-191 6. Turbulent Flow 192-195 7. Boundary Layer 196-198 8. Open Channel Flow 199-204 9. Turbo Machinery 205-209









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1)Water flows through a 100mm diameter pipe with a velocity of 0.015m/sec. If the kinematic viscosity ofwater is pipe material is , the friction factor of the

[A]0.0015 [B]0.032[C]0.037 [D]0.048

2) Flow rate of a fluid (density = 1000 ) in a small diameter tube is .The length and thediameter of the tube are 2m and 0.5mm, respectively. The pressure drop in 2m length is equal to 2.0MPa.The viscosity of the fluid is

[A] [B][C] [D]

3)A solid sphere (diameter 6 mm) is rising through oil (mass density 900 kg/m3, dynamic viscosity 0.7kg/ms) at a constant velocity of 1cm/s. what is the specific weight of the material from which the sphere ismade? (Take )

[A] [B][C] [D]

4)Cavitation is caused by

[A]high velocity [B] low pressure[C]high pressure [D]high temperature

5)The unit of dynamic viscosity of a fluid is

[A] / s [B]Ns / [C]Pa s / [D]kg /

6)A fluid is said to be Newtonian when the shear stress is

[A]directly proportional to the velocity gradient [B] inversely proportional to the velocity gradient[C]independent of the velocity gradient [D]none of the above.

7)The dimenation of surface tension is

[A] [B][C] [D]

8)If 'p' is the gauge pressure within a spherical droplet, then gauge pressure within a bubble of the samefluid and of same size will

[A]p/4 [B]p/2[C]p [D]2p

9)Kinematic viscosity of air at is given to be . Its kinematic viscosity at will be varyapproximately

[A] [B][C] [D]

10)An aeroplane is cruising at a speed of 800 kmph at an altitude, where the air temperature is . The flightMach number at this speed is nearly

[A]1.5 [B]0.254[C]0.67 [D]2.04

11)For a compressible fluid, sonic velocity is

[A]a property of the fluid[B]always given by where , R and T are

respectively the ratio of specific heats, gasconstant and, temperature in K

[C]always given by , where p, and s arerespectively pressure, density and entropy

[D]always greater than the velocity of fluid. at anylocation.

Property of fluids



____________________________________________________________________________________________________________________ Pg.No.169




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12)An incompressible fluid (kinematic viscosity, 7,4 x ls, specific gravity, 0.88) is held between twoparallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary,then fluid attains a linear velocity profile in the gap of 0.5 mm between these plates : the shear stress inPascals on the surface of top plate is

[A] 0.651 x [B]0.651[C]6.51 [D]0.651 x

13)For a Newtonian fluid

[A]Shear stress is proportional to shear strain [B]Rate of shear stress is proportional to shearstrain

[C]Shear stress is proportional to rate of shear strain [D]Rate of shear stress is proportional to rate ofshear strain.

Property of fluids



____________________________________________________________________________________________________________________ Pg.No.170


Key Paper

1. D 2. C 3. D 4. C 5. B

6. A 7. D 8. D 9. A 10. C

11. B 12. B 13. C

Property of fluids



____________________________________________________________________________________________________________________ Pg.No.171


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A very wide rectangular channel carries a discharge of perm width. The channel has a bed slopeof0.004 and Manning's roughness coefficient, n= 0.015. At a certain section of the channel, the flow depth islm.

1)What Gradua lly Varied Flow profile exists at this secton?

[A] [B][C] [D]

2)At what distance from this section the flow depth will be 0.9 m ? (Use the direct step method employing asingle step

[A]65 m upstream [B]50 m downstream[C]50 m upstream [D]65 m downstream

3)A 15 cm length of steel rod with relative density of 7.4 is submerged in a two layer fluid. The bottom layeris mercury and the top layer is water. The height of top surface of the rod above the liquid interface in 'cm'is

[A]8.24 [B]7.82[C]7.64 [D]7.38

4)In a n iceberg, 15%of the volume projects above the sea surface . It the specific weight of sea water is10.5 , the specific weight of iceberg in is

[A]12.52 [B]9.81[C]8.93 [D]7.83

5)In which one of the following arrangement would the vertical force on the cylinder due towater be themaximum?

[A] [B]

[C][D]

6)The force F needed to support the liquid of density d and the vessel on top (Fig. 1) is

[A]gd [ha - (H - h) A] [B]gdHA[C]GdHa [D]gd(H -h)A.

Fluid statics



____________________________________________________________________________________________________________________ Pg.No.172






7)A mercury manometer is used to measure the static pressure at a point in a water pipe as shown in Fig.The level difference of mercury in the two limbs is 10 mm. The gauge pressure at that point is

[A]1236 Pa [B]1333 Pa[C]zero [D]98 Pa

8)Refer to Figure, the absolute pressure of gas A in the bulb is

[A]771.2 mm Hg [B]752.65 mm Hg[C]767.35 mm Hg [D]748.8 mm Hg

9)In given Figure if the pressure of gas in bulb A is 50 cm Hg vacuum and = 76 cm Hg, then height ofcolumn H is equal to

[A]26 cm [B]50 cm[C]76 cm [D]126 cm

10)A static fluid can have

[A]non-zero normal and shear stress [B]negative normal stress and zero shear stress[C]positive normal stress and zero shear stress [D]zero normal stress and non-zero stress.

Fluid statics



____________________________________________________________________________________________________________________ Pg.No.173








11)The horizontal and vertical hydrostatic forces and . on the semi-circular gate having a width w into theplane of Fig. are

[A] [B][C] [D]

12)A cylindrical body of cross-sectional area A, height H and density , is immersed to a depth h in a liquid ofdensity , and tied to the bottom with a string. The tension in the string is (See Figure)

[A]pghA [B] ( - p) ghA[C](p - ) ghA [D](ph - H)gA

13)For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE ?

[A]Metacentre should be below centre of gravity. [B]Metacentre should be above centre of gravity.[C]Metacentre and centre of gravity must lie on the

same horizontal line.[D]Metacentre and centre of gravity must lie on the

same vertical line.14)For a body completely submerged in a fluid, the centre of gravity (G) and centre of Buoyancy (O) are

known. The body is considered to be in stable equilibrium if

[A]O does not coincide with the centre of mass ofthe displaced fluid

[B]G coincides with the centre of mass of thedisplaced fluid

[C]O lies below G [D]O lies above G15)The reading of differential manometer of a Venturimeter ,placed at to the horizontal is 11 cm.If the

Ventruimeter is turned to horizontal position, the manometer reading will be.

[A]Zero [B]

[C] [D]16)A stream function is given by . The flow rate across a line joining points A{3,0) and

6{0,2) is

[A]0.4 units [B]1.1 units[C]4 units [D]5 units

Fluid statics



____________________________________________________________________________________________________________________ Pg.No.174





.

17)In the inclined manometer shown in the figure below , the reservoir is large. Its surface may be assumed toremain at a fixed elevation. A is connected to a gas pipeline and the deflection noted on the inclined glasstube is 100 mm. Assuming and the manometric fluid as oil with spcific gravity of 0.86, the pressureat A is

[A]43 mm water (vacuum) [B]43 mm water[C]86 mm water [D]100 mm water

18)A thin flat plate 0.5 m x 0.7 m in size settles in a large tank of water with a terminal velocity of 0.12 m/s.

The co-efficient of drag for a laminar boundary layer and for a for a turbulent boundarylayer, where , is the plate Reynolds number.Assume = N-s/ and p = 1000 kg/ The submerged weight of the plate is

[A]0.0115 N [B]0.0118 N[C]0.0231 N [D]0.0376 N

19)Two pipelines, one carrying oil (mass density 900 kg/ m3 ) and the other water, are connected toa manometer as shown in the figure.By what amount the pressure in the water pipe should be increasedso that the mercury levels in both the limbs of the manometer become equal ? (Mass density of mercury= and )

[A]24.7 kPa [B]26.5 kPa[C]26.7 kPa [D]28.9 kPa

Fluid statics



____________________________________________________________________________________________________________________ Pg.No.175


Key Paper

1. D 2. B 3. D 4. C 5. B

6. B 7. B 8. A 9. D 10. B

11. D 12. D 13. B 14. D 15. C

16. C 17. B 18. A 19. B

Fluid statics



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1)For a two dimensional flow field, the stream function is given as . The magnitude ofdischarge occurring between the stream lines passing through points (0,3) and (3,4) is:

[A]6 [B]3[C]1.5 [D]2

2)An inert tracer is injected continuously from a point in an unsteady flow field. The locus of locations of allthe tracer particles at an instance of time represents

[A]Streamline [B]Pathline[C]Steamtube [D]Streakline

3)A partially open sluice gate discharges water into a rectangular channel. The tail water depth in thechannelis 3 m and Froude number is . If a free hydraulic jump is to be formed at a downstream of the sluicegate after the vena contracta of the jet coming out from the sluice gate, the sluice gate opening should be(coefficient of contraction )

[A]0.3m [B]0.4m[C]0.69m [D]0.9m

4)Cross-section of an object (having same section normal to the paper) submerged into a fluid consists of asquare of sides 2 m and triangle as shown in the figure. The object is hinged at point P that is one meterbelow the fluid free surface. If the object is to be kept in the position as shown in the figure, the value 'x'should be

[A] [B][C]4 m [D]8 m

5)The circulation 'G' around a circle of radius 2 units for the velocity field u = 2x + 3y and v = 2y is

[A] [B][C] [D]

6)A volocity field is given as where x andy are in metres. The acceleration of the a fluid particleat (x, y) = (1, 1) in the x direction is

[A]0 m/ [B]5.00 m/[C]6.00 m/ [D]8.48 m/

7)The velocity in m/s at a point in a two-dimensional flow is given as . The equation of the streamline passing through the point is

[A]3dx - 2dy = 0 [B]2x + 3y = 0[C]3dx + 2dy = 0 [D]xy = 6

8)For a two-dimensional irrotational flow the velocity potential is defined as . Whtch of the following is a possible stream function, for this flow

[A] [B][C] [D]

9)The relation that must hold for the flow to be irrotational is

[A] [B]

[C] [D]

Fluid kinematics



____________________________________________________________________________________________________________________ Pg.No.177













10)ln a steady radial flow into an in take the velocity is found to vary as ( ),where r is the radial distance.The acceleration of the flow is propottional to

[A] [B][C] [D]

11)Two flow patterns are represented by their stream functions , and as given below:,

If these two parterns are superposed 0n One another, the resulting streamline pattern can be representedby one of the following:

[A]A family of parallel straight lines [B]A family of circles[C]A family of parabolas [D]A family of hyperbolas

12) Streamlines, pathlines and streaklines are virtually identical for

[A]Uniform flow [B]Flow of ideal fluids[C]steady flow [D]Non uniform flow

13)In a flow field, the streamlines and equipotential lines

[A]Are parallel [B] are orthogonal everywhere in the flow field

[C]cut at any angle [D] cut orthogonally except at the stagnationpoints.

14) For a fluid element in a two dimensional flow field (x-y plane), it will undergo

[A] translation [B] translation and rotation[C]translation and deformation [D]deformation

15) Net force on a control volume due to uniform normal pressure alone

[A]depends upon the shape of the control volume [B] translation and rotation[C]translation and deformation [D]deformation only

16)Existence of velocity potential implies that

[A] fluid is in continuum [B] fluid is irrotational[C]fluid is ideal [D]fluid is compressible

17)The velocity components in the x and y directions are given by

,

The value of , for a possible flow field involving an incompressible fluid is

[A] [B][C] [D]3

18)The SI unit of kinematic viscosity (v) is

[A] [B]kg/m-sec[C] [D]

19)T}re 2-D flow with, velocity is

[A]compressible and irrotational [B]compressible and not irrotational[C]incompressible and irrotational [D]incompressible and not irrotational

20)A streamline and an equipotential line in a flow field

[A]are parallel to each other [B]are perpendicular to each other[C]intersect at an acute angle [D]are identical

Fluid kinematics



____________________________________________________________________________________________________________________ Pg.No.178










21)You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. Thefollowing three flow choices, expressed in terms of the two-dimensional velocity fields in the xy-plane, aremade available.P. u=2y, v=-3xQ. u=3xy, v=0R. u=-2x, v=2yWhich flow(s) should be recommended when the application requires the flow to be incompressible andirrotational?

[A]P and R [B]Q[C]Q and R [D]R

22)A fluid flow is represented by the velocity 1 field , where a is d constant. The equation ofstream line passing through a point (1, 2) is

[A]x-2y = 0 [B]2x+y=0[C]2x-y = 0 [D]x + 2y =0

23)For a fluid flow through a divergent pipe of length L having inlet and outlet radii of and respectively anda constant flow rate of Q, assuming the velocity to be axial and uniform at any cross-section, theaceeleration at the exit is

[A] [B]

[C] [D]

24)A closed cylinder having a radius R and height H is frlled with oil of density . If the cylinder is rotatedabout its axis at an angular velocity of , then thrust at the bottom of the cylinder is

[A] [B]

[C] [D]

25)For air flow over a flat plate, velocity (U) and boundary layer thickness ( ) can be expressed respectively,as

; If the free stream velocity is 2 m/s, and air has kinematic viscosity of 1.5 x /s and density of 1.23 kg/ ,then wall shear stress at x = 1 m, is

[A]2.36 x N/ [B]43.6 x N/[C]4.36 x N/ [D]2.18 x N/

26)The velocity components in the x and y directions of a two dimensional potential flow are u and v,respectively. Then is equal to.

[A] [B][C] [D]

27)A two-dimensional flow field has velocities along the x and y directions given by u = t and v = -2xytrespectively, where t is time. The equation of streamlines is

[A] y = constant [B]x = constant[C]xy = constant [D]not possible to determine

28)A leaf is caught in a whirlpool. At a given instant, the leafis at a distance of 120 m from the centre of thewhirlpool. The whirlpool can be described by the following velocity distribution ;

and ,where r (in metres) is the distance from the centre of the whirlpool. What will be the distance of the leaffrom the centre when it has moved through half a revolution?

[A]48 m [B]64 m[C]120 m [D]142 m

Fluid kinematics



____________________________________________________________________________________________________________________ Pg.No.179







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29)For the continuity equation given by = 0 to be valid, where is the velocity vector, which one of thefollowing is a necessary condition ?

[A]steady flow [B] irrotational flow[C]inviscid flow [D]incompressible flow.

30)In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by , where r isthe distance along the axis of the nozzle from its inlet plane and L is the length of the nozzle. The timerequired for a fluid particle on the axis to travel from the inlet to the exit plane of the nozzle is

[A] [B][C] [D]

31)Which combination of the following statements about steady incompressible forced vortex flow is correct ?P: Shear stress is zero at all points in the flow.Q : Vorticity is zero at all points in the flow.R: Velocity is directly proportional to the radius from the centre of the vortex.S: Total mechanical enerry per unit mass is constant in the entire flow field.

[A]P and Q [B]R and S[C]P and R [D]P and S


32)The gap between a moving circular plate and a stationary surface is being continuously reduced, as thecircular plate comes down at a uniform speed V towards the stationary bottom surface, as shown in theFigure. In the process, the fluid contained between the two plates flows out radially. The fluid is assumedto be incompressible and inviscid.

The radial velocity at any radius r, when the gap width is h, is

[A] [B][C] [D]

33)The radial component of the fluid acceleration at r = R is

[A] [B]

[C] [D]

Fluid kinematics



____________________________________________________________________________________________________________________ Pg.No.180


Key Paper

1. B 2. D 3. C 4. A 5. B

6. D 7. A 8. C 9. A 10. A

11. B 12. C 13. B 14. B 15. C

16. B 17. D 18. A 19. D 20. B

21. D 22. C 23. C 24. D 25. C

26. D 27. A 28. B 29. D 30. B

31. B 32. A 33. B

Fluid kinematics



____________________________________________________________________________________________________________________ Pg.No.181


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1)Group-I gives a list of devices and Group-II gives the list of usesP. Pitot tube 1. Measuring pressure in a pipeQ. Manometer 2. Measuring velocity of flow in a pipeR. Venturimeter 3. Measuring air and gas velocityS. Anemometer 4. Measuring discharge in a pipeThe correct match of Group-I with Group-II is

[A] P-1, Q-2, R-4, S-3 [B]P-2, Q-1, R-3, S-4[C] P-2, Q-1, R-4, S-3 [D]P-4, Q-1, R-3, S-2

2)A tank and a deflector are placed on a frictionless trolley. The tank issues water jet (mass density of water= which strikes the deflector and truns by . If the velocity of jet leaving the deflector is 4 m/sand discharge is the force recorded by the spring will be

[A]100 N [B][C]200 N [D]

3)At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at thesame elevation. Both the points are at the same elevation. The fluid density is . The flow can beassumed to be in compressible, inviscid, steady and irrotational. The difference in pressures and atpoints 1 and 2 is

[A] [B][C] [D]

4)A frictionless fluid of density r flow through a bent pipe as shown below .If A is the cross sectional area andV is the velocity of flow, the forces exerted on segment 1 - 2 of the pipe in the x and y directions are,respectively

[A] [B][C]0 ; 0 [D]

5)A horizontal jet strikes a frictionless vertical plate (the plan view is shown in the figure). It is the divided intotwo parts, as shown in the figure. If the impact loss can be neglected, what is the value of ?

[A] [B][C] [D]

6)In a Bernoulli equation, used in pipe flow, each term represents

Fluid dynamics



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[A]Energy per unit weight [B]Energy per unit mass[C]Energy per unit volume [D]Energy per unit flow length

7)The kinetic energy correction factor for a fully developed laminar flow through a circular pipe is

[A]1.00 [B]1.33[C]2.00 [D]1.50

8)A nozzle discharging water under head H has an outlet area "n" and discharge coefficient = 1.0. Avertical plate is acted upon by the fluid force when held across the free jet and by the fluid force , when

held against the nozzle to stop the flow. The ratio is

[A]1/2 [B]1[C] [D]2

9)A body moving through still water at 6m/sec produces a water velocity of 4m/sec at a point 1m ahead. Thedifference in pressure between the nose and the point 1m ahead would be

[A]2,000 N/ [B]10,000 N/[C]19,620 N/ [D]98,100 N/

10)Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is20 mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/ . Assuming steady, inviscidflow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, thediameter in mm of the stream 0.5 m below the tap is approximately

[A]10 [B]15[C]20 [D]25

11)Navier Stoke's equation represents the conservation of

[A]energy [B]mass[C]pressure [D]momentum

12)Water flows through a vertical contraction from a pipe of diameter d to another of diameter d/2 . The flowvelocity at the inlet to the contraction is 2 m/s and pressure . If the height of the contractionmeasures 2m, then pressure at the exit of the contraction will be very nearly

[A] [B][C] [D]

13)A water container is kept on a weighing balance. Water from a tap is falling vertically into the containerwith a volume flow rate of Q; the velocity of the water when it hits the water surface is U. At a particularinstant of time the total mass of the container and water is m. The force registered by the weighing balanceat this instant of time is

[A]mg + p QU [B]mg + 2 p QU[C]mg +p Q /2 [D]p Q /2

Fluid dynamics



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14)A smooth pipe of diameter 200 mm carries water. The pressure in the pipe at section Sl (elevation: 10 m)is 50 kPa. At section S2 (elevation : 12 m) the pressure is 20 kPa and velocity is 2 m . Density of wateris 1000 kg and acceleration due to gravity is 9.8 m . Which of the following is TRUE ?

[A] flow is from S1 to S2 and head loss is 0.53m [B] flow is from S2 to S1 and head loss is 0.53m[C]flow is from S1 to S2 and head loss is 1.06 m [D]flow is from S2 to S1 and·head loss is 1.06 m

15)A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that thechanges in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

[A] [B]

[C] [D]

16)Figure shows the schematic for the measurement of velocity of air through a constant -area duct using a pitot tube and a water-tube manometer . The differential head of water in the two columns of the manometer is 10 mm. Take acceleration due to gravity as

. The velocity of air in m/s is

[A]6.4 [B]9.0[C]12.8 [D]25.6

17)Match the approaches given below to perform stated kinematics / dynamics analysis of machine


18)A venturimeter of 20 mm throat diameter is used to measure the velocity of water in a horizontal pipe of 40mm diameter. If the pressure difference between the pipe and throat sections is found to be 30 kPa then,neglecting frictional losses, the flow velocity is

[A]0.2 m/s [B]1.0 m/s[C]1.4 m/s [D]2.0 m/s

Fluid dynamics



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.

19)A U-tube manometer with a small quantity of mercury is used to measure the static pressure differencebetween two locations A and B in a conical section through which an incompressible fluid flows. At aparticular flow rate, the mercury column appears as shown in the Fig. . The density of mercury is and . Which of the following is correct?

[A]Flow direction is A to B and = 20KPa [B]Flow direction is B to A and =1.4 KPa[C]Flow direction is A to B and = 20 KPa [D]Flow direction is B to A and = 1.4 KPa

Fluid dynamics



____________________________________________________________________________________________________________________ Pg.No.185


Key Paper

1. C 2. D 3. B 4. C 5. B

6. A 7. C 8. B 9. B 10. B

11. D 12. C 13. A 14. C 15. A

16. C 17. B 18. D 19. A

Fluid dynamics



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.

.








A pipeline (diameter 0.3 m, length 3 km) carries water from pint P to point R (see figure). The piezometricheads at P and Rare to be maintained at 100m and 80 m, respectively. To increase the discharge, asecond pipe is added in parallel to the existing pipe from Q to R.The length of the additional pipe is also2km.Assume the friction factor, f = 0.04 for all pipes and ignore minor losses.

1)What is the increase in discharge if the additional pipe has same diameter (0.3 m) ?

[A]0% [B]33%[C]41% [D]67%

2)If there is no restriction on the diameter of the additional pipe,what would be the maximum increase indischarge theoretically possible from this arrangement ?

[A]0% [B]33%[C]41% [D]73%


The laminar flow takes place between closely spaced parallel plates as shown in figure below. The velocityprofile is given by . The gap height, h, is 5 mm and the space is filled with oil (specific gravity = 0.86viscosity m = 2 x N-s/m1). The bottom plate is stationary and the top plate moves with a steadyvelocity of V = 5 cm/s. The area of the plate is 0.25 .a

3)The rate of rotation of a fluid particle is given by

[A] [B][C] [D]

4)The power required to keep the plate in steady motion is

[A] watts [B] watts[C] watts [D] watts

5)While deriving an expression for loss of head due to a sudden expansion in a pipe, in addition to thecontinuity and impulse - momentum equations, one of the following assumptions is made:

[A]Head loss due to friction is equal to the head lossin eddying motion

[B]The mean pressure in eddying fluid is equal tothe downstream pressure

[C]The mean pressure in eddying fluids is equal tothe upstream pressure [D]Head lost in eddies is neglected

6)If a single pipe of length Land diameter D is to be·replaced by three pipes of same material, same lengthand equal diameter d (d <D), to convey the same total discharge under the same head loss,. then d and Dare relatd by

[A] [B][C] [D]

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7)Three reservoirs A, Band Care inter connected by pipes as shown in the Figure. Water surface elevationsin the reservoirs and the piezometric head at the junction J are indicated in the Figure.

Discharge , and are related as

[A] [B][C] [D]

8)In flow through a pipe, the transition from laminar to turbulent flow does not depend on

[A]velocity of the fluid [B]density of the fluid[C]diameter of the pipe [D]length of the pipe

9)For laminar flow through a long pipe, the pressure drop per unit length increases

[A] in linear proportion to the cross-sectional area [B] in proportion to the diameter of the pipe

[C]in inverse proportion to cross-sectional area [D]in inverse proportion to the square of cross-sectional area.

10)The maximum velocity of a one dimensional incompressible fully developed viscous flow, between twofixed parallel plates, is 6 .The mean velocity (in ) of the flow is

[A]2 [B]3[C]4 [D]5

11)Water at C is flowing through a 1.0km long G.I pipe of 200mm diameter at the rate of 0.07 /s. If value ofDarcy friction factor for this pipe is 0.02 and density of water is 1000kg/ , the pumping power (in kW)required to maintain the flow is

[A]1.8 [B]17.4[C]20.5 [D]41.0

12)The velocity profile in fully developed laminar flow in a pipe of diameter D is given by wherer is the radial distance from the center. If the viscosity of the fluid is p, the pressure drop across a length Lof the pipe is

[A] [B][C] [D]

13)Consider an incompressible laminar boundary layer flow over a flat plate of length L, aligned with thedirection of an oncoming uniform free stream. If F is the ratio of the drag force on the front half of the plateto the drag force on the rear half, then

[A]F <1/2 [B]F= 1/2[C]F = 1 [D]F >1

14)Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straightcircular pipe of constant cross-sectional area at a Reynolds number of 5. The ratio of inertia force toviscous force on a fluid particle is

[A]5 [B]1/5[C]0 [D]

Laminar flow



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15)The circular water pipes shown in the sketch are flowing full. The velocity of flow (in m/s) in the branchpipe “R” is

[A]3 [B]4 [C] 5 [D] 6

16)A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m intheir water levels. The pipe is to be replaced by two pipes of the same length and equal diameter d toconvey 25% more discharge under the same head loss. If the friction factor is assumed to be the samefor all the pipes, the value of d is approximately equal to which of the following options?

[A]37.5 cm [B]40.0 em[C]45.0 cm [D]50.0 cm

17)A spillway discharges flood flow at a rate of 9 per metre width. If the depth of flow on the horizontalapron at the toe of the spillway is 46 cm, the tail water depth needed to form a hydraulic jump isapproximately given by which of the following options?

[A]2.54 m [B]4.90 m[C]5.77 m [D]6.23 m

18)A 2 km long pipe of 0.2 m diameter connects two reservoirs. The difference between water levels in the reservoirs is 8 m. The Darcy-Weisbachfriction factor of the pipe is 0.04. Accounting for frictional, entryand exit losses, the velocity in the pipe (in m/s) is:

[A]0.63 [B]0.35[C]2.52 [D]1.25

19)Water flows with a flow rate of through a pipe AB of 10m length and of uniformcross section. The end ‘B’ is above end ‘A’ and the pipe makes an angle of to the horizontal. For apressure of at the end ‘B’, the corresponding pressure at the end ‘A’ is

[A] [B][C] [D]

20)The thickness of the laminar boundary layer on a flat plate at a point A is 2 cm and at a point 8, 1mdownstream of A, is 3 cm. What is the distance of A from the leading edge of the plate?

[A]0.50 m [B]0.80 m[C]1.00 m [D]1.25 m

21) The flow of water (mass density = 1000 and kinematic viscosity ) in a commercial pipe,having equivalent roughness as 0.12mm , yields an average shear stress at the pipe boundary = . The value of ( being the thickness of laminar sub-layer) for this pipe is

[A]0.25 [B]0.50[C]6.0 [D]8.0

22)A wide channel is 1 m deep and has a velocity of flow, V, as 2.13 m/s. If a disturbance is caused, anelementary wawe can travel upstream with a velocity of

[A]1.00 m/s [B]2.13 m/s[C]3.13 m/s [D]5.26 m/s

Laminar flow



____________________________________________________________________________________________________________________ Pg.No.189





.

23)A fire protection system is supplied from a water tower with a bend pipe as shown in the figure. The pipefriction f is 0.03. Ignoring all minor losses, the maximum discharge, Q in the pipe is

[A]31.7 lit/sec [B]24.0 lit/sec[C]15.9 lit/sec [D]12.0 lit/sec


24)An upward flow of oil (mass density 800 kg/ , dynamic viscosity 0.8 kg/m-s) takes place under laminarconditions in an inclined pipe of 0.1 m diameter as shown in the figure. The pressures at section 1 and 2are measured p1=435 kN/ and = 200 kN/

The discharge in the pipe is equal to

[A]0.100 [B]0.127 [C]0.144 [D]0.164

25)If the flow is reversed, keeping the same discharge, and the pressure at section 1 is maintained as 435kN/ , the pressure at section 2 is equal to

[A]488 [B]549 [C]586 [D]614

Laminar flow



____________________________________________________________________________________________________________________ Pg.No.190


Key Paper

1. C 2. C 3. A 4. C 5. C

6. A 7. B 8. C 9. C 10. C

11. B 12. D 13. D 14. A 15. B

16. D 17. C 18. A 19. D 20. B

21. D 22. A 23. B 24. B 25. D

Laminar flow



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A syringe with a frictionless plunger contains water and has at its end a 100 mm long needle of 1 mmdiameter. The internal diameter of the syringe is 10 mm. Water density is . The plunger is pushedin at 10 mm/s and the water comes out as a jet

1)Assuming ideal flow the force F in newtons required on the plunger to push out the water is

[A]0 [B]0.04[C]0.13 [D]1.15

2)Neglect losses in the cylinder and assume fully developed laminar viscous flow throughout the needle theDarcy friction factor is 64/Re. Where Re is the Reynolds number. Given that the viscosity of water

, the force F in newtons required on the plunger is

[A]0.13 [B]0.16[C]0.3 [D]4.4

3)Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of length 500 m.The volumetric flow rate is 0.2 /s. The head loss (in m) due to friction is (assume g = 9.81 m/ )

[A]116.18 [B]0.116[C]18.22 [D]232.36

4)The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is

given by the expression where is a constant. The average velocity of fluid inthe pipe is

[A] [B]

[C] [D]

5)A siphon draws water from a reservoir and discharges it out at atmospheric pressure. Assuming ideal fluidand the reservoir is large, the velocity at the point P in the siphon tube is (See Figure)

[A] [B]

Turbulent flow



____________________________________________________________________________________________________________________ Pg.No.192







[C] [D]6) Prandtl's mixing length in turbulent flow signifies

[A] the average distance perpendicular to the meanflow covered by the mixing particles.

[B] the ratio of mean free path to characteristic lengthof the flow field.

[C]the wavelength corresponding to the lowestfrequency present in the flow field. [D]the magnitudeof turbulent kinetic energy.

7)The Reynolds number for flow of a certain fluid in a circular tube is specified as- 2500. What will be theReynolds number when the tube diameter is increased by 20% and the fluid velocity is decreased by 40%keeping fluid the same ?

[A]1200 [B]1800[C]3600 [D]200

8)The discharge velocity at the pipe exit in fig. is

[A] [B][C] [D]0

9)For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, thepressure drop over a length L and the wall shear stress are related by

[A] [B]

[C] [D]

10)If velocity of water inside a smooth tube is doubled, then turbulent flow heat transfer coefficient betweenthe water and the tube will

[A] remain unchanged [B] increase to double its value[C]increase but will not reach double its value [D]increase to more than double its value


11)Consider a steady incompressible flow through a channel as shown below

The velocity profile is uniform with a value of at the inlet section A. The velocity profile at section Bdownstream is

The ratio is

Turbulent flow



____________________________________________________________________________________________________________________ Pg.No.193




.

[A] [B]1[C] [D]

12)The ratio ( Where and are the pressures at sections A and B, respectively, and is the densityof the fluid) is

[A] [B]

[C] [D]

Turbulent flow



____________________________________________________________________________________________________________________ Pg.No.194


Key Paper

1. B 2. C 3. A 4. A 5. C

6. A 7. B 8. B 9. A 10. C

11. A 12. C

Turbulent flow



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1)The flow of glycerin (kinematic viscosity ) in an open channel is to be modeled in alaboratory flume using water ( ) as the flowing fluid. If both gravity and viscosity are important,what should be the length scale (i.e. ratio of prototype to model dimensions) for maintaining dynamicsimilarity.

[A]1 [B]22[C]63 [D]500

2)A river reach of2.0km long with maximum flood discharge of 10000 Is is to be physically modeled in thelaboratory where maximum available discharge is 0.20 /s.For a geometrically similar model based onequality of Froude number ,the length of the river reach (m) in the model is

[A]26.4 [B]25.0[C]20.5 [D]18.0

3)A 1:50 scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 1000 The discharge to be maintained in the model test is

[A] [B][C] [D]

4)A flat plate is kept in an infinite fluid medium .The fluid has a uniform free-stream velocity parallel to theplate. For the la minar boundary layer formed on the plate, pick the correct option matching Columns I andII. Column-I Column-IIP. Boundary layer thickness 1. decreases in the flow directionQ. Shear stress at the plate 2. Increases in Lhe flow directionPressu re gradient along the plate 3. remains unchangedCodes: P Q R

[A]1 2 3 [B]2 2 2[C]1 1 1 [D]2 1 3

5)A laboratory model of a river is built to a geometric scale of 1:100. The fluid used in the model is oil ofmass density . The highest flood in the river is . The corresponding discharge in themodel shall be

[A] [B][C] [D]

6)Velocity distribution in a boundary layer flow over a plate is given by where, is thedistance measured normal to the plate; is is the boundary layer thickness;and is the maximum velocityat .if the shear stress ,acting on the plate is given by where, is the dynamic viscosityof the fluid,K takes the value of

[A]0 [B]1[C]1.5 [D]none of the above

7)In a 1/50 model of a spillway, the discharge was measured to be 0.3 /see, The corresponding prototypedischarge in /sec is

[A]2.0 [B]15.0[C]106.0 [D]5303.0

8)Both Reynolds and Froude numbers assume significance in one of following examples:

[A]Motion of submarine at large depths [B]Motion of ship in deep seas[C]Cruising of a misssile in air [D]Flow over spillways

9)The settlement of prototype in granular material may be estimated using plate load test data from thefollowing expression:

[A] [B]

Boundary layer



____________________________________________________________________________________________________________________ Pg.No.196







.

[C] [D]

10)if x is the distance measured from the leading edge of a flat plate, then laminar boundary layer thicknessvaries as

[A]1 / x [B][C] [D]

11)Flow separation in flow past a solid object is caused by

[A]a reduction of pressure to vapour pressure [B]a negative pressure gradient[C]a positive pressure gradient [D]the boundary layer thickness reducing to zero.

12)An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by afactor of 4, then the boundary layer thickness at the same location, in mm will be

[A]4 [B]2[C]0.5 [D]0.25


13)A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at U = 10 m/s. (SeeFigure)

The thickness of the boundary layer at section r-s is 10 mm, the breadth of the plate is 1 m (into the paper)and the density of the gas p = 1.0 kg/ . Assume that the boundary layer is thin, two-dimensional, andfollows a linear velocity distribution, u = U(y/ ), at the section r-s, where y is the height from plate. Themass flow rate (in kg/s) across the section q-r is

[A]zero [B]0.05[C]0.10 [D]0.15

14)The integrated drag force (in N) on the plate, between p-s, is

[A]0.67 [B]0.33[C]0.17 [D]zero

Boundary layer



____________________________________________________________________________________________________________________ Pg.No.197


Key Paper

1. C 2. D 3. A 4. B 5. B

6. B 7. D 8. D 9. A 10. D

11. C 12. C 13. B 14. C

Boundary layer



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. 2 Marks GATE-CE-2008,GATE-CE-2008,GATE-CE-2008( )










A rectangular channel6.0m wide carries a discharge of 16.0 under unifonn condition with normal depthof 1.60m. Manning 's n is 0.015.

1)The longitudinal slope of the channel is

[A]0.000585 [B]0.000485[C]0.000385 [D]0.000285

2)A hump is to be provided on the channel bed. The maximum height of the hump without affecting theupstream flow condition is

[A]0.50 m [B]3.8 m[C]4.1 m [D]4.5 m

3)The channel width is to be contracted. The minimum width to which the channel can be contracted withoutaffecting the upstream flow condition is

[A]3.0 m [B]3.8 m[C]4.1 m [D]4.5 m

4)Critical depth at a section of a rectangular channel is 1.5 m. The specific energy at that section is

[A]5m [B]8m[C]12m [D]12.8m

5)There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is lessthan the normal depth. What gradually varied flow profile will occur in the channel for this flow rate?

[A] [B][C] [D]

6)For a pipe of radius, r, flowing half full under the action of gravity, the hydraulic depth is

[A] r [B] r/4[C]r/2 [D]0.379 r

7)A steady flow occurs in an open channel with lateral inflow of q /s per unit width as shown in the figure.The mass conservation equation is

[A]dq/dx = 0 [B]dQ/dx = 0[C] [D]

8)The height of a hydraulic jump in the stilling pool of 1.25 scale model was observed to be 10 cm. Thecorresponding prototype height of the jump is

[A]not determinable from the data given [B]2.5 m[C]0.5 m [D]0.1 m

9)A triangular open channel has a vertex angle of and carries flow at a critical depth of 0.30m. thedischarge in the channel is

[A] [B][C] [D]

Open Channel Flow



____________________________________________________________________________________________________________________ Pg.No.199












10)The flow rate in a wide rectangular open channel is per meter width. The channel bed slope is0.002. The Manning’s roughness coefficient is 0.012. The slope of the channel is classified as

[A]Critical [B]Horizontal[C]Mild [D]Steep

11)A hydraulic jump lakes place in a triangular channel of vertex angle ,as shown in figure.The discharge is and the pre-jump depth is 0.5 m. What will be the post-jump depth ? (Take )

[A]0.57 m [B]0.91 m[C]1.02 m [D]1.57 m

12)In a lined rectangular canal, the Froude number f incoming flow is 3.0. A hydraulic jump forms when itmeets the pool of water. The depth of flow after the jump formation is 1.51 m.Froude number of flow after the hydraulic jump is

[A]0.30 [B]0.71[C]0.41 [D]none of these

13)The sequent depth ratio of a hydraulic jump in a rectangular horizontal channel is10.30.The FroudeNumber at the beginning of the jump is

[A]5.64 [B]9.81[C]8.93 [D]7.83

14)Water flows at a depth of 0.1m with a velocity of 6m/s in a rectangular channel. The alternate depth is

[A]0.30 m [B]0.40 m[C]0.86 m [D]0.81 m

15)Water flows at a rate of in a rectangular channel 3 m wide. The critical depth of flow is

[A]1.13 m [B]2 m[C]1.45 m [D]1.04 m

16)In a river, discharge is 173 mp3/s; water surface slope"is 1 in 6000; and stage at the gauge station is 10.0m. If during a flood, the stage at the gauge station is same and the water surfae slope is 1 in 2000, theflood discharge in , is approximately

[A]371 [B]100[C]519 [D]300

17)The downstream end of long prismatic channel of mild slope ends in a pool created by a dam. Theresulting non-uniform water surface profile can be described as one of the following.

[A] profile ending in a hydraulic pump [B] profile that lies above normal depth line[C] profile that lies between critical and normal

depth lines.[D] profile that lies between critical and normal

depth lines.18)At the same mean velocity, the ratio of head loss per unit length for a sewer pipe flowing full to that for the

same pipe flowing half full would be

[A]2.0 [B]1.63[C]1.00 [D]0.61

19)A person standing on the bank of a canal drops a stone on the water surface. He notices that thedisturbance on the water in not traveling up-stream. This is because the flow in th e canal is

[A]sub-critical [B]super-critical

Open Channel Flow



____________________________________________________________________________________________________________________ Pg.No.200










[C]steady [D]uniform20)A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed

slope is 0.002. The channel is lined with smooth concrete (Manning’s n = 0.012). The hydraulic radius (inm) for a depth of flow of 3.0 m is

[A]20.0 [B]3.5[C]3.0 [D]2.1

21)A rectangular open channel of width 5.0 m is carrying a discharge of 100 /s. The Froude number of theflow is 0.8. The depth of flow (in m) in the channel is

[A]4 [B]5[C]16 [D]20

22)A mild-sloped channel is followed by a steep-sloped channel. The profiles of gradually varied flow in thechannel are

[A] [B][C] [D]

23)The flow in a rectangular channel is subcritical. If width of the channel is reduced at a certain section, thewater surface under no-choke condition will

[A]Drop at a downstream section [B]Rise at a downstream section[C]Rise at an downstream section [D]Not undergo any change

24)For a rectangular channel section, Group I lists geometrical elements and Group II gives proportions forhydraulically efficient section.

is the follow depth corresponding to hydraulically efficient section. The correct match of Group I withGroup II is

[A]P - 2 , Q - 4 , R - 1 , S - 3 [B]P - 3 , Q - 1 , R - 4 , S - 2 [C]P - 3 , Q - 4 , R - 1 , S - 2 [D]P - 3 , Q - 4 , R - 2 , S - 1

25)The Froude number of flown in a rectangular channel is 0.8. If the depth of flow is 1.5m, the critical depthis

[A]1.80m [B]1.56m[C]1.36m [D]1.29m

26)The top width and the depth of flow in a triangular channel were measured as 4 m and 1 m, respectively.The measured velocities on the centre line at the water surface, 0.2 m and 0.8 m below the surface are0.7 m/s, 0.6 m/s and 0.4 m/s, respectively. Using two-point method of velocity measurement, the discharge(in /s) in the channel is

[A]1.4 [B]1.2[C]1.0 [D]0.8

27)The flow in a horizontal, frictionless rectangular open channel is supercritical. A smooth hump is built onthe channel floor. As the height of hump is increased, choked condition is attained. With further increase inthe height of the hump, the water surface will

[A] rise at a section upstream of the hump [B]drop at a section upstream of the hump[C]drop at the hump [D]rise at the hump

Open Channel Flow



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28)Group-I contains dimensionless parameters and Group- II contains the ratios. Group-I Group-IIP. Mach Number 1. Ratio of inertial force and gravitational forceQ. Reynolds Number 2. Ratio of fluid velocity and velocity of soundR. Weber Number 3. Ratio of inertial force and viscous forceS. Froude Number 4. Ratio of inertial force and surface tension forceThe correct match of dimensionless parameters in Group- I with ratios in Group-II is:

[A]P-3, Q-2, R-4, S-1 [B]P-3, Q-4, R-2, S-1[C]P-2, Q-3, R-4, S-1 [D]P-1, Q-3, R-2, S-4

29)The normal depth in a wide rectangular channel is increased by 10%. The percentage increase in thedischarge in the channel is:

[A]20.1 [B]15.4[C]10.5 [D]17.2

30)For sub critical flow in an open channel, the control section for gradually varied flow profiles is

[A]at the downstream end [B]at the upstream end[C]at both upstream and downstream ends [D]at any intermediate section

31)The necessary and sufficient condition for a surface to be caued as a free surface is

[A]no stress should be acting on it [B] tensile stress acting on it must be zero[C]shear stress acting on it must be zero [D]no point on it should be under any stress

32)A channel with a mild slope is followed by a horizontal channel and then by a steep channel. Whatgradually varied flow profiles will occur?

[A] [B][C] [D]

33)Direct step method of computation for gradually varied flow is

[A]applicable to non-prismatic channels [B]applicable to prismatic channels[C]applicable to both prismatic and non-prismatic

channels[D]not applicable to both prismatic and non-prismatic

channels34)The depth of flow in an alluvial channel is 1.5 m. If critical velocity ratio is 1.1 and Manning 's n is 0.018,

the critical velocity of the channel as per Kennedy's method is

[A]0.713 m/s [B]0784 m/s[C]0.879 m/s [D]1.108 m/s

35)A rectangular open channel of width 4.5m is carrying a discharge of . The critical depth of thechannel is

[A]7.09m [B]3.69m[C]2.16m [D]1.31m

36)A hydraulic jump occurs in a rectangular, horizontal, frictionless channel. What would be the pre-jumpdepth if the discharge per unit width and the energy loss is 1 m?

[A]0.2 m [B]0.3 m[C]0.8 m [D]0.9 m

37)A very wide rectangular channel is designed to carry a discharge of 5 per meter width. The design isbased on the Manning's equation with the roughness coefficient obtained from the grain size usingStrickler's equation and results in a normal depth of 1.0 m. By mistake, however, the engineer used thegrain diameter in mm in the Strickler's equation instead of in meter. What should be the correct normaldepth?

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.

[A]0.32 m [B]0.50 m[C]2.00 m [D]3.20 m

38)A horizontal bed channel is followed by a steep bed channel as shown in the figure. The gradually variedprofiles over the horizontal and steep beds are

[A] and respectively [B] and respectively[C] and respectively [D] and respectively

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Key Paper

1. A 2. B 3. C 4. D 5. B

6. B 7. B 8. B 9. B 10. C

11. D 12. C 13. B 14. B 15. A

16. D 17. D 18. A 19. B 20. D

21. A 22. B 23. C 24. B 25. B

26. C 27. B 28. C 29. D 30. A

31. A 32. D 33. B 34. B 35. B

36. B 37. B 38. A

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1)Identify the FALSE statement from the following: The specific speed of the pump increases with

[A] increase in shaft speed [B] increase in discharge[C]decrease in gravitational acceleration [D]increase in head

2)The allowable net positive suction head (NPSH) for a pump provided by the manufacturer for a flow of0.05 /s is 3.3 m.The temperature of water is ( vapour pressure head absolute = 0.44 m),atmospheric pressure is 100 kPa absolute and the head loss from the reservoir to pump is 0.3 N-m/N. Themaximum height of the pump above the suction reservoir is

[A]10.19 m [B]6.89 m[C]6.15 m [D]2.86 m

3)A pump can lift water at a discharge of to a head of 25 m. The critical cavitation number ( ) forthe pump is found to be 0.144. The pump is to be installed at a location where the barometric pressure is 9.8 m of water and the vapour pressure of water is 0.30 of water. The intake pipe friction loss is 0.40 m.Using he minimum value of NPSH (Net Positive Suction Head), the maximum allowable elevation abovethe sump water surface at which the pump can be located is

[A]9.80 m [B]6.20 m[C]5.50 m [D]none of the above

4)the pump head is 75m, discharge is and the motor speed is 1440 rpm at rated condition, thespecific-speed of the pump is about

[A]4 [B]26[C]38 [D]1440

5)A hydraulic turbine has a discharge of , when operating under a head of 20 m with a speed of 500rpm.If it is to operate under a head of 15m,for the same discharge, the rotational speed in rpm willapproximately be

[A]433 [B]403[C]627 [D]388

6)A hydraulic turbine develops a power on metric horse power while running at a speed of 100revolutions per minute, under a head of 40 m. Its specific speed is nearst to one of the following:

[A]100 [B]628[C]523 [D]314

7)The following is the arrangement of rotary pumps in descending order of specific speed at their bestefficiency:

[A]positively displacement, centrifugal, axial [B]centrifugal, positive displacement, axial[C]axial, centrifugal, positive displacement [D]axial, positive displacement, centrifugal

8)The theoretical mechanical efficiency of a jet engine (neglecting frictional and thermal losses), whendriving a vehicle, has its maximum

[A]only when the vehicle moves at sonic velocity [B]when outlet gases approach zero absolutevelocity

[C]when the vehicle speed approaches themagnitude of the relative velocity of gases atnozzle exit.

[D]only when the relative velocity at nozzle exit is atits maximum

9)Jet pumps are often used in process industry for their

[A]high efficiency [B]easy maintenance

[C]large capacity [D]capacity to transport gases, liquids and mixturesof both

10)Cavitation in a hydraulic turbine is most likely to occur at the turbine

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[A]entry [B]exit[C]stator exit [D]rotor exit

11)Specific speed of a Kaplan turbine ranges between


12)For a single stage impulse turbine with a rotor diameter of 2 m and a speed of 3000 rpm when the nozzleangle is , the optimum velocity of steam in m./s is

[A]334 [B]356[C]668 [D]711

13)The specific speed of a centrifugal compressor is generally

[A]higher than that of an axial compressor [B] less than that of a reciprocating compressor[C]independent of the type of compressor, but

depends only on the size of the compressor[D]more than the specific speed of the reciprocating

compressor but less that of the axial compressor.14)Kaplan turbine is

[A]a high head mixed flow turbine [B]a low head axial flow turbine[C]an outward flow reaction turbine [D]an impulse inward flow turbine.

15)If and are the nozzle exit velocity and nozzle angle in an impulse turbine, the optimum blade velocity isgiven by

[A] [B][C] [D]

16)In order to have maximum power from a Pelton turbine, the bucket speed must be

[A]equal to the jet speed. [B]equal to half of the jet speed.[C]equal to twice the jet speed. [D]independent of the jet speed.

17)Which of the following is a pressure compounded turbine ?

[A]parsons [B]Curtis[C]Rateau [D]all the three

18)When the speed of a centrifugal pump is doubled, then power required to drive the pump will

[A] increase 8 times [B] increase 4 times[C]double [D]remains the same.

19)The Rateau turbine belongs to the category of

[A]pressure compounded turbine [B] reaction turbine[C]velocity compounded turbine [D]redial flow turbine

20)Match the following:P curtis 1 Reaction steam turbineQ rateau 2 Gas turbineR Kaplan 3 velocity compoundingS Francis 4 pressure compounding

5 impulse water turbine6 Axial Turbine7 Mixed flow turbine8 Centrifugal pump

[A]P-2, Q-1, R- 7, S-6 [B]P-3, Q-1, R-5, S-7

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[C]P-1, Q-3, R-1, S-5 [D]P-3, Q-4, R-7, S-6.21)A centrifugal pump running at 500 rpm and at its maximum efficiency is delivering a head of 30 m at a flow

rate of 60 liters per minute. If the rpm is changed to 1000, then the head If in metres and flow rate Q inlitres per minute at maximum efficiency are estimated to be

[A]H=60, Q=120 [B]H=120, Q=120[C]H=60, Q=480 [D]H=120, Q=30

22)A hydraulic turbine develops 1000 kW power for a head of 40 m. If the head is reduced to 20 m, the powerdeveloped (in kW) is

[A]177 [B]354[C]500 [D]707

23)A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the density of the liquid as . The isentropic specific work done by the pump in kJ/kg is

[A]0.10 [B]0.30[C]2.50 [D]2.93

24)A centrifugal pump is required to pump water to an open water tank situated 4 km away from the locationof the pump through a pipe of diameter 0.2 m having Darcy's friction factor .of 0.01. The average speed ofwater in the pipe of 2 m/s. If it is to maintain a constant head of 5 m in the tank, neglecting other minorlosses, then absolute discharge pressure at the pump exit is


25)At a hydro electric power plant site, available head and flow rate are 24.5 m and 10.1 /s respectively. Ifthe turbine to be installed is required to run at 4.0 revolution per second (rps) with an overall efficiency of90%, then suitable type of turbine for this site is

[A]Francis [B]Kaplan[C]Pelton [D]Propeller

26)Match the following:P. Reciprocating 1. Plant with power output pump below 100 kWQ. Axial flow pump 2. Plant with power output between 100 kW to I MWR. Microhydel plant 3. Positive displacementS. Backward curved vanes 4. Draft tube

5. High flow rate, low pressure ratio6. Centrifugal pump impeller

[A]P-3 Q-5 R-6 S-2 [B]P-3 Q-5 R-2 s-6[C]P-3 Q-5 R-1 s-6 [D]P-4 Q-5 R-1 S-6.

27)In a Pelton wheel, the bucket peripheral speed is 10 m/s, the water jet velocity is 25 m/s and volumetricflow rate of the jet is 0.1 /s. If the jet deflection angle is

and the flow is ideal, the power developed is

[A]7.5 kW [B]15.0 kW[C]22.5 kW [D]37.5 kW

28)A large hydraulic turbine is to generate 300 kW at 1000 rpm under a head of 40 m. For initial testing, a 1 :4 scale model of the turbine operates under a head of 10 m. The power generated by the model (in kW)will be

[A]2.34 [B]4.68[C]9.38 [D]18.75

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29)A horizontal-shaft centrifugal pump lifts water at . The suction nozzle is one meter below pumpcenterline. The pressure at this point equals 200 kPa gauge and velocity is 3 m/s. Steam tables showsaturation pressure at is 25 kPa, and specific volume of the saturated liquid is 0.001020 /hg. Thepump Net Positive Suction Head (NPSH) in meters is (See Figure)

[A]24 [B]26[C]28 [D]30

30)In the velocity diagram shown in Fig. u = blade velocity, c = absolute fluid velocity and w = relativevelocity of fluid and the subscripts 1and 2 refer to inlet and outlet.

[A]an impulse turbine [B]a reaction turbine[C]a centrifugal compressor [D]an axial flow compressor

31)The inlet angle of runner blades of a Francis turbine is . The blades are so shaped that the tangentialcomponent of velocity at blade outlet is zero. The flow velocity remains constant through out the bladepassage and is equal to half of the blade velocity at runner inlet. The blade efficiency of the runner is

[A]25 % [B]50 %[C]80 % [D]89 %

32)Water, having a density of 1000 kg/ , issues from a nozzle with a velocity of 10 m/s and the jet strikes abucket mounted on a Pelton wheel. The wheel rotates at 10 rad/s. The mean diameter of the wheel is 1 m.The jet is split into two equal streams by the bucket, such that each stream is deflected by , as shownin the Figure. Friction in the bucket may be neglected. Magnitude of the torque exerted by the water on thewheel, per unit mass flow rate of the incoming jet, is

[A]0 (N.m)/(kg/s) [B]1.25 (N.m)/(kg/s)[C]2.5 (N.m)/(kg/s) [D]3.75 (N.m)/(kg/s).

33)A model of a hydraulic turbine is tested at a head of 1/4th of that under which the full scale turbine works.The diameter of the model is half of that of the full scale turbine. If N is the RPM of the full scale turbine,then the RPM of the model will be

[A]N/4 [B]N/2[C]N [D]2N

34)Match the items in Columns I and II.Column I Column IIP: Centrifugal compressor 1. Axial flowQ : Centrifugal pump 2. SurgingR : Pelton wheel 3. PrimingS : Kaplan turbine 4. Pure impulse

[A]P-2, Q-3,.R-4, S-1 [B]P-2, Q-3,.R-1, S-4[C]P-3, Q-4, R-1, S-2 [D]P-L,Q-2, R-3, S-4.

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Key Paper

1. D 2. C 3. A 4. C 5. A

6. A 7. C 8. C 9. D 10. D

11. C 12. C 13. D 14. B 15. D

16. B 17. C 18. B 19. A 20. D

21. B 22. B 23. D 24. B 25. A

26. C 27. C 28. A 29. A 30. B

31. C 32. D 33. C 34. A

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Index- Production Planning and Control

Sl.No. Name of the Topic Pg.No.s 1. Casting 211-214 2. Welding 215-218 3. Metal Cutting 219-224 4. Metal Forming 225-228 5. Sheet Metal Operation 229-231 6. Metrology 232-236 7. Machining 237-241 8. Advanced machine Methods 242-244 9. Nontraditional Machining Methods 245-248









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1)In a green-sand moulding process, uniform ramming leads to

[A] less chance of gas porosity [B]uniform flow of molten metal into the mould cavity[C]greater dimensional stability of the casting [D]less sand expansion type of casting defect

2)Centrifugally cast products have

[A] large grain structure with high porosity [B] fine grain structure with high density

[C]fine grain structure with low density [D]segregation of slug towards the outer skin of thecasting

3)Light impurities in the molten metal are prevented from reaching the mould cavity by providing a

[A]strainer [B]button well[C]skim bob [D]all of the above

4)Chills are used in moulds to

[A]achieve directional solidification [B] reduce the possibility of blow holes[C]reduce freezing time [D]smoothen metal flow for reducing splatter.

5)A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same material,which is 8 times heavier than the original casting, will be

[A]10 [B]20[C]24 [D]40

6)Which of the following materials requires the largest shrinkage allowance, while making a pattern forcasting ?

[A]Aluminum [B]Brass[C]cast iron [D]plain Carbon steel

7)The primary purpose of a sprue in a casting mould is to

[A] feed the casting at a rate consistent with the rateof solidification [B]act as a reservoir for molten metal

[C]feed molen metal from the pouring basin to thegate

[D]help feed the casting until all solidification takesplace.

8)Shrinkage allowance on pattern is provided to compensate for shrinkage when

[A] the temperature of liquid metal drops frompouring to freezing temperature

[B] the metal changes from liquid to solid state atfreezing temperature

[C]the temperature of solid phase drops fromfreezing to room temperature

[D]the temperature of metal drops from pouring toroom temperature.

9)In centrifugal casting, the impurities are

[A]uniformly distributed [B] forced towards the outer surface[C]trapped near the mean radius of the casting [D]collected at the centre of the casting.

10)The height of the down-square is 175 mm and its cross-sectional area at the base is . The cross-sectional area of the horizontal runner is also . Assuming no losses, indicate the correct choice forthe time (in seconds) required to fill a mold cavity of volume (Use ).

[A]2.67 [B]8.65[C]26.72 [D]84.50

11)Hardness of green sand mould increases with

[A] increase in moisture content beyond 6 percent [B] increase in permeability

[C]decrease in permeability [D]increase in both moisture content andpermeability.

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12)With a solidification factor of 0.97 x s/ , the solidification time (in seconds) for a spherical casting of200 mm diameter is

[A]539 [B]1078[C]4311 [D]3233

13)In a gating system, the ratio 1 : 2 : 4 represents

[A]sprue base area: runner area: ingate area[B]pouring basin area : ingate area : runner area

[C]sprue base area : ingate area : casting area [D]runner area : ingate area : casting area.14)Green sand mould indicates that

[A]polymeric mould has been cured [B]mould has been totally dried[C]mould is green in colour [D]mould contains moisture

15)Two streams of liquid metal, which are not hot enough to fuse properly, result into a casting defect knownas

[A]cold shut [B]swell[C]sand wash [D]scab

16)A cubic casting of 50 mm side undergoes volumetric solidification shrinkage and volumetric solidcontraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The sideof the cube after solidification and contraction is

[A]48.32 mm [B]49.90 mm[C]49.94 mm [D]49.96 mm

17)Misrun is a casting defect which occurs due to

[A]very high pouring temperature of the metal [B] insufficient fluidity of the molten metal[C]absorption of gases by the liquid metal [D]improper alignment of the mould flasks,

18)Gray cast iron blocks 200 x 100 x 10 mm are to be cast in sand moulds. Shrinkage allowance for patternmaking is 1%. The ratio of the volume of pattern to that of the casting will be

[A]0.97 [B]0.99[C]1.01 [D]1.03

19)Match the items of List-I (Equipment) with the items of List-II (Process) and select the correct answer usingthe given codes.List I (Equipment) List II (Process)P-Hot Chamber Machine 1. CleaningQ-Muller 2. Core makingR-Dielectric baker 3.Die castingS-Sand blaster 4.Annealing

5.sand mixing


20)An expendable pattern is used in

[A]slush casting [B]squeeze casting[C]centrifugal casting [D]investment casting.

21)A mould has a downsprue whose length is 20 cm and the cross-sectional area at the base of thedownsprue is . The downsprue feeds a horizontal runner leading into the mould cavity of volume

.The time required to fill the mould cavity will be

[A]4.05 s [B]5.05 s[C]6.05s [D]7.25s

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.

22)In a sand casting operation, the total liquid head is maintained constant such that it is equal to the mouldheight. The time taken to fill the mould with a top gate is . If the same mould is filled with a bottom gate,then the time taken is . Ignore the time required to fill the runner and frictional effects. Assumeatmospheric pressure at the top molten metal surfaces. The relation between and is

[A] [B][C] [D]

23)Volume of a cube of side 'l' and, volume of a sphere of radius'r' are equal. Both the cube and the sphereare solid and of same material. They are being cast. The ratio of the solidification time of the cube to thetime of the sphere is

[A] [B][C] [D]

24)While cooling, a cubical casting of side 40 mm undergoes 3%, 4% and,5% volume shrinkage during theliquid state, phase transition and solid state, respectively. The volume of metal compensated from the riseris

[A]2% [B]7%[C]8% [D]9%

25)The process utilizing mainly thermal energy for removing material is

[A]USM [B]ECM[C]AJM [D]LBM

26)A cylindrical riser of dia. ‘d’, height ‘h’ is situated at the top of casting and casting is of close type sandmold. Assume riser has constant volume, forthe least rate of solidification h : d will be

[A]1 : 2 [B]2 : 1[C]1 : 4 [D]4 : 1

27)A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws showthe following frequencies of occurrence: 1 → 0.167; 2 → 0.167; 3 → 0.152; 4 → 0.166; 5 → 0.168; 6 → 0.180.We call this die

[A] irregular [B]biased[C]Gaussian [D]insufficient

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Key Paper

1. C 2. B 3. D 4. A 5. B

6. A 7. C 8. C 9. D 10. A

11. C 12. B 13. A 14. D 15. A

16. A 17. B 18. A 19. D 20. D

21. B 22. C 23. D 24. B 25. D

26. A 27. B

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1)For resistance spot welding of 1.5 mm thick steel sheets, the current required is of the order of

[A]10 A [B]100 A[C]1000 A [D]10000 A

2)In d.c. welding, the straight polarity (electrode negative) results in

[A] lower penetration [B] lower deposition rate[C]less heating of work piece [D]smaller weld pod

3)The electrodes used in arc welding are coated. This coating is not expected to

[A]provide protective atmosphere to weld [B]stabilize the arc[C]add alloying elements [D]prevents electrode from contamination

4)Match the CORRECT pairs.


5)For butt-welding 40 mm thick steel plates, when the expected quantity of such jobs is 5000 per month overa period of 10 years, choose the best suitable welding process out of the following available alternatives.

[A]Submerged arc welding [B]Oxy-acetylene gas welding[C]Electron beam welding [D]MIG welding

6)Which of the following are welding processes does not use consumable electrodes ?

[A]GMAW [B]GTAW[C]Submerged arc welding [D]none of these.

7)Two plates of the same metal having equal thickness are to be butt welded with electric arc. When theplate thickness changes, welding is achieved by

[A]adjusting the current [B]adjusting the duration of current[C]changing the electrode size [D]changing the electrode coating

8)The temperature of a carburising flame in gas welding is ............... that of a neutral or an oxidising flame.

[A] lower than [B]higher than[C]equal to [D]unrelated to.

9)Resistance spot welding is performed on two plates of 1.5 mm thickness with 6 mm diameter electrode,using 15000 A current for a time duration of 0.25 seconds. Assuming the interface resistance to be ,the heat generated to form the weld is

[A]5625 W-sec [B]8437 W-sec[C]22500 W-sec [D]33750 W-sec

10)In Oxyacetylene gas welding, temperature at the inner cone of the flame is around

[A] [B][C] [D]

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11)Match the following:Work material Type of joiningP Aluminium 1. Submerged Arc weldingQ Die Steel 2. SolderingR CopperWire 3. Thermit WeldingS Titanium sheet . 4. Atomic hydrogen welding

5.Gas Tungsten Arc welding6. Laser Beam Welding

[A]P-2Q-5R-1S-3

[B]P-6Q-3R-4S-4

[C]P-4Q-1R-6S-2

[D]P-5Q-4R-2S-6

12)Two pipes of inner diameter 100 mm and outer diameter 110 mm each are joined by flash-butt weldingusing 30 V power supply. At the interface, 1mm of material melts from each pipe which has a resistance of42.4 . If the unit melt energy is 64.4 MJ , then time required for welding (in s) is

[A]1 [B]5[C]10 [D]20

13)In a DC arc welding operation, the voltage-arc length characteristic was obtained as = 20+5l where thearc length l was varied between 5 mm and 7 mm. Here denotes the arc voltage in Volts. The arc currentwas varied from 400 A to 500 A. Assuming linear power source characteristic, the open circuit voltage andthe short circuit current for the welding operation are

[A]45 V, 450 A [B]75 V, 750 A[C]95 V, 950 A [D]150 V, 1500 A

14) Which one among the following welding processes uses non-consumable electrode ?

[A]Gas metal arc welding [B]submerged arc welding[C]Gas tungstun arc welding [D]Fulx coated arc welding

15)Two 1 mm thick steel sheets are to be spot welded at a current of 5000 A. Assuming effective resistanceto be 200 micro-ohms and current flow time of 0.2 second, heat generated during the process will be

[A]0.2 Joule [B]1 Joule[C]5 Joule [D]1000 Joules

16)The strength of a brazed joint

[A]decreases with increases in gap between the twojoining surfaces

[B] increases with increase in gap between the twojoining surfaces

[C]decreases up to certain gap between the twojoining surfaces beyond which it increases

[D]increases up to certain gap between the twojoining surfaces beyond which it decreases.

17)Which among the NC operations given below are continuos path operations?Arc Welding (Aw) Milling (M)Drilling (D) Punching is Sheet Metal (P)Laser Cutting of Spot Welding (SW)Sheet Metal (LC)

[A]AW,LC and M [B]AW,D,LC and M[C]S,LC,P and SW [D]D,LC, and SW

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18)Spot welding of two 1 mm thick sheets of steel (density = ) is carried out successfully by passinga certain amount of current for 0.1 second through the electrodes. The resultant weld nugget formed is 5mm in diameter and 1.5 mm thick. If the latent heat of fusion of steel is 1400 kJ/kg and the effectiveresistance in the welding operation in the current passing through the electrodes is approximately

[A]1480 A [B]3300 A[C]4060 A [D]9400 A

19) A welding operation is time-studied during which an operator was pace-rated as 120%. The operator took,on an average, 8 minutes for producing the weld-joint. If a total of 10% allowances are allowed for thisoperation, the expected standard production rate of the weld-joint (in units per 8 hour day) is

[A]45 [B]50[C]55 [D]60

20)In an arc welding process, the voltage and current are 25 V and 300 A respectively. The arc heat transferefficiency is 0.85 and welding speed is 8 mm/sec. The net heat input (in J/mm) is

[A]64 [B]797[C]1103 [D]79700

21)Which one of the following is a solid state joining process ?

[A]gas tungsten arc welding [B] resistance spot welding[C]friction welding [D]submerged arc welding

22)In arc welding of a butt joint, the welding speed is to be selected such that highest cooling rate is achieved.Melting efficiency and heat transfer efficiency are 0.5 and 0.7, respectively. The area of the weld cross-section is 5 m and the unit energy required to melt the metal is 10 J/m . If the welding power is 2 kW,the welding speed in mm/s is closest to

[A]4 [B]14[C]24 [D]34

23)A direct current welding machine with a linear power source characteristic provides open circuit voltage of80 V and short circuit current of 800 A. During welding with the machine, the measured arc current is 500A corresponding to an arc length of 5.0 mm and the measured arc current is 460 A corresponding to anarc length of 7.0 mm. The linear voltage (E) - arc length (L) - characteristic of the welding arc can be givenas (where E is in Volt and L is in mm)

[A]E=20 + 2L [B]E = 20 + 8L[C]E = 80+2L [D]E= 80 + 8 L

24)Two metallic sheets, each of 2.0 mm thickness, are welded in a lap joint configuration by resistance spotwelding at a welding current of 10 kA and welding time of 10 millisecond. A spherical fusion zoneextending up to the full thickness of each sheet is formed. The properties of the metallic sheets are givenas :Ambient temperature = 293 KMelting temperature = 1793 KLatent heat of fusion = 300 KJ/kgDensity = 7000 Specific heat = 800 J/kg K.Assume:(i) Contact resistance along sheet-sheet interface is 500 micro-ohm and along electrode-sheet interface iszero ;(ii) no conductive heat loss through the bulk sheet materials ; and (iii) the complete weld fusion zone is at the melting temperature.The melting efficiency (in %) of the process is

[A]50.37 [B]60.37[C]70.37 [D]80.37

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Key Paper

1. D 2. B 3. D 4. A 5. B

6. B 7. A 8. A 9. A 10. A

11. D 12. C 13. C 14. C 15. D

16. D 17. B 18. C 19. A 20. B

21. C 22. B 23. A 24. C

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1)A milling cutter having 8 teeth is rotating at 150 rpm. If the feed per tooth is 0.1, the table speed in mm perminute is

[A]120 [B]187[C]125 [D]70

2)Cutting power consumption in turning can be significantly reduced by

[A] increasing rake angle of the tool [B] increasing the cutting angles of the tool[C]widening the nose radius of the tool [D]increasing the clearance angle.

3)Plain milling of mild steel plate produces

[A] irregular shaped discontinuous chips [B] regular shaped discontinuous chips[C]continuous chips without built up edge [D]jointed chips.

4)The rake angle in a drill

[A] increases from centre to periphery [B]decreases from centre to periphery[C]remains constant [D]is irrelevant to the drilling operation

5)In a typical metal cutting operation, using a cutting tool of positive rake , it was observed that theshear angle was . The friction angle is

[A] [B][C] [D]

6)A cutting tool has a radius of 1.8 mm. The feed rate for a theoretical surface roughness of is

[A]0.36 mm/rev [B]0.187 mm/rev[C]0.036 mm/rev [D]0.0187 mm/rev

7)A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. Therotational speed of the workpiece is 160 rpm. The material removal rate in m /s is

[A]160 [B]167.6[C]1600 [D]1675.5

8)Two cutting tools are being compared for a machining operation. The tool life equations are: Carbide tool: = 3000 HSS tool: = 200where V is the cutting speed in m/min and T is the tool life in min. The carbide tool will provide higher toollife if the cutting speed in m/min exceeds

[A]15.0 [B]39.4[C]49.3 [D]60.0

9)What is approximate percentage change in the life t, of a tool with zero rake angle used in orthogonalcutting when its clearance angle , is changed from to ?(Hint : Flank wear rate is proportional to )

[A]30% increase [B]30% decrease[C]70% increase [D]70% decrease

10)A slot is to be milled centrally on a block with a dimension of 40 0.05 mm. A milling cutter of 20 mm widthis located with reference to the side of the block within 0.02 mm. The maximum offset in mm between thecentre lines of the slot and the block is

[A] 0.070 [B]0..070[C] 0.020 [D]0.045

11)A lead-screw with half nuts in a lathe, free to rotate in both directions has

[A]V-threads [B]Whitworth threads[C]Buttress threads [D]Acme threads.

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12)Trepanning is performed for

[A] finishing a drilled hole [B]producing a large hole without drilling[C]truing a hole for alignment [D]enlarging a drilled hole.

13)The hardness of a grinding wheel is determined by the

[A]hardness of abrasive grains [B]ability of the bond to retain abrasives

[C]hardness of the bond [D]ability of the grinding wheel to penetrate the workpiece.

14)A built-up-edge is formed while machining

[A]ductile materials at high speed [B]ductile materials at low speed[C]brittle materials at high speed [D]brittle materials at low speed.

15)The time taken to drill a hole through a 25 mm thick plate with the drill rotating at 300 r.p.m. and moving ata feed rate of 0.25 mm/revolution is

[A]10 sec [B]20 sec[C]60 sec [D]100 sec

16)During orthogonal cutting of mild steel with a rake angle tool, the chip thickness ratio was obtained as0.4. The shear angle (in degrees) evaluated from this data is

[A]6.53 [B]20.22[C]22.94 [D]50.00

17)Details pertaining to an orthogonal metal cutting process are given below.Chip thickness ratio 0.4Undeformed thickness 0.6 mmRake angleCutting speed 2.5 m/sMean thickness of primary shear zone 25 micronsThe shear strain rate in during the process is

[A]0.1781 x [B]0.7754 x [C]1.0104 x [D]4.397 x

18)I n a single pass drilling operation, a through hole of 15 mm diameter is to be drilled in a steel plate of 50mm thickness. Drill spindle speed is 500 rpm, feed is 0.2 mm/rev and drill point angle is . Assuming 2mm clearance at approach and exit, the total drill time (in seconds) is

[A]35.1 [B]32.4[C]31.2 [D]30.1

19)Minimum shear strain in orthogonal turning with a cutting tool of zero rake angle is

[A]0.0 [B]0.5[C]1.0 [D]2.0

20)Match the items in Column I and Column II.


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21)A single-point cutting tool with 12° rake angle is used to machine a steel work-piece. The depth of cut, i.e.uncut thickness is 0.81 mm. The chip thickness under orthogonal machining condition is 1.8 mm. Theshear angle is approximately

[A] [B][C] [D]

22)Through holes of 10 mm diameter are to be drilled in a steel plate of 20 mm thickness. Drill spindle speedis 300 rpm, feed 0.2 mm/rev and drill point angle is . Assuming drill overtravel of 2 mm, the time forproducing a hole will be

[A]4 seconds [B]25 seconds[C]100 seconds [D]110 seconds

23)In a machining operation, doubling the cutting speed reduces the tool life to th of the original value. Theexponent n in Taylor's tool life equation V = C,is

[A]1/8 [B]1/4[C]1/3 [D]1/2

24)The Figure below shows a graph which qualitatively relates cutting speed and cost per piecs produced.

The three curves 1,2 and 3 respectively represent

[A]machining cost, non-productive cost, toolchanging cost

[B]non-productive cost, machining cost, toolchanging cost

[C]tool changing cost, machining cost, non-productive cost,

[D]tool changing cost, non-productive cost,machining cost.

25)A 600 mm x 30 mm flat surface of a plate is to be finish machined on a shaper. The plate has been fixedwith the 600 mm side along the tool travel direction. If the tool over-travel at each end of the plate is 20mm, average cutting speed ig 8 m/min, feed rate is 0.3 mm/ stroke and the ratio of return time to cuttingtime of the tool is 1:2, the time required for machining will be

[A]8 minutes [B]12 minutes[C]16 minutes [D]20 minutes

26)Internal gear cutting operation can be performed by

[A]milling [B]shaping with rack cutter[C]shaping with pinion cutter [D]hobbing.

27)In orthogonal turning of a low carbon steel bar of diameter 150 mm with uncoated carbide tool, the cuttingvelocity is 90 m/min. The feed is 0.24 mm/rev and the depth of cut is 2 mm. The chip thickness obtained is0.48 mm. If the orthogonal rake angle is zero and the principal cutting edge angle is , the shear angle indegree is

[A]20.56 [B]26.56[C]30.56 [D]36.56

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28)In a single point turning tool, the side rake angle and orthogonal rake angle are equal. is the principalcutting edge angle and its range is . The chip flows in the orthogonal plane. The value of isclosest to

[A] [B][C] [D]

29)The Figure shows an incomplete schematic of a conventional lathe to be used for cutting threads with,different pitches. The speed gear box is shown and the feed gear box is to be placed. P, Q, R and Sdenote locations and have no other significance. Changes in should NOT affect the pitch of the threadbeing cut and changes in should NOT affect the cutting speed. The correct connections and the correctplacement of are given by

[A]Q and E are connected. is placed between Pand Q.

[B]S and E are connected. is placed between Rand S.

[C]Q and E are connected. is placed between Qand E.

[D]S and E are connected. is placed between Sand E.

30)In electrodischarge machining (EDM), if the thermal conductivity of tool is high and the specific heat ofworkpiece is low, then the tool wear rate and material removal rate are expected to be respectively

[A]high and high [B] low and low[C]high and low [D]low and high

31)In orthogonal turning of medium carbon steel, the specific machining energy is 2.0 . The cuttingvelocity, feed and depth of cut are 120 m/min, 0.2 mm/rev and 2 mm respectively. The main cutting forcein N is

[A]40 [B]80[C]400 [D]800

32)In orthogonal turning of low carbon steel pipe with principal cutting edge angle of the main cutting forceis 1000 N and the feed force is 800 N. The shear angle is and orthogonal rake angle is zero. EmployingMerchant's theory, the ratio of friction force to normal force acting on the cutting tool is

[A]1.56 [B]1.25[C]0.80 [D]0.64


33)In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm andcutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to thefriction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N.

Q. The orthogonal rake angle of the cutting tool in degree is

[A]zero [B]3.58[C]5 [D]7.16

34)The normal force acting at the chip-tool interface in N is

[A]1000 [B]1500[C]2000 [D]2500

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35)A low carbon steel bar of 147 mm diameter with a length of 630 mm is being turned with uncoated carbideinsert. The observed tool lives are 24 min and 12 min for cutting velocities of 90 m/min and 120 m/minrespectively. The feed and depth of cut are 0.2 mm/rev and 2 mm respectively. Use the unmachineddiameter to calculate the cutting velocity.

When tool life is 20 min, the cutting velocity in m/min is

[A]87 [B]97[C]107 [D]114

36)Neglect over-travel or approach of the tool. When tool life is 20 min, the machining time in min for a singlepass is

[A]5 [B]10[C]15 [D]20


37)A cylindrical container of radius R = 1 m, wall thickness 1 mm is filled with water up to a depth of 2 m andsuspended along its upper rim. The density of water is 1000 kg/ and acceleration due to gravity is 10m/ . The self weight of the cylinder is negligible. The formula for hoop stress in a thin-walled cylinder canbe used at all points along the height of the cylindrical container. (See Figure)

The axial and circumferential stress ( , ) experienced by the cylinder wall at mid-depth (1 m as shown)are

[A] (10, 10) MPa [B] (5, 10) MPa[C](10, 5) MPa [D](5, 5) MPa

38)If the Young's modulus and Poisson's ratio of the container material are 100 GPa and 0.3, respectively ;the axial strain in the cylinder wall at mid-depth is

[A]2 x [B]6 x [C]7 x [D]1.2 x


39)Orthogonal turning is performed on a cylindrical workpiece with shear strength of 250 MPa. The followingconditions are used : cutting velocity is 180 m/min, feed is 0.20 mm/ rev, depth of cut is 3 mm, chipthickness ratio = 0.5. The orthogonal rake angle is 7'. Apply Merchant's theory for analysis.

The shear plane angle (in degrees) and the shear force respectively are

[A]52 : 320 N [B]565 N : 400 N[C]28 : 400 N [D]28 : 320 N

40)The cutting and frictional forces, respectively, are

[A]568 N ; 387 N [B]565 N ; 381 N[C]440 N ; 342 N [D]480 N; 356 N

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Key Paper

1. A 2. A 3. C 4. A 5. C

6. B 7. D 8. B 9. B 10. C

11. D 12. B 13. C 14. B 15. B

16. C 17. C 18. D 19. D 20. B

21. B 22. B 23. C 24. B 25. B

26. C 27. B 28. D 29. D 30. D

31. D 32. C 33. A 34. B 35. B

36. C 37. B 38. A 39. D 40. B

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1)The process of hot extrusion is used to produce

[A] (a) curtain rods made of aluminium [B]steel pipes for domestic water supply[C]stainless steel tubes used in furniture. [D]large size pipes used in citywater mains.

2)A wire of 0.1 mm diameter is drawn from a rod of 15 mm diameter. Dies giving reductions of 20%, 4OV%and, 80% are available. For minimum error in the final size, the number of stages and reduction at eachstage respectively would be

[A]3 stages and, 80% reduction for all three stages [B]4 stages and 80% reduction for first three stagesfollowed by a finishing stage of 20% reduction

[C]5 stages and reduction of 80%, 8O%, 40%,40%,2O% in a sequence [D]none of the above.

3)A strip with a cross-section 150 mm x 4.5 mm is being rolled with 20% reduction of area using 450 mmdiameter rolls. The angle subtended by the deformation zone at the roll centre is (in radian)

[A]0.01 [B]0.02[C]0.03 [D]0.06

4)In a rolling process, the state of stress of the material undergoing deformation is

[A]pure compression [B]pure shear[C]compression and shear [D]tension and shear

5)Identify the stress-state in the flange portion of a partially drawn cylindrical cup when deep-drawing withouta blank holder

[A]Tensile in all three directions [B]No stress in the flange at all, because there is noblank-holder

[C]Tensile stress in one direction and compressivein the other direction

[D]Compressive in two directions and tensile in thethird direction.

6)Hot rolling of mild steel is carried out

[A]at recrystallization temperature [B]between C to C[C]below recrystallization temperature [D]above recrystallization temperature

7)In a blanking operation, the clearance is provided on

[A] the die [B]both the die and the punch equally[C]the punch [D]brittle the punch nor the die.

8)For rigid perfectly-plastic work material negligible interface friction and no redundant work the theoreticallymaximum possible reduction in the wire drawing operation is

[A]0.36 [B]0.63[C]1.00 [D]2.72

9)A brass billet is to be extruded from its initial diameter of 100 mm to a final diameter of 50 mm. Theworking temperature of C and the extrusion constant is 250 MPa. The force required for extrusion is

[A]5.44 MN [B]2.72 MN[C]1.36 MN [D]0.36 MN

10)A threaded nut of M16, ISO metric t;rye, having 2 mm pitch with a pitch diameter of 14.701 mm is to bechecked for its pitch diameter using two or three numbers of balls or rollers of the following sizes

[A]Rollers of 2 mm [B]Rollers of 1.155 mm [C]Balls of 2 mm [D]Balls of 1.155 mm

Metal forming



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11)Match the following metal forming processes with their associated stresses in the workpiece.Metal forming process Type of stress1. Coining P. Tensile2. Wire Drawing Q. Shear3. Blanking R. Tensile and compressive4. Deep Drawing S. Compressive

[A]1-S, 2-P, 3-Q, 4-R [B]1-S, 2-P, 3-R, 4-Q[C]1-P, 2-Q, 3-S, 4-R [D]1-P, 2-R, 3-Q, 4-S

12)A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to aheight of 25 mm. The percentage change in diameter is

[A]0 [B]2.07[C]20.7 [D]41.4

13)In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and thickness8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is

[A]0.006 [B]0.031[C]0.062 [D]0.600

14)In a rolling process, sheet of 25 mm thickness is rolled to 20 mm thickness. Roll is of diameter 600 mmand it rotates at 100 rpm. The roll strip contact length will be

[A]5 mm [B]39 mm[C]78 mm [D]120 mm

15)Match the following:Product ProcessP. Molded luggage 1. Injection moldingQ. Packaging containers for liquid 2. Hot rollingR. Long structural shapes 3. Impact extrusionS. Collapsible tubes 4. Transfer molding

5. Blow molding6. Coining

[A]P-1 Q-4 R-6 S-3 [B]P-4 Q-5 R-2 S-3[C]P-1 Q-5 R-3 S-2 [D]P-5 Q-1 R-2 S-2.

16)In a wire drawing operation, diameter of a steel wire is reduced from 10 mm to 8 mm. The mean flowstress of the material is 400 MPa. The ideal force required for drawing (ignoring friction and redundantwork) is

[A]4.48 kN [B]8.97 kN[C]20.11 kN [D]31.41 kN

17)In a single pass rolling operation, a 20 mm thick plate with plate width of 100 mm, is reduced to 18 mm.The roller radius is 250 mm and rotational speed is 10 rpm. The average flow stress for the plate materialis 300 MPa. The power required for the rolling operation in kW is closest to

[A]15.2 [B]18.2[C]30.4 [D]45.6

18)In the deep drawing of cups, blanks show a tendency to wrinkle up around the periphery (flange). Themost likely cause and remedy of the phenomenon are, respectively,

[A]Buckling due to circumferential compression ;Increase blank holder pressure

[B]High blank holder pressure and high friction ;Reduce blank holder pressure and apply lubricant

[C]High temperature causing increase incircumferential length; Apply coolant to blank

[D]Buckling due to circumferential compression ;decrease blank holder pressure.

Metal forming



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19)In open-die forging, a disc of diameter 200 mm and height 60 mm is compressed without any barrellingeffect. The final diameter of the disc is 400 mm. The true strain is

[A]1.986 [B]1.686[C]1.386 [D]0.602

20)The thickness of a metallic sheet is reduced from an initial value of 16 mm to a final value of 10 mm in onesingle pass rolling with a pair of cylindrical rollers each of diameter of 400 mm. The bite angle in degreewill be

[A]5.936 [B]7.936[C]8.936 [D]9.936

21)Match the correct combination for following metal working processes :processes Associated state of stressP.Blanking 1. TensionQ.Stretch forming 2.CompressionR.Coining 3.ShearS.Deep drawing 4.Tension and compression 5.Tension and shear

[A]P - 2 ,Q -1 ,R -3 ,S-4 [B]P - 3,Q - 4,R - 1,S - 4[C]P -5,Q-4,R-3,s-4 [D]p-3,Q-1,R-2,S-4

22)A 200 mm long down sprue has an area of cross-section of where the pouring basin meets thedown sprue (i.e., at the beginning of the down sprue). A constant head of molten metal is maintained bythe pouring basin. The molten metal flow rate is . Considering the end of down sprue to beopen to atmosphere and an acceleration due to gravity of , the area of the down sprue in at itsend (avoiding aspiration effect) should be

[A]650.0 [B]350.0[C]290.7 [D]190.0

Metal forming



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Key Paper

1. C 2. D 3. D 4. C 5. C

6. D 7. C 8. B 9. B 10. B

11. A 12. D 13. C 14. B 15. B

16. B 17. A 18. A 19. C 20. D

21. D 22. C

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1)The thickness of the blank needed to produce, by power spanning a missile cone of thickness 1.5 mm andhalf cone angle 30°, is:

[A]3.0 mm [B]2.5 mm[C]2.0 mm [D]1.5 m

2) In deep drawing of sheets, the values of limiting draw ratio depends on

[A]percentage elongation of sheet metal [B]yield strengthof sheet metal[C]type of press used [D]thickness of sheet.

3)A 50 mm diameter disc is to punched out from a carbon steel sheet 1.0 mm thick. The diameter of thepunch should be

[A]49.925 mm [B]50.00 mm[C]50.075 mm [D]none of these

4)The cutting force in punching and blanking operations mainly depends on

[A] the modulus of elasticity of metal [B] the shear strength of metal[C]the bluk modulus of metal [D]the yield strength of metal.

5)A shell of 100 mm diameter and 100 mm height with the corner radius of 0.4 mm is to be produced by cupdrawing. The required blank diameter is

[A]118 mm [B]161 mm[C]224 mm [D]312 mm

6)A metal disc of 20 mm diameter is to be punched from a sheet of 2 mm thickness. The punch and the dieclearance is 30%. The required punch diameter is

[A]19.88 mm [B]19.94 mm[C]20.06 mm [D]20.12 mm

7)The maximum possible draft in cold rolling of sheet increases with the

[A] increase in coefficient of friction [B]decrease in coefficient of friction[C]decrease in roll radius [D]increase in roll velocity

8)Calculate the punch size in mm, for a circular blanking operation for which details are given below.Size of the blank 25 mmThickness of the sheet 2 mmRadial clearance between punch and die 0.06 mmDie allowance 0.05 mm

[A]24.83 [B]24.89[C]25.01 [D]25.17

9)The shear strength of a sheet metal is 300 MPa. The blanking force required to produce a blank of 100mm diameter from a 1.5 mm thick sheet is close to

[A]45 kN [B]70 kN[C]141 kN [D]3500 kN

10)10 mm diameter holes are to be punched in a steel sheet of 3 mm thickness. Shear strength of thematerial is 400 N/m and penetration is 40%. Shear provided on the punch is 2 mm. The blanking forceduring the operation will be

[A]22.6 kN [B]37.7 kN[C]61.6 kN [D]94.3 kN

Sheet metal operation



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11)A 2 mm thick metal sheet is to be bent at an angle of one radian with a bend radius of 100 mm. If thestretch factor is 0.5, the bend allowance is

[A]99 mm [B]100 mm[C]101 mm [D]102 mm

12)A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any charge in itswidth. The friction coefficient at the work-roll interface is 0.1. The. minimum possible thickness of the sheetthat can be produced in a single pass is

[A]1.0 mm [B]1.5 mm[C]2.5 mm [D]3.7 mm

13)The force requirement in a blanking operation oflow carbon steel sheet is 5.0 kN. The thickness of thesheet is 'f' and diameter of the blanked part is 'd'. For the same work material, if the diameter of theblanked part is increased to 1.5d and thickness is reduced to 0.4f, the new blanking force in kN is

[A]3.0 [B]4.5[C]5.0 [D]8.0


14)In shear cutting operation, a sheet of 5 mm thickness is cut along a length of 200 mm. The cutting blade is400 mm long (see Fig. 7) and zero-shear (S = 0) is provided on the edge. The ultimate shear strength ofthe sheet is 100 MPa and penetration to thickness ratio is 0.2. Neglect friction.

Fig. 7Assuming force vs displacement curve to be rectangular, the work done (in J) is

[A]100 [B]200[C]250 [D]300

15)A shear of 20 mm (S = 20 mm) is now provided on the blade. Assuming force vs displacement curve to betrapezoidal, the maximum force (in kN) exerted is

[A]5 [B]10[C]20 [D]40




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Key Paper

1. A 2. D 3. D 4. B 5. C

6. B 7. A 8. A 9. C 10. A

11. C 12. C 13. A 14. A 15. B




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1)In an orthogonal cutting test on mild steel, the following data were obtainedCutting speed : 40 m/minDepth of cut : 0.3 mmTool rake angle : + Chip thickness : 1.5 mmCutting force : 900 NThrust force : 450 NUsing Merchant's analysis, the friction angle during the machining will be

[A] [B][C] [D]

2)Two shafts A and B have their diameters specified as 100 ± 0.1 mm and 0.1 ± 0.0001 mm respectively.Which of the following statements is/are true?

[A]Tolerance in the dimension is greater in shaft A [B]The relative error in the dimension is greater inshaft A

[C]Tolerance in the dimension is greater in shaft B [D]The relative error in the dimension is same forshaft A and shaft B

3)A shaft (diameter ) and a hole (diameter ) when assembled would yield

[A] transition [B] interference fit[C]clearance fit [D]none of these

4)Three blocks , and , are to be inserted in a channel of width S maintaining a minimum gap of width T= 0.125 mm, as shown in Figure. For P = 18.75 0.08 ;Q = 25.00 0.12 ; R = 28.125 0.1 and S = 72.35 + X, (where all dimensions are in mm), the tolerance X is

[A]+0.38 [B] -0.38[C]+0.05 [D]-0.05

5)Auto collimator is used to check

[A] roughness [B] flatness[C]angle [D]automobile balance

6)Ideal surface roughness, as measured by the maximum height of unevennes, is best achieved when thematerial is removed by

[A]an end mill [B]a grinding wheel[C]a tool with zero nose radius [D]a ball mill

7)In the specification of dimensions and fits,

[A]allowance is equal to bilateral tolerance [B]allowance is equal to unilateral tolerance

[C]allowance is independent of tolerance[D]allowance is equal to the difference between

maximum and minimum dimension specified bythe tolerance.

8)Cylindrical pins of mm diameter are electroplated in a shop. Thickness of the plating is micron.Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is

[A]25.042 [B]25.052[C]25.074 [D]25.084

Metrology



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9)A fit is specified as 25 H8/e8. The tolerance value for a nominal diameter of 25 mm in IT8 is 33 micronsand fundamental deviation for the shaft is - 40 microns. The maximum clearance of the fit in microns is

[A] -7 [B]7[C]73 [D]106

10)Allowance in limits and fits refers to

[A]maximum clearance between shaft and hole [B]minimum clearance between shaft and hole[C]difference between maximum and minimum size

of hole[D]difference between maximum and minimum size

of shaft.11)The dimensional limits on a shaft of 25h7 are

[A]25.000,25.021mm [B]25.000, 24.979 mm[C]25.000, 25.007 mm [D]25.000,24.993 mm.

12)Two slip gauges of 10 mm width measuring 1.000 mm and 1.002 mm are kept side by side in contact witheach other length wise. An optical flat is kept resting on the slip gauges as shown in the Figure.Monochromatic light of wavelength 0.0058928 mm is used in the inspection. The total number of straightfringes that can be observed on both slip gauges is

[A]2 [B]6[C]8 [D]13

13)A shaft has a dimension .The respective values of fundamental deviation and tolerance are

[A] -0.025, 0.008 [B] -0.025, 0.016[C]-0.009, 0.008 [D]-0.009, 0.016

14)A taper hole is inspected using a CMM, with a·probe of 2 mm diameter. At a height, Z = 10 mm from thebottom, 5 points are touched and a diameter of circle (not compensated for probe size) is obtained as 20mm. Similarly, a 40 mm diameter is obtained at a height Z = 40 mm. The smaller diameter (in mm) of holeat Z = 0 is (See Fig. 5)

Fig. 5

[A]13.334 [B]15.334[C]15.442 [D]15.542

15)In an interchangeable assembly, shafts of size mm mate with holes of size mm. Themaximum interference (in microns) in the assembly is

[A]40 [B]30[C]20 [D]10

16) A hole is of dimension . The corresponding shaft is of dimension . The resultingassembly has

[A] loose running fit [B] transition fit[C]close running fit [D]interference fit

Metrology



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17)What are the upper and lower limits of the shaft represented by 60 ?Use the following data:Diameter 60 lies in the diameter step of 50-80mmFundamental tolerance unit, i, in =0.45 +0.001D, where D is the representative size in mm;Tolerance value for IT8=25i. Fundamental deviation for ‘f’ shaft = -5.5

[A]Lower limit = 59.924mm, Upper Limit =59.970mm

[B]Lower limit = 59.954mm, Upper Limit =60.000mm

[C]Lower limit = 59.970mm, Upper Limit =60.016mm

[D]Lower limit = 60.000mm, Upper Limit =60.046mm

18)In an interchangeable assembly, shafts of size mm mate with holes of size mm. Themaximum possible clearance in the assembly will be

[A]10 microns [B]20 microns[C]30 microns [D]60 microns.

19)GO and NO-GO plug gages are to be designed for a hole mm. Gage tolerances can be taken as10% of the hole tolerance. Following ISO system of gage design, sizes of GO and NO-GO gage will berespectively

[A]20.010 mm and 20.050 mm [B]20.014 mm and 20.046 mm[C]20.006 mm and 20.054 mm [D]20.014 mm and 20.054 mm.

20)Match the following:Feature to be inspected Instrument.P. Pitch and Angle errors of screw thread 1. Auto CollimatorQ. Flatness error of surface plate 2. Optical InteraferometerR. Alignment error of a machine and Dial Gauge slideway 3. Dividing HeadS, Profile of a cam 4. Spirit Level

5. Sine bar6. Tool Maker's Microscope


21)In order to have interference fit, it is essential that the lower limit of the shaft should be

[A]greater than the upper limit of the hole [B] lesser than the upper limit of the hole[C]greater than the lower limit of the hole [D]lesser than the lower limit of the hole

22)Two tools P and Q have signatures and (both ASA)respectively. They are used to turn components under the same machining conditions. If and denotethe peak-to-valley heights of surfaces produced by the tools P and Q the ratio / will be

[A] [B][C] [D]

23)For generating a Coon's surface we require

[A]a set of grid points on the surface [B]a set of grid control points

[C]four bounding curves defining the surface [D]two bounding curves and a set of grid controlpoints.

Metrology



____________________________________________________________________________________________________________________ Pg.No.234






.

24)A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel mounted on thetaper hole inside a drill spindle. The mandrel axis is an extension of the drill spindle taper hole axis and theprotruding portion of the mandrel surface is perfectly cylindrical. Measurements are taken with the sensorplaced at two positions P and Q as shown in the Figure. The readings are recorded as = maximumdeflection minus minimum deflection, corresponding to sensor position at X over one rotation.

If = >0, which one of the following would be consistent with the observation ?

[A]The drill spindle rotational axis is coincident withthe drill spindle taper hole axis

[B]The drill spindle rotational axis intersects the drillspindle taper hole axis at point P

[C]The drill spindle rotational axis is parallel to thedrill spindle taper hole axis

[D]The drill spindle rotational axis intersects the drillspindle taper hole axis at point Q.

25)A hole is specified . The mating shaft has a clearance fit with minimum clearance of 0.01 mm.The tolerance on the shaft is 0.04 mm. The maximum clearance in mm between the hole and the shaft is

[A]0.04 [B]0.05[C]0.10 [D]0.11

26)Which one of the following instruments is widely used to check and calibrate geometric features ofmachine tools during their assembly?

[A]Ultrasonic probe [B]Coordinate Measuring Machine (CMM)[C]Laser interferometer [D]Vernier calipers

27)For the given assembly: 25 H7/g8, match Group A with Group B

[A]P-I, Q-III, R-IV, S-II [B]P-I, Q-IV, R-III, S-II[C]P-II, Q-III, R-IV, S-I [D]P-II, Q-IV, R-III, S-I

Metrology



____________________________________________________________________________________________________________________ Pg.No.235


Key Paper

1. B 2. A 3. C 4. D 5. C

6. C 7. C 8. D 9. D 10. A

11. D 12. B 13. D 14. A 15. C

16. C 17. A 18. C 19. B 20. B

21. A 22. B 23. C 24. C 25. C

26. C 27. D

Metrology



____________________________________________________________________________________________________________________ Pg.No.236


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In an orthogonal machining operation :Uncut thickness = 0.5 mmCutting speed = 20 m/minRake angle = Width of cut = 5 mmChip thickness = 0.7 mmThrust force = 200 NCutting force = 1200 NAssume Merchant's theory.

1)The values of shear angle and shear strain, respectively, are

[A] and 1.98 [B] and 4.23[C] and 2.97 [D] and 1.65

2)The coefficient of friction at the tool-chip interface is

[A]0.23 [B]0.46[C]0.85 [D]0.95

3)The percentage of total energy dissipated due to friction at the tool-chip interface is

[A]30 % [B]42%[C]58% [D]70%


A cylinder is turned on a lathe with orthogonal machining principle. Spindle rotates at 20O rpm. The axialfeed rate is 0.25 mm per revolution. Depth of cut is 0.4 mm. The rake angle is . In the analysis it isfound that the shear angle is .

4)The thickness of the produced chip is

[A]0.511 mm [B]0.528 mm[C]0.818 mm [D]0.846 mm

5)In the above problem, the coefficient of friction at the chip tool interface obtained using Earnest andMerchant theory is

[A]0.18 [B]0.36[C]0.71 [D]0.908

6)Cold working of steel is defined as working

[A]at its recrystallization temperature [B]above its recrystallization temperature

[C]below its recrystallization temperature [D]at two thirds of the melting temperature of themetal.

7)Quality screw threads are produced by

[A] thread milling [B] thread chasing[C]thread cutting with single point tool [D]thread casting.

8)A batch of 10 cutting tools could produce 500 components while working at 50 rpm with a tool feed of 0.25mm/rev and depth of cut of 1 mm. A similar batch of 10 tools of the same specification could produce 122components while working at 80 rpm with a feed of 0.25 mm/rev and 1 mm depth of cut. How merrycomponents can be produced with one cutting tool at 60 rpm ?

[A]29 [B]31[C]37 [D]42

Machining



____________________________________________________________________________________________________________________ Pg.No.237









9)A part shown in the Fig. is machined to the sizes given below , ,

With 100% confidence, the resultant dimension W will have the specification

[A] [B][C] [D]

10)For tool A, Taylor's tool life exponent (n) is 0.45 and constant (K) is 90. Similarly for tool B, n = 0.3 and K =60. The cutting speed (in m/min) above which tool A will have a higher tool life than tool B is

[A]26.7 [B]42.5[C]80.7 [D]142.9

11)Friction at the tool-chip interface can be reduced by

[A]decreasing the rake angle [B] increasing the depth of cut[C]decreasing the cutting speed [D]increasing the cutting speed

12)Typical machining operations are to be performed on hard-to-machine materials by using the processeslisted below. Choose the best set of Operation-Process combinationsOperation ProcessP. Debugging (internal surface) 1. Plasma Arc MachiningQ. Die sinking 2. Abrasive Flow MachiningR. Fine hole drilling in thin sheets 3. Electric Dischrarge MachiningS, Tool sharpening 4. Ultrasonic Machining

5. Laser beam Machining6. Electrochemical Grinding


13)A zigzag cavity in a block of high strength alloy is to be frnish machined. This can be carried out by using

[A]electric discharge machining [B]electro-chemical machining[C]laser beam machining [D]abrasive flow machining

14)When 3-2-1 principle is used to support and locate a three-dimensional workpiece during machining, thenumber of degress of freedom that are restricted is

[A]7 [B]8[C]9 [D]10

15)A ring gage is used to measure

[A]outside diameter but not roundness [B] roundness but not outside diameter[C]both outside diameter and roundness [D]only external threads.

Machining



____________________________________________________________________________________________________________________ Pg.No.238











16)Match the items in columns I and II.Column I Column IIP. Wrinkling 1. Yield point elongationQ. Orange peel 2. AnisotropyR. Stretcher strains 3. Large grain sizeS. Earing 4. Insufficient blank holding force 5. Fine grain size 6. Excessive blank holding force

[A]P-6, Q-3, R-1, S-2 [B]P-4, Q-5, R-6, S-1[C]P-2, Q-5, R-3, S-4 [D]P-4, Q-3, R-1, S-2.

17)If each abrasive grain is viewed as a cutting tool, then which of the following represents the cuttingparameters in common grinding operations ?

[A]Large negative rake angle, low shear angle andhigh cutting speed

[B]Large positive rake angle, low shear angle andhigh cutting speed

[C]Large negative rake angle, high shear angle andlow cutting Speed

[D]Zero rake angle, high shear and high cuttingspeed.

18)Match the items in columns I and II.Column I Column IIP. Charpy test 1. FluidityQ. Knoop test 2. MicrohardnessR. Spiral test 3. FormabilityS. Cupping test 4. Toughness 5. Permeability

[A]P-4, Q-5, R-3, S-2 [B]P-3, Q-5, R-1, S-4[C]P-2, Q-4, R-3, S-5 [D]P-4, Q-2, R-1, S-3.

19)Total slip will occur in a belt drive when

[A]angle of rest is zero [B]angle of creep is zero[C]angle of rest is greater than angle of creep [D]angle of creep is greater than angle of rest.

20)Helix angle of fast helix drill is normally

[A] [B][C] [D]

21)Tool life of 10 hours is obtained when cutting with single point tool at 68 m/min. If Taylor's constant C =257.35, tool life on doubling the velocity will be

[A]5 hours [B]25.7 min[C]38.3 min [D]unchanged

22)A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire method.The diameter of the best size wire in mm is

[A]0.866 [B]1.000[C]1.154 [D]2.000

23)Failure of a bead weld between a heavy steel section and a thin section is mainly due to the formation of

[A]spheroidite [B]bainite[C]carbon free zone due to buring of carbon at high

temperature [D]martensite

24)In an orthogonal machining operation, the chip thickness and the uncut thickness are equal to 0.45 mm Ifthe tool rake angle is , the shear plane angle is

[A] [B][C] [D]

Machining



____________________________________________________________________________________________________________________ Pg.No.239







.

25)Abrasive material used in grinding wheel selected for grinding ferrous alloys is

[A]silicon carbide [B]diamond[C]aluminium oxide [D]boron carbide

26)Disposable patterns are made of

[A]wood [B] rubber[C]metal [D]polystyrene

27)The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is 400N. The turning was performed using 2 mm depth of cut and 0.1 mm/rev feed rate. The specific cuttingpressure (in N/mm2) is

[A]1000 [B]2000[C]3000 [D]4000

28)Match the Machine Tools (Group A) with the probable Operations (Group B)


29)A rectangular hole of size 100 mm × 50 mm is to be made on a 5 mm thick sheet of steel having ultimatetensile strength and shear strength of 500 MPa and 300 MPa, respectively. The hole is made by punchingprocess. Neglecting the effect of clearance, the punching force (in kN) is

[A]300 [B]450[C]600 [D]750

Machining



____________________________________________________________________________________________________________________ Pg.No.240


Key Paper

1. D 2. B 3. A 4. C 5. D

6. C 7. A 8. A 9. B 10. A

11. A 12. D 13. B 14. C 15. C

16. D 17. A 18. D 19. A 20. D

21. B 22. C 23. B 24. A 25. C

26. D 27. B 28. C 29. B

Machining



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1)In a point-to-point type of NC system

[A]control of position and velocity of the tool isessential [B]control of only position of the tool is sufficient

[C]control of only velocity of the tool is sufficient [D]neither position nor velocity need to be controlled2)With reference to NC machines, which of the following statements is wrong.

[A]Both closed-loop and open-loop control systemsare used

[B]Paper tapes, floppy tapes and cassettes are usedfor data storage

[C]Digitizers may be used as interactive inputdevices [D]Post processor is an item of hardware

3)In a point-to-point control NC machine, the slides are positioned by an integrally mounted stepper motordrive. If the specification of the motor is pulse, and the pitch of the lead screw is 3.6 mm, what is theexpected positioning accuracy ?

[A]1 [B]10 [C]50 [D]100

4)In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes throughthe origin and makes an angle of counterclockwise with the X-axis. The coordinates of the transformedpoint will be

[A] (7.5, 5) [B] (10, 5)[C](7.5, -5) [D](10, -5)

5)Choose the correct statement :

[A] A fixture is used to guide the tool as well as tolocate and clamp the workpiece

[B]A jig is used to guide the tool as well as to locateand clamp the workpiece

[C]Jigs are used on CNC machines to locate andclamp the workpiece and also to guide the tool

[D]No arrangement to guide the tool is provided in ajig.

6)In computer aided drafting practice, an arc is defined by

[A] two end points only [B]centre and radius[C]radius and one end point [D]two end points and centre.

7)In finish machining of an island on a casting with CNC milling machine, an end mill with 10 mm diameter isemployed. The corner points of the island are represented by (0, 0), (0, 30), (50, 30), and (50, 0). Byapplying cutter radius right compensation, the trajectory of the cutter will be

[A] (-5,0), (- 5, 35), (55, 35),(55, - 5), (- 5, -5) [B] (0, - 5), (55, - 5), (55, 35),(- 5, 35), (- 5,-5)[C](5, 5), (5,25), (45,25),(45,5), (5, 5) [D](5,5), (45, 5), (45, 25),(5,25), (5,5).

8)In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for2O% of the time. What would be the 95% confidence interval of this estimate if 100 observations weremade ?

[A] (0.16, 0.24) [B] (0.12, 0.28)[C](0.08, 0.32) [D]none of these.

9)3-2-1 method of location in a jig or fixture would collectivity restrict the workpiece in n degrees of freedom,where the value of n is

[A]6 [B]8[C]9 [D]12

10)In an NC machining operation the tool has to be moved from point (5, 4) to point (7, 2) along a circularpath with centre at (5,2). Before starting the operation, the tool is at (5, 4). The correct G and M code forthis motion is

[A]N010 G03 X7.0 Y2.0 I5.0 J2.0 [B]N010 G02 X7.0 Y2.0 I5.0 J2.0

Advanced machining methods



____________________________________________________________________________________________________________________ Pg.No.242










[C]N010 G01 X7.0 Y2.0 I5.0 J2.0 [D]N010 G00 X7.0 Y2.0 I5.0 J2.011)In a CNC program block, N002 002 G91 X40 Z40 ..., G02 and G91 refer to

[A]circular interpolation in counter clockwisedirection and incremental dimension

[B]circular interpolation in counter clockwisedirection and absolute dimension

[C]circular interpolation in clockwise direction andincremental dimension

[D]circular interpolation in clockwise direction andabsolute dimension

12)During the execution of a CNC part program blockNO20 GO2 X45.0 Y25.0 R5.0the type of tool motion will be

[A]circular Interpolation - clockwise [B]circular Interpolation counterclockwise[C]linear Interpolation [D]rapid feed.

13)In a 2-D CAD package, clockwise circular arc of radius 5, specified from (15, 10) to (10, 15) will have itscenter at

[A] (10, 10) [B] (15,10)[C](15,15) [D](10,15)

14)NC contouring is an example of

[A]continuous path positioning [B]point-to-point positioning[C]absolute positioning [D]incremental positioning.

15)The tool of an NC machine has to move along a circular arc from (5, 5) to (10, 10) while performing anoperation. The centre of the arc is at (10, 5). Which one of the followinC NC tool path commands performsthe above mentioned operation?

[A]N010 G02 X10 Y10 X5 Y5 R5 [B]N010 G03 x10 Y10 x5 Y5 R5[C]N010 G01X5 Y5 X10 Y10 R5 [D]N010 Go2 X5 Y5 X10 Y10 R5.

16)Which type of motor is NOT used in axis or spindle drives of CNC machine tools ?

[A] induction motor [B]dc servo motor[C]stepper motor [D]linear servo motor


17)In the feed drive of a Point-to-Point open loop CNC drive, a stepper motor rotating at 200 steps/rev drivesa table through a gear box and lead screw-nut mechanism (pitch = 4 mm, number of starts = 1). The gear

ratio = is given by The stepper motor (driven by voltage pulses from a pulsegenerator) executes 1 step/pulse of the pulse generator. The frequency of the pulse train from the pulsegenerator is f = 10,000 pulses per minute. (see Figure)

The Basic Length Unit (BLU), i.e., the table movement corresponding to 1 pulse of the pulse generator, is

[A]0.5 microns [B]5 microns[C]50 microns [D]500 microns

18)A customer insists on a modification to change the BLU of the CNC drive to 10 microns without changingthe table speed. The modification can be accomplished by

[A]changing U to and reducing f to [B]changing U to and increasing f to 2f[C]changing U to and keeping / unchanged [D]keeping U unchanged and increasing f to 2f.




____________________________________________________________________________________________________________________ Pg.No.243


Key Paper

1. B 2. D 3. B 4. B 5. B

6. D 7. A 8. B 9. C 10. B

11. C 12. A 13. C 14. B 15. D

16. A 17. B 18. C




____________________________________________________________________________________________________________________ Pg.No.244


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1)In a series RLC high Q circuit, the current peaks at a frequency

[A]equal to the resonant frequency [B]greater than the resonant frequency[C]less than the resonant frequency [D]none of the above

2)In Ultrasonic Machining (USM) the material removal rate would

[A] increase [B]decrease[C]increase and then decrease (d) decrease and

then increase[D]With increasing mean grain diameter of the

abrasive material.3)The two main criteria for selecting the electrolyte in Electrochemical Machining (ECM) is that the

electrolyte should

[A]be chemically stable [B]not allow dissolution of cathode material[C]not allow dissolution of anode material [D]have high electrical conductivity

4)In ultrasonic machining process, the material removal rate will be higher for materials with

[A]higher toughness [B]higher ductility[C]lower toughness [D]higher fracture strain

5)Among the conventional machining processes, maximum specific energy is consumed in

[A] turning [B]drilling[C]planing [D]grinding

6)Selection electrolyte for ECM is as follows :

[A]non-passivating electrolyte for stock removal andpassivating electrolyte for finish control

[B]passivating electrolyte for stock removal and non-passivating electrolyte for finish control

[C]selection of electrolyte is dependent on currentdensity

[D]electrolyte selection is based on tool-workelectrodes.

7)Inter electrode gap in ECG is controlled by

[A]controlling the pressure of electrolyte flow [B]controlling the applied static load[C]controlling the size of diamond particle in the

wheel [D]controlling the texture of the work piece.

8)In machining using abrasive material, increasing abrasive grain size

[A] increases the material removal rate [B]decreases the material removal rate[C]first decreases and then increases the material

removal rate[D]first increases and then decreases the material

removal rate.9)In Electro-Discharge Machining (EDM), the tool is made of

[A]Copper [B]High speed steel[C]Cast iron [D]plain carbon steel

10)During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 Awith 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomicweight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% currentefficiency, the expected material removal rate in gm/s will be

[A]0.11 [B]0.23[C]0.30 [D]0.52

11)Deep hole drilling of small diameter, say 0.2 mm is done with EDM by selecting the tool material as

[A]copper wire [B] tungsten wire[C]brass wire [D]tungsten carbide.

Nontraditional machining methods



____________________________________________________________________________________________________________________ Pg.No.245









12)In ECM, the material removal is due to

[A]corrosion [B]erosion[C]fusion [D]ion displacement

13)As tool and work are not in contact in EDM process

[A]no relative motion occurs between them [B]no wear of tool occurs[C]no power is consumed during metal cutting [D]no force between tool and work occurs.

14)In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, thematerial removal rate

[A] increases continuously. [B]decreases continuously.[C]decreases, becomes stable and then increases. [D]increases, becomes stable and then decreases.

15)A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rateused for milling is 50 mm/min. Milling time for the slot (in seconds) is

[A]120 [B]170[C]180 [D]240

16)Electrochemical machining is performed to remove material from an iron surface of 20mm×20mm underthe following conditions:Inter electrode gap = 0.2mmSupply voltage (DC) = 12VSpecific resistance of electrolyte = 2 cmAtomic weight of Iron = 55.85Valency of Iron = 2Faraday 's constant = 96540 Coulombs

The material removal rate (in g/s) is

[A]0.3471 [B]3.471[C]34.71 [D]347.1

17)Match the following


18)Match the following non-traditional machining processes with the corresponding material removalmechanisms:





____________________________________________________________________________________________________________________ Pg.No.246






.

19)The mechanism of material removal in EDM process is

[A]Melting and Evaporation [B]Melting and Corrosion[C]Erosion and Cavitation [D]Cavitation and Evaporation.

20)Arrange the processes in the increasing order of their maximum material removal rate.Electrochemical Machining (ECM)Ultrasonic Machining (USM)Electron Beam Machining (EBM)Laser Beam Machining (LBM) andElectric Discharge Machining (EDM)

[A]USM, LBM, EBM, EDM, ECM [B]EBM, LBM, USM, ECM, EDM[C]LBM, EBM, USM, ECM, EDM [D]LBM, EBM, USM, EDM, ECM.

21)A researcher conducts electrochemical machining (ECM) on a binary alloy (density 6000 kg/ ) of iron(atomic weight 56, valency 2) and metal P (atomic weight 24, valency 4). Faraday's constant = 96500coulomb/mole. Volumetric material removal rate of the alloy is 50 m /s at a current of 2000 A. Thepercentage of the metal P in the alloy is closest to

[A]40 [B]25[C]15 [D]79

22)Match the most suitable manufacturing processes for the following parts :parts manufacturing processP. Computer chip 1. Electrochemical MachiningQ.Metal forming dies and molds 2.Ultrasonic machiningR. Turbine blade 3.Electro discharge machiningS.Glass 4.photochemical machining





____________________________________________________________________________________________________________________ Pg.No.247


Key Paper

1. A 2. C 3. D 4. C 5. D

6. A 7. C 8. A 9. A 10. C

11. C 12. D 13. D 14. D 15. B

16. A 17. C 18. A 19. A 20. B

21. B 22. A




____________________________________________________________________________________________________________________ Pg.No.248






Index- Machine Design

Sl.No. Name of the Topic Pg.No.s 1. Static Loading 250-257 2. Fatigue 258-260 3. Bolted, Riveted and Welded Joints 261-263 4. Gears 264-267 5. Rolling Contact Bearings 268-269 6. Sliding Contact Bearings 270-272 7. Brakes 273-274 8. Clutches 275-276 9. Keys & Couplings 277-278









.

.







The state of stress at a point "p" in a two dimensional loading is such that the Mohr's circle is a point located at 175 MPa on thepositive normal stress axis.

1)Determine the maximum and minimum principal stresses respectively from the Mohr"s circle

[A]+175 MPa -175 MPa [B]+175 MPa + 175 MPa[C]0 - 175 MPa [D]0,0


The circular disc shown in its plan view in the Fig. rotates in a plane parallel to the horizontal plane aboutthe point O at a uniform angular velocity . Two other points A and B are located on the line OZ atdistances and from O respectively.

2)The velocity of point B with respect to point A is a vector of magnitude

[A]0 [B] and direction opposite to the direction ofmotion of point B

[C] and direction same as the direction ofmotion of point B [D] and direction being from 0 to Z

3)The acceleration of point B with respect to point A is a vector of magnitude

[A]0 [B] and direction same as the direction ofmotion of point B

[C] and direction opposite to be direction ofmotion of point B [D] and direction being from Z to 0

4)Determine the directions of maximum and minimum principal stresses at the point "P" from the Mohr'scircle

[A] [B][C] [D]All directions

5)Square key of side "d/4" each and length I is used to transmit torque "T" from the shaft of diameter "d" tothe hub of a pulley. Assuming the leugth of the key to be equal to the thickness of the pulley, the averageshear stress developed in the key is given by

[A] [B][C] [D]

6)The state of plane-stress at a point is given by = -200 MPa, = 100 MPa and = 100 MPa.Themaximum shear stress (in MPa) is

[A]111.8 [B]150.1[C]180.3 [D]223.6

Static Loading



____________________________________________________________________________________________________________________ Pg.No.250







7)A bracket (shown in Fig. 1) is rigidly mounted on wall using four rivets. Each rivet is 6 mm in diameter andhas an effective length of 12 mm

fig 1Direct shear stress (in MPa) in the most heavily loaded rivet is

[A]4.4 [B]8.8[C]17.6 [D]35.2

8)A lightly loaded full journal bearing has journal diameter of 50 mm, bush bore of 50.05 mm and bushlength of 20 mm. If rotational speed of journal is 1200 rpm and average viscosity of liquid lubricant is 0.03Pa s, the power loss (in W) will be

[A]37 [B]74[C]118 [D]237

9)T he state of stress at a point under plane stress condition is = 40 MPa, = 100 MPa and = 40 MPa.

The radius of the Mohr’s circle representing the given state of stress in MPa is

[A]40 [B]50[C]60 [D]100

10)A solid circular shaft needs to be designed to transmit a torque of 50 N.m. If the allowable shear stress ofthe material is 140 MPa, assuming a factor of safety of 2, the minimum allowable design diameter in mm is

[A]8 [B]16[C]24 [D]32

11)Match the following criteria of material failure, under biaxial stresses and and yield stress ,with theircorresponding graphic representations

[A]P-M ,Q-L,R-N [B]P-N,Q-M,R-L[C]P-M,Q-N,R-N [D]P-N,Q-L,R-M

12)If the principal stresses in a plane stress problem, are = 100MPa, = 40MPa , the magnitude of themaximum shear stress (in MPa) will be

Static Loading



____________________________________________________________________________________________________________________ Pg.No.251








[A]60 [B]50[C]30 [D]20

13)A solid circular shaft of diameter d is subjected to a combined bending moment M and torque, T. The

material property to be used for designing the shaft using the relation is

[A]ultimate tensile strength ( ) [B] tensile yield strength ( )[C]torsional yield strength ( ) [D]endurance strength ( )

14)The Figure shows the state of stress at a certain point in a stressed body. The magnitudes of normalstresses in the x and y direction are 100 MPa and 20 MPa respectively. The radius of Mohr's stress circletepresenting this state of stress is

[A]120 [B]80[C]60 [D]40

15)The Mohr's circle of plane stress for a point in a body is shown in Fig. The design is to be done on thebasls of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer choosesa ductile material whose yield strength is


16)According to Von-Mises distortion energy theory, the distortion energy under three dimensional stressstate is represented by

[A] [B][C] [D]

17)For the component loaded with a force F as shown in the Figure, the axial stress at the corner point P is

[A] [B][C] [D]

Static Loading



____________________________________________________________________________________________________________________ Pg.No.252









18)A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It is further subjectedto a torque of 10 kNm. The maximum principal stress experienced on the shaft is closest to


19)In a cam design, the rise motion is given by a simple harmonic motion (SHM), s = where h, istotal rise, is camshaft angle, is the total angle of the rise interval. The jerk is given by

[A] [B]

[C] [D]

20)A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of .The Young's modulus is E and the co-efficient of linear expansion is a. The thermal stress in the rod is

[A]0 [B][C] [D]

21)A 200 x 100 x 50 mm steel block is subjected to a hydrostatic pressure of 15 MPa . The Young's modulusand poisson's ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of theblock in is

[A]85 [B]90[C]100 [D]110

22)A stepped steel shaft shown below is subjected to 10 Nm torque. If the modulus of rigidity is 80 GPa, thestrain energy in the shaft in N mm is

[A]4.12 [B]3.46[C]1.73 [D]0.86

23)The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressiveforce of 10 kN due to the internal pressure. The end conditions for the rod may be assumed. as guided atthe piston end and hinged at the other end. The Young's modulus is 200 GPa. The factor of safety for thepiston rod is

[A]0.68 [B]2.75[C]5.62 [D]11.0

24)Carburized machine components have high endurance limit because carburization

[A] raises the yield point of the material [B]produces a better surface finish

[C]introduces a compressive layer on the surface [D]suppresses any stress concentration produced inthe component

Static Loading



____________________________________________________________________________________________________________________ Pg.No.253











25)A large uniform plate containing a rivet-hole is subjected to uniform uniaxial tension of 95 MPa. Themaximum stress in the plate is:

[A]100 MPa [B]285 MPa[C]190 MPa [D]Indeterminate

26)Fatigue strength of a rod subjected to cyclic axial force is less than that of a rotating beam of the samedimensions subjected to steady lateral force because

[A]axial stiffness is less than bending stiffness [B]of absence of centrifugal effects in the rod

[C]the number of discontinuities vulnerable to fatigueare more in the rod

[D]at a particular time the rod has only one type ofstress whereas the beam has both the tensileand compressive stresses

27) , and are the rectangular stress component at a point. The radius of Mohr’s circle is:

[A] [B]

[C] [D]

28)A test specimen is stressed slightly beyond the yield point and then unloaded, Its yield strength will

[A]decrease [B] increase[C]remains same [D]becomes equal to ultimate tensile strength.

29)If the two principal strains at a point are and , then the maximum shear strain is

[A] [B][C] [D]

30)A small element at the critical section of a component is in a bi-axial state of stress with the two principalstresses being 360 MPa and 140 MPa. The maximum working stress according to Distortion EnergyTheory is


31)The normal stesses at a point are and ; the shear stress at this point is 4 MPa. Themaximum principal stress at this point is


32)Which theory of failure will you use for aluminium components under steady loading

[A]Principal stress theory [B]principal strain theory[C]Strain energy theory [D]maximum shear stress theory

33)Two threaded bolts A and B of same material and length are subjected to identical tensile load. If theelastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, themean diameter of bolt B in mm is

[A]16 [B]24[C]36 [D]48

34)In a bi-axial stress problem, the stresses in x and y directions = 200 MPa and = 100 MPa. Themaximum principal stress in MPa, is

Static Loading



____________________________________________________________________________________________________________________ Pg.No.254









[A]50 [B]100[C]150 [D]200

35)The stress-strain behaviour of a m"a6t1e.rial is shown in Fig. 5. Its resilience and toughness, in Nm./ , arerespectively

[A]28 x , 76 x [B]28 x , 48 x [C]14 x , 90 x [D]76 x , 104 x

36)The total area under the stress-strain curve of a mild steel specimen tested up to failure under tension is ameasure of

[A]ductility [B]ultimate strength[C]stiffness [D]toughness.

37)The number of components in a stress tensor defining stress at a point in three dimensions is

[A]3 [B]4[C]6 [D]9

38)The maximum principle stress for the stress state shown in the Fig. is

[A] [B][C] [D]

39)The relationship between Young's modulus (E), Bulk modulus (K) and Poisson's ratio ( ) is given by

[A]E = 3 K (1-2 ) [B]K = 3E(1-2 )[C]E = 3 K(1- ) [D]K = 3 E(1- )

40)Two identical circular rods of same diameter and same length are subjected to same magnitude of axialtensile force.One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. Theother rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materialsto be homogeneous and isotropic and the axial force causes the same amount of uniform stress in boththe rods. The stresses developed are within the proportional limit of the respective materials. Which of thefollowing observations is correct ?

[A]Both rods elongate by the same amount [B]Mild steel rod elongates more than the cast ironrod

Static Loading



____________________________________________________________________________________________________________________ Pg.No.255



.

[C]Cast iron rod elongates more than the mild steelrod

[D]As the stresses are equal strains are also equalin both the rods.

41)Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. Ifthe shaft diameter is doubled then the maximum shear stress developed corresponding to the sametorque will be


Static Loading



____________________________________________________________________________________________________________________ Pg.No.256


Key Paper

1. B 2. C 3. D 4. D 5. C

6. C 7. B 8. B 9. B 10. B

11. C 12. C 13. C 14. C 15. C

16. C 17. D 18. B 19. D 20. C

21. B 22. C 23. C 24. C 25. A

26. D 27. D 28. B 29. D 30. C

31. C 32. D 33. B 34. D 35. C

36. D 37. C 38. B 39. D 40. C

41. C

Static Loading



____________________________________________________________________________________________________________________ Pg.No.257


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1)A manufacturer of rivets claims that the failure load in shear of his product is 500 ± 25N. This specificationimplies that

[A]no rivet is weaker than 475N and stronger than525N

[B] the standard deviation of strength of randomsample of rivets is 25 N

[C]there is an equal probability of failure strength tobe either 475N or 525N

[D]there is approximately two-to-one chance that thestrength of a rivet lies between 475N to 525N

2)A 750 hours life test is performed on ten components. If one component fails after 350 hours of operationand all others survive the test, then the failure per hour is

[A]0.000141 [B]0.000133[C]0.00141 [D]0.00133

3)A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the areaof cross-section in m of the bar for a factor of safety of 2 is

[A]400 [B]600[C]750 [D]1000

4)Under repeated loading a material has the stress-strain curve shown in Fig. Which of the followingstatements is true ?

[A]The smaller the shaded area, the better thematerial damping

[B]The larger the shaded area, the better thematerial damping

[C]Material damping is an independent materialproperty and does not depend on this curve [D]None of these.

5)When using a simple moving average to forecast demand, one would

[A]give equal weight to all demand data [B]assign more weight to the recent demand data[C]include new demand data in the average without

discarding the earlier data[D]include new demand data in the average after

discarding some of the earlier demand data.6)A static load is mounted at the centre of a shaft rotating at uniform angular velocity. This shaft will be

designed for

[A] the maximum compressive stress (static) [B] the maximum tensile stress (static)[C]the maximum bending moment (static) [D]fatigue loading.

7)A wire rope is designated as 6 x 19 standard hoisting. The numbers 6 x 19 represent

[A]diameter in millimeter x length in meter [B]diameter in centimeter x length in meter[C]number of strands x number of wires in each

strand[D]number of wires in each strand x number of

strands.8)The S-N curve for steel becomes asymptotic nearly at

Fatigue



____________________________________________________________________________________________________________________ Pg.No.258






.

[A] cycles [B] cycles[C] cycles [D] cycles

9)A cylindrical shaft is subjected to an alternating stress of 100 MPa. Fatigue strength to sustain 1000 cyclesis 490 MPa. If the corrected endurarce strength is 70 MPa, estimated shaft life will be

[A]1071 cycles [B]15000 cycles[C]281914 cycles [D]928643 cycles

10)An axial residual compressive stress due to a manufacturing process is present on the outer surface of arotating shaft subjected to bending load. Under a given bending load, the fatigue life of the shaft in thepresence of the residual compressive stress is

[A]decreased [B] increased or decreased, depending on theexternal bending load

[C]neither decreased nor increased [D]increased.11)A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal

pressure varying from 4 to 8 MPa. Assume that the yield, ultimate, and endurance strength of material are600, 800 and 400 MPa respectively. The factor of safety as per Goodman's relation is

[A]2.0 [B]1.6[C]1.4 [D]1.2

Fatigue



____________________________________________________________________________________________________________________ Pg.No.259


Key Paper

1. A 2. A 3. D 4. A 5. D

6. D 7. C 8. C 9. C 10. D

11. B

Fatigue



____________________________________________________________________________________________________________________ Pg.No.260


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A single riveted lap joint of two similar plates as shown in the figure below has the following geometricaland material details.

width of the plate w = 200 mm, thickness of the plate t = 5 mm, number of rivets n = 3, diameter of the rivet= 10 mm, diameter of the rivet hole = 11 mm, allowable tensile stress of the plate = 200 MPa,

allowable shear stress of the rivet = 100 MPa and allowable bearing stress of the rivet = 150 MPa.

1)If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is

[A]83 [B]125[C]167 [D]501

2)If the rivets are to be designed to avoid crushing failure, the maximum permissible load P in kN is

[A]7.50 [B]15.00[C]22.50 [D]30.00

3)A fillet welded joint is subjected to transverse loading F as shown in the figure. Both legs of the fillets are of10 mm size and the weld length is 30 mm. If the allowable shear stress of the weld is 94 MPa, consideringthe minimum throat area of the weld, the maximum allowable transverse load in kN is

[A]14.44 [B]17.92[C]19.33 [D]22.16

4)In a bolted joint two members are connected with an axial tightening force of 2200 N. If the bolt used hasmetric threads of 4 mm pitch, then torque required for achieving the tightening force is (See Figure)

[A]0.7 Nm [B]1.0 Nm[C]4.6 Nm [D]2.8 Nm

5)A 60 mm long and 6 mm thick fillet weld carries a steady load of 15 kN along the weld. The shear strengthof the weld material is equal to 200 MPa. The factor of safety is

[A]2.4 [B]3.4[C]4.8 [D]6.8

Bolted,Riveted and Welded Joints



____________________________________________________________________________________________________________________ Pg.No.261






.

6)A bolted joint is shown below. The maximum shear stress, in MPa, in the bolts at A and B, respectively are

[A]242.6,42.5 [B]42.5,242.6[C]42.5,42.5 [D]242.6,242.6

7)A block-brake shown below has a face width of 300 mm and a mean coefficient of friction of 0.25. For anactivating force of 400 N, the braking torque in Nm is

[A]30 [B]40[C]45 [D]60

8)If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the tearing efficiency of the joint is

[A]0.50 [B]0.75[C]0.25 [D]0.87

9)Bolts in the flanged end of pressure vessel are usually pre-tensioned. Indicate which of the followingstatements in not true ?

[A]Pre-tensioning helps to seal the pressure vessel [B]Pre-tensioniug increases the fatigue life of thebolts

[C]Pre-tensioning reduces the maximum tensilestress in the bolts

[D]Pre-tensioning helps to reduce the effect ofpressure pulsations in the pressure vessel.




____________________________________________________________________________________________________________________ Pg.No.262


Key Paper

1. C 2. C 3. C 4. C 5. B

6. A 7. C 8. B 9. C




____________________________________________________________________________________________________________________ Pg.No.263


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A gear set has a pinion with 20 teeth and a gear with 40 teeth. The pinion runs at 30 rev/ s and transmits apower of 20 kW. The teeth are on the full-depth system and have a module of 5 mm. The length of theline of action is 19 mm

1)The centre distance for the above gear set in mm is

[A]140 [B]150[C]160 [D]170

2)The contact ratio of the contacting tooth is

[A]1.21 [B]1.25[C]1.29 [D]1.33

3)The resultant force on the contacting gear tooth in N is

[A]77.23 [B]212.20[C]2258 [D]289.43


A planetary gear train has four gears and one carrier. Angular velocities of the gears are , , andrespectively. The carrier rotates with angular velocity (See Figure)

4)What is the relation between the angular velocities of Gear 1 and Gear 4 ?

[A] [B][C] [D]

5)For = 60 rpm clockwise (cw) when looked from the left, what is the angular velocity of the carrier and itsdirection so that Gear 4 rotates in counterclockwise (ccw) direction at twice the angular velocity of Gear Iwhen looked from the left ?

[A]130 rpm,cw [B]223 rpm,ccw[C]256 rpm,cw [D]156 rpm,ccw


Gears



____________________________________________________________________________________________________________________ Pg.No.264








A compacting machine shown in the Figure below is used to create a desired thrust force by using a rackand pinion arrangement. The input gear is mounted on the motor shaft. The gears have involute teeth of 2mm module.

6)If the drive efficiency is 807o, then torque required on the input shaft to create 1000 N output thrust is

[A]20 Nm [B]25 Nm[C]32 Nm [D]50 Nm

7)If the pressure angle of the rack is , then force acting along the line of action between the rack and thegear teeth is

[A]252 N [B]342 N[C]532 N [D]600 N


The overall gear ratio in a 2 stage speed reduction gear box (with all spur gears) is 12. The input andoutput shafts of the gear box are collinear. The countershaft which is parallel to the input and output shaftshas a gear ( teeth) and pinion ( = 15 teeth) to mesh with pinion ( = 16 teeth) on the input shaft andgear ( teeth) on the output shaft respectively. It was decided to use a gear ratio of 4 with 3 module in thefirst stage and 4 module in the second stage.

8) and are


9)The centre distance in the second stage is

[A]90 mm [B]120 mm[C]160 mm [D]240 mm

10)Two mating spur gears have 40 and 120 teeth respectively. The pinion rotates at 1200 rpm and transmitsa torque of 20 N.m. The torque transmitted by the gear is

[A]6.6 Nm [B]20 Nm[C]40 Nm [D]60 Nm

11)Twenty degree full depth involute profiled 19-tooth pinion and 37-tooth gear are in mesh. If the module is 5mm, the center distance between the gear pair will be

[A]140 mm [B]150 mm[C]280 mm [D]300 mm

Gears



____________________________________________________________________________________________________________________ Pg.No.265








.

12)The function f(x) = -6 + 9x + 25 has

[A]a maxima at x=1 and a minima at x=3 [B]a maxima at x=3 and a minima at x=1[C]no maxima, but a minima at x = 3 [D]a maxima at x = 1, but no minima.

13)In spur gears, the circle on which the involute is generated is called the

[A]pitch circle [B]clearance circle[C]base circle [D]addendum circle

14)The efficiency of a power screw is maximum when the lead angle is

[A] [B][C] [D]

15)The minimum number of teeth on the pinion to operate without interference in standard full height involuteteeth gear mechanism with pressure angle is

[A]14 [B]12[C]18 [D]32


16)A full depth involute spur pinion of 4mm module and 21 teeth is to transmit 15kW at 960rpm. Its facewidth is 25mm.

Q. The tangential force transmitted (in N) is

[A]3552 [B]2611[C]1776 [D]1305

17)Given that the tooth geometry factor is 0.32 and the combined effect of dynamic load and allied factorsintensifying the stress is 1.5; the minimum allowable stress (in MPa) for the gear material is

[A]242.0 [B]166.5[C]121.0 [D]74.0

Gears



____________________________________________________________________________________________________________________ Pg.No.266


Key Paper

1. B 2. C 3. C 4. A 5. D

6. B 7. C 8. A 9. B 10. D

11. A 12. A 13. C 14. A 15. C

16. A 17. B

Gears



____________________________________________________________________________________________________________________ Pg.No.267


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1)Spherical roller bearings are normally used

[A] for increased radial load [B] for increased thrust load[C]when there is less radial space [D]to compensate for angular misalignment

2)The life of a ball-bearing is inversely proportional to

[A] [B][C] [D]

3)The dynamic load capacity of 6806 bearing is 22 kN. The maximum radial load it can sustain to operate at600 rev/min, for 2000 hours is

[A]4.16 kN [B]3.60 kN[C]6.25 kN [D]5.29 kN

4)The basic load rating of a ball bearing is

[A] the maximum static radial load that can beapplied without causing any plastic deformationof bearing components.

[B] the radial load at which 9O% of the group ofapparently indentical bearings run for one millionrevolutions before the first evidence of failure.

[C]the maximum radial load that can be appliedduring operation without any plastic deformationof bearing components.

[D]a combination of radial and axial loads that canbe applied without any plastic deformation.

5)The life of a ball bearing at a load of 10 kN is 8000 hours. Its life in hours if the load is increased to 20 kN,keeping all other conditions the same, is

[A]4000 [B]2000[C]1000 [D]500

6)Two identical ball bearings P and Q are operating at loads 30 kN and 45 kN respectively. The ratio of thelife of bearing P to the life of bearing Q is

[A]81/16 [B]27/8[C]9/4 [D]3/2

7)The rotor shaft of a large electric motor supported between short bearings at both deflection of 1.8mm inthe middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at boththe ends, the likely critical speed (in rpm) of the shaft is

[A]350 [B]705[C]2810 [D]4430

8)A ball bearing operating at a load F has 8000 hours of life. The life of the bearing, in hours, when the loadis doubled to 2Fis

[A]8000 [B]6000[C]4000 [D]1000

Rolling Contact Bearings



____________________________________________________________________________________________________________________ Pg.No.268


Key Paper

1. D 2. B 3. D 4. B 5. C

6. B 7. B 8. D

Rolling Contact Bearings



____________________________________________________________________________________________________________________ Pg.No.269


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1)Starting friction is low in

[A]Hydrostatic lubrication [B]Hydrodynamic lubrication[C]Mixed (or semi-fluid) lubrication [D]Boundary lubrication

2)The yield strength of a steel shaft is twice its endurance limit. Which of the following torque fluctuationsrepresent the most critical situation according to Soderberg criterion?

[A] -T to +T [B][C]0 to +T [D]

3)In thick film hydrodynamic journal bearings, the coefficient of friction

[A] increase with increases in load [B] is independent of load[C]decreases with increase in load [D]may increase or decrease with increase in load

4)To restore stable operating condition in a hydrodynamic journal bearing, when it encounters highermagnitude loads,

[A]oil viscosity is to be decreased [B]oil viscosity is to be increased[C]oil viscosity index is to be increased [D]oil viscosity index is to be decreased.

5)For the data listed below for two journal bearings A and B, predict the flow conditions in the bearings

[A] liminar in both A and B [B] turbular in both A and B[C]laminor in A and turbulent in B [D]turbulent in A and laminor B

6)A shaft subjected to torsion experiences a pure shear stress on the surface. The maximum principalstress on the surface which is at to the axis will have a value

[A] cos [B]2 cos [C] [D]2 sin cos

7)The homogeneous state of stress for a metal part undergoing plastic deformation is

where the stress component values are in MPa. Using von Mises yield criterion, the value of estimatedshear yield stress, in MPa is

[A]9.50 [B]16.07[C]28.52 [D]49.41

8)Which one of the following is a criterion in the design of hydrodynamic journal bearings?

[A]Sommerfeld number [B] rating life[C]specific dynamic capacity [D]Rotation factor

9)A journal bearing has shaft diameter of 40 mm and a length of 40 mm. The shaft is rotating at 20 rad/s andthe viscosity of the lubricant is 20 MPa.s. The clearance is 0.020 mm. The loss of torque due to theviscosity of the lubricant is approximately

Sliding Contact Bearings



____________________________________________________________________________________________________________________ Pg.No.270



.

[A]0.040 Nm [B]0.252 Nm[C]0.400 Nm [D]0.652 Nm

10)A natural feed journal bearing of diameter 50 mm and length 50 mm operating at 20 revolution/secondcarries a load of 2.0 kN. The lubricant used has a viscosity of 20 MPa s. The radial clearance is 50 pm.The Sommerfeld number for the bearing is

[A]0.062 [B]0.125[C]0.250 [D]0.785




____________________________________________________________________________________________________________________ Pg.No.271


Key Paper

1. A 2. A 3. C 4. B 5. D

6. D 7. B 8. A 9. A 10. B




____________________________________________________________________________________________________________________ Pg.No.272


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.

1)In a band brake the ratio of tight side band tension to the tension on the slack side is 3. If the angle ofoverlap of band on the drum is the coefficient of friction required between drum and the band is

[A]0.20 [B]0.25[C]0.30 [D]0.35

2)A band brake having band-width of 80 mm, drum diameter of 250 mm, coefficient of friction of 0.25 andangle of wrap of 270 degrees is required to exert a friction torque of 1000 Nm. The maxi mum tension (inkN) developed in the band is

[A]1.88 [B]3.56[C]6.12 [D]11.56

3)A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in thefigure, where the wrapping angle is . If the coefficient of friction between the drum and the band is 0.25,the braking torque applied, in N.m is

[A]100.6 [B]54.4[C]22.1 [D]15.7

Brakes



____________________________________________________________________________________________________________________ Pg.No.273


Key Paper

1. D 2. D 3. B

Brakes



____________________________________________________________________________________________________________________ Pg.No.274


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.

1)A disk clutch is required to transmit 5 kW at 2000 rpm. The disk has a friction lining with coefficient offriction equal to 0.25. Bore radius of friction liniag is equal to 25 mm. Assume uniform contact pressure of 1MPa. the value of outside radius of the friction lining is

[A]39.4 mm [B]49.5 mm[C]97.9 mm [D]142.9 mm

2)A clutch has outer and inner diameters 100 mm and 40 mm respectively. Assuming a uniform pressure of2 MPa and coefficient of friction of liner material 0.4, the torque carrying capacity of the clutch is

[A]148 Nm [B]196 Nm[C]372 Nm [D]490 Nm


3)A band brake Fig. consists of a lever attached to one end ofthe band. The other end of the band is fixed tothe ground. The wheel has a radius of 200 mm and the wrap angle of the band is . The braking forceapplied to the lever is limited to 100 N, and the coefficient of friction between the band and the wheel is0.5. No other information is given.

Q. The maximum tension that can be generated in the band during braking is

[A]1200 N [B]2110 N[C]3224 N [D]4420 N

4)The maximum wheel torque that can be completely braked is

[A]200 N.m [B]382 N.m[C]604 N.m [D]844 N.m

Clutches



____________________________________________________________________________________________________________________ Pg.No.275


Key Paper

1. A 2. B 3. B 4. B

Clutches



____________________________________________________________________________________________________________________ Pg.No.276


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.




.

1)A key connecting a flange coupling to a shaft is likely to fail in

[A]shear [B] tension[C]torsion [D]bending

2)The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to

[A]shear force and bending moment [B]axial force[C]torsion [D]torsion and bending moment

3)The coupling used to connect two shafts with large angular misalignment is

[A]a Flange coupling [B]an Oldham's coupling[C]a Flexible bush coupling [D]a Hooke's joint.

Keys & Couplings



____________________________________________________________________________________________________________________ Pg.No.277


Key Paper

1. A 2. A 3. D

Keys & Couplings



____________________________________________________________________________________________________________________ Pg.No.278






Index- Theory of Machines

Sl.No. Name of the Topic Pg.No.s 1. Analysis of planar mechanism 280-288 2. Dynamic analysis of single crank mechanism 289-293 3. Gear/Gear trains 294-298 4. Fly Wheels 299-300 5. Mechanical vibrations 301-308









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1)Instantaneous centre of a body rolling with sliding on a stationary curved surface lies

[A]at the point of contact [B]on the common normal at the point of contact[C]on the common tangent at the point of contact [D]at the centre of curvature of the stationary surface

2)The number of degrees of freedom of a five link plane mechanism with five revolute pairs as shown in thefigure is:

[A]3 [B]4[C]2 [D]1

3)The cross head velocity in the slider crank mechanism, for the position shown in Figure

where is the linear velocity of the crank pin.

[A] [B][C] [D]

4)Consider the triangle formed by the connecting rod and the crank of an IC engine as at the two sides of thetriangle. If the maximum area of this traingle occurs when the crank angle is , the ratio of connectingrod length to crank radius is

[A]5 [B]4[C]3.73 [D]3

5)A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block issliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in thefigure below. If OA = 1 m, the magnitude of the absolute acceleration of the block at location A in is

[A]3 [B]4[C]5 [D]6

Analysis of planar mechanism



____________________________________________________________________________________________________________________ Pg.No.280






6)For the planar mechanism shown in Fig. , select the most appropriate choice for the motion of link 2 whenlink 4 is moved upwards.

[A]Link 2 rotates clock wise [B]Link 2 rotates counter - clockwise[C]Link 2 does not move [D]Link 2 motion cannot be determind

7)A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP =2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is

[A]PQ [B]QR[C]RS [D]SP

8)As shown in Fig, a personA is standing at the centre ofa rotating platform facing person B who is riding abicycle, heading East. The relevant speeds and distances are shown in given figure. person a bicycle,heading East. At the instant under consideration, what is the apparent velocity of B as seen by A ?

[A]3 m/s heading East [B]3 m/s heading west[C]8 m/s heading East [D]13 m/s heading East

9)For the audio cassette mechanism shown in Fig. given below, where is the instantaneous centre ofrotation (point) of the two spools ?

[A]Point P lies to the left of both the spools but atinfinity along the line joining A and H

[B]Point P lies in between the two spools on the linejoining A and H, such that PH =2AP

[C]Point P lies to the right of both the spools on theline joining A and H, such that AH = HP

[D]Point P lies at the intersection of the line joining Band C and the line joining G and F.




____________________________________________________________________________________________________________________ Pg.No.281










10)the minimum number of links in a single degree-of-freedom planar mechanism with both higher and Iowerkinematic pairs is

[A]2 [B]3[C]4 [D]5

11)The Coriolis component of acceleration is present in

[A]4-bar mechanisms with 4 turning pairs [B]shaper mechanism[C]slider-crank mechanism [D]Scotch Yoke mechanism

12)Mass M slides in a frictionless slot in the horizontal direction and the bob of mass m is hinged to mass M atC, through a rigid massless rod. This system is released from rest with . At the instant when ,the velocities of m and M can be determined using the fact that, for the system (i.e., m and, M together)

[A] the linear momentum in x and y directions areconserved but the energy is not conserved

[B] the linear momentum in x and y directions areconserved and the energy is also conserved

[C]the linear momentum in x direction is conservedand the energy is also conserved

[D]the linear momentum in y direction is conservedand the energy is also conserved

13)The mechanism used in a shaping machine is

[A]a closed 4-bar chain having 4 revolute pairs [B]a closed 6-bar chain having 6 revolute pairs[C]a closed 4-bar chain having 2 revolute and 2

sliding pairs [D]an inversion of the single slider-crank chain.

14)The lengths of the links of a 4-bar linkage with revolute pairs only are p, q, r and s units. Given that p <q <r<s. Which of these links should be the fixed one, for obtaining a "double crank" mechanism ?

[A] link of length p [B] link of length g[C]link of length r [D]link of length s.

15)When a cylinder is located in a Vee-block, then number of degrees of freedom which are arrested is

[A]2 [B]4[C]7 [D]8

16)Mobility of a statically indeterminate structure is

[A] -1 [B]0[C]1 [D] 2

17)There are two points P and Q on a planer rigid body.The relative velocity between the two points

[A]should always be along PQ [B]can be oriented along any direction

[C]should always be perpendicular to PQ [D]should be along QP when the body undergoespure translation.

18)Which of the following statements in INCORRECT?




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[A]Grashoffs rule states that for a planar crank-rocker four bar mechanism, the sum of theshortest and longest link lengths cannot be lessthan the sum of the remaining two link lengths.

[B] Inversion of a mechanism are created by fixingdifferent links one at a time.

[C]Geneva mechanism is an intermittent motiondevice.

[D]Gruebler's criterion assumes mobility of a planarmechanism to be one.

19)For the configuration shown in Fig. 4, the angular velocity of link AB is 10 rad/s counterclockwise. Themagnitude of the relative sliding velocity (in m ) of slider B with respect to rigid link CD is

fig 4

[A]0 [B]0.86[C]1.25 [D]2.50

20)A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity and angularacceleration α. The magnitude of the acceleration of the point of contact on the disc is

[A]zero [B] r[C] [D]r

21)A double-parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of themechanism is

[A] -1 [B]0[C]1 [D]2

22)In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angularvelocity (rad/s) of the follower link for the instant shown in the figure is

note: All dimensions are in mm.

[A]0.05 [B]0.1[C]5.0 [D]10.0

23)For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CDis 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is




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[A]3 [B]3/2[C]1 [D]2/3

24)A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick returnmechanism is 2:1. If the radius of the crank O1P is 125 mm, then the distance 'd' (in mm) between thecrank centre to lever pivot centre point should be

[A]144.3 [B]216.5[C]240.0 [D]250.0

25)In the Figure shown, the relative velocity of link l with respect to link 2 is 12 m/sec. Link 2 rotates at aconstant speed of 120 rpm. The magnitude of Coriolis component of acceleration of link 1 is

[A]302 m/ [B]604 m/[C]906 m/ [D]1208 m/

26)

The Figure below shows a planar mechanism with single degree offreedom. The instant center 24 for the given configuration is located at a position

[A]L [B]M[C]N [D]




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27)A uniform stiff rod of length 800 mm and having a weight of 300 N is pivoted at one end and connected toa spring at the other end. For keeping the rod vertical in a stable position the minimum value of springconstant &needed is (See Figure)

[A]300 N/m [B]400 N/m[C]500 N/m [D]1000 N/m

28)The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is

[A]1 [B]2[C]3 [D]4

29)Match the followingType of Mechanism Motion achievedP. Scott-Russel mechanism 1. Intermittent . motionQ. Geneva mechanism 2. Quick return motionR. Off-set slider-crank 3. Simple harmonic mechanism motionS. Scotch Yoke mechanism 4. Straight line motion

[A]P-2 Q-3 R-1 S-4 [B]P-3 Q-2 R-4 S-1[C]P-4 Q-1.R-2 S-3 [D]P-4 Q-3 R-1 S-2.

30)Match the following with respect to spatial mechanisms.Type of Joint Degrees of constraintP - Revolute 1. ThreeQ - Cylindrical 2. FiveR - Spherical 3. Four

4. Two5. Zero

[A]P-1 Q-3 R-3 [B]P-5 Q-4 R-3[C]P-2 Q-3 R-1 [D]P-4 Q-5 B-3.

31)For a four-bar linkage in toggle position, the value of mechanical advantage is

[A]0.0 [B]0.5[C]1.0 [D]

32)The number of inversions for a slider crank mechanism is

[A]6 [B]5[C]4 [D]3




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33)A shell is fired from a connon Fig. At the instant the shell is just about to leave the barrel, its velocityrelative to the barrel is 3 m/s, while the barrel is swinging upwards with a constant angular velocity of 2rad/s. The magnitude of the absolute velocity of the shell is

[A]3 m/s [B]4 m/s[C]5 m/s [D]7 m/s

34)Match the items in columns I and IIColumn I Column IIP. Higher Kinematic pair 1. Grubler's equationQ. Lower kinematic pair 2. Line contactR. Quick-return mechanism 3. Euler's equationS. Mobility of a linkage 4. Planer

5. Shaper6. Surface contact

[A]P-2, Q-6, R-4, S-3 [B]P-6, Q-2, R-4, S-1 ;[C]P-6, Q-2, R-5, S-3 [D]P-2, Q-6, R-5, S-1.

35)In a four-bar linkage, S denotes the shortest link length, .L is the longest link length, P and Q are thelengths of other two links. At least one of the three moving links will rotate by if

[A]S+ L P + Q [B]S + L >P+Q[C]S+ P L + Q [D]S + P >L + Q.

36)A planar mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of themechanism, using Gruebler'e criterion, is

[A]0 [B]1[C]2 [D]3

37)A circular disk of radius .R rolls without slipping at a velocity v. The magnitude of the velocity at point P(See Figure) is

[A] [B]

[C] [D]




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.

38)The iuput link of a four bar linkage is rotated at 2 rad/s in counter clockwise direction as shown below.The angular velocity of the coupler PQ in rad/s, at an instant when is

[A]4 [B][C]1 [D]




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Key Paper

1. B 2. C 3. B 4. C 5. C

6. B 7. C 8. D 9. D 10. C

11. B 12. C 13. D 14. A 15. D

16. A 17. C 18. A 19. A 20. D

21. C 22. B 23. D 24. D 25. A

26. D 27. C 28. C 29. C 30. C

31. D 32. C 33. C 34. D 35. A

36. B 37. A 38. C




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An instantaneous configuration of a four-bar mechanism, whose plane is horizontal, is shown in the Fig. below. At this instant, the angular velocity and angular acceleration of link are = 8 rad/s and ,respectively, and the driving torque ( ) is zero. The link is balanced so that its centre of mass falls at

1)Which kind of 4-bar mechanism is ?

[A]Double- crank mechanism [B]crank- rocker mechanism[C]Double-rocker mechanism [D]parallelogram mechanism

2)At the instant considered, what is the magnitude of the angular velocity of ?

[A]1 rad/s [B]3 rad/s[C]8 rad/s [D]64/3 rad/s

3)At the same instant, if the component of the force at joint A along AB is 30 N, then the magnitude of thejoint reaction at

[A] is zero [B] is 30 N[C]is 78 N [D]cannot be determined from the given data

4)AB and CD two uniform and identical bars of mass 10 kg each, as shown in Fig. The hinges atA and B arefrictionless. The assembly is released from rest and motion occurs in the vertical plane. At the instant thatthe hinge B passes the point B', the angle between the two bars will be

[A]60 degrees [B]37.4 degrees[C]30 degrees [D]45 degrees

Dynamic analysis of single crank mechanism



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5)A mass of 35 kg is suspended from a weightless bar AC, which is supported by a cable CB and a pin at Aas shown in the figure. The pin reactions at A on the barAB are

[A] =343.4 N, =755.4 N [B] = 343.4 N, = 0[C] =755.4 N, = 343.4 N [D] =755.5 N, = 0

6)The percentage improvement in power capacity of a flat belt drive, when the wrap angle at the drivingpulley is increased from to by an idler arrangement for a friction coefficient of 0.3, is

[A]25.21 [B]33.92[C]40.17 [D]67.85

7)A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in next 5second interval. The acceleration ofthe car is

[A]7 [B]50 [C]25 [D]10

8)The difference between tensions on the tight and slack sides of a belt drive is 3000 N. If the belt speed is15 m/s, the transmitted power in kW is

[A]45 [B]22.5[C]90 [D]100

9)The profile of a cam in a particular zone is given by and . The normal to the cam profileat is at an angle (with respect to x axis)

[A] [B][C] [D]0

10)If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slenderrotating shaft, the first critical speed of the shaft in rpm is

[A]200 [B]450[C]600 [D]900

11)A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F asshown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitudeof vertical reaction developed at the support is

[A]zero [B]W/4[C]W/2 [D]W




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12)The ratio of tension on the tight side to that on the slack side in a flat belt drive is

[A]proportional to the product of coefficient of frictionand lap angle

[B]an exponential function of the product ofcoefficient of friction and lap angle.

[C]proportional to the lap angle [D]proportional to the coefficient of friction.13)With regard to belt drives with given pulley diameters, centre distance and coefficient of friction between

the pulley and the belt materials, which of the statement below are false ?

[A]A crossed flat belt configuration can transmitmore power than an open flat belt configuration

[B]A "V" belt has greater power transmissioncapacity than an open flat belt

[C]Power transmission is greater when belt tensionis higher due to centrifugal effects than the samebelt drive when centrifugal effects are absent.

[D]Power transmission is the greatest just before thepoint of slipping is reached.

14)For a spring-loaded roller-follower driven with a disc cam,

[A] the pressure angle should be larger during risethan that during return for ease of transmittingmotion

[B] the pressure angle should be smaller during risethan that during return for ease of transmittingmotion

[C]the pressure angle should be large during rise aswell as during return for ease of transmittingmotion

[D]the pressure angle does not affect the ease oftransmitting motion.

15)In an experiment to find the velocity and acceleration of a particular cam rotating at 10 rad./s, the values ofdisplacements and velocities are recorded. The slope of displacement curve at an angle of ' 'is 1.5 m/sand the slope of velocity curve at the same angle is - 0.5 m/ . The velocity and acceleration of the cam atthe instant are respectively

[A]15 m/s and -5m/ [B]15 m/s and 5m/[C]1.2 m/s and -0.5 m/ [D]1.2 m/s and 0.5 m/

16)A participle P is projected from the earth surface at latitude with escape velocity . Thevelocity direction makes an angle a with the local vertical. The particle will escape the earth's gravitationalfield

[A]only when [B]only when [C]only when [D]irrespetive of the value of




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.

17)A rigid body shown in the Figure (a) has a mass of 10 kg. It rotates with a uniform angular velocity ' '. Abalancing mass of 20 kg is attached as shown in Figure(b). The percentage increase in mass moment ofinertia as a result of this addition is

[A]25 % [B]50 %[C]100 % [D]200 %

18)A simple pendulum of length 5 m, with a bob of mass 1 kg, is in simple harmonic motion, as it passesthrough its mean position, the bob has a speed of 5 m/s. The net force on the bob at the mean position is

[A]zero [B]2.5 N[C]5 N [D]25 N

19)A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solidwheel has a mass of 20 kg and a radius of 1 m. Assuming that the wheel and the ground are both rigid andthat the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impactis approximately.

[A]zero [B]1/3 rad/s[C] [D]10/3 m/s

20)In a cam-follower mechanism, the follower needs to rise through 20 mm during 60° of cam rotation, thefirst 30° with a constant acceleration and then with a deceleration of the same magnitude. The initial andfinal speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speedof the follower is

[A]0.60 m/s [B]1.20 m/s[C]1.68 m/s [D]2.40 m/s

21)A rotating disc of 1 m diameter has two eccentric masses of0.5 kg each at radii of 50 mm and 60 mm atangular positions of 0° and 150°, respectively. A balancing mass of 0.1 kg is to be used to balance therotor. What is the radial position of the balancing mass?

[A]50 mm [B]120 mm[C]150 mm [D]280 mm

22)If a system is in equilibrium and the position of the system depends upon many . independent variables,the principle of virtual work states that the partial derivatives of its total potential energy with respect toeach of the independent variable must be

[A] -1.0 [B]0[C]1.0 [D]




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Key Paper

1. B 2. B 3. B 4. C 5. D

6. D 7. D 8. A 9. C 10. A

11. B 12. B 13. C 14. C 15. A

16. A 17. B 18. A 19. B 20. D

21. C 22. B




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1)A mass m attached to a light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, theperiod increases by I sec. The value of m is

[A]1 kg [B]1.6 kg[C]2 kg [D]2.4 kg

2)The arm OA of an epicyclic gear train shown in Fig. revolves counter clockwise about O with an angularvelocity of 4 rad/s. Both gears are of same size. The angular velocity of gear C, if the sun gear B is fixed, is

[A]4 rad/s [B]8 rad/s[C]10 rad/s [D]12 rad/s

3)To make a worm drive reversible, it is necessary to increase

[A]centre distance [B]worm diameter factor[C]number of starts [D]reduction ratio.

4)A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively.Gears Q and R are mounted on the same shaft as shown in the figure below. The diameter of the gear Qis twice that of the gear R. If the module of the gear R is 2 mm, the center distance in mm between gearsP and S is

[A]40 [B]80[C]120 [D]160

5)A 1.5 kW motor is running at t44O revl min. It is to be connected to a stirrer running at 36 rev/min. Thegearing arrangement suitable for this application is

[A]differential gear [B]helical gear[C]spur gear [D]worm gear

6)Large speed reductions (Greated than 20) in one stage of a gear train are possible through

[A]Spur gearing [B]Worm gearing[C]Bevel gearing [D]Helical gearing.

7)The sun gear in the Fig. is driven clockwise at 100 rpm. The ring gear is held stationary. For the numberof teeth shown on the gears the arm rotates at

Gear/Gear trains



____________________________________________________________________________________________________________________ Pg.No.294








[A]0 rpm [B]20 rpm[C]33.33 rpm [D]66.67 rpm

8)Tooth interference in an external involute spur gear pair can be reduced by

[A]decreasing center distance between gear pair [B]decreasing module.[C]decreasing pressure angle. [D]increasing number of gear teeth.

9)For the epicyclic gear arrangement shown in the Fig. 3, = 100 rad/s clockwise (CW) and = 80 rad/scounter

fig 3clockwise (CCW). The angular velocity (in rad/s) is

[A]0 [B]70 CW[C]140 CCW [D]140 CW

10)The following are the data for two crossed helical gears used for speed reduction:Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle If the input speed is 1440 rpm, the output speed in rpm is

[A]1200 [B]900[C]875 [D]720

11)An automotive engine weighing 240kg is supported on four springs with linear characteristics. Each of thefront two springs have a stiffness of 16MN/m while the stiffness of each rear spring is 32MN/m. The enginespeed (in rpm), at which resonance is likely to occur, is

[A]6040 [B]3020[C]1424 [D]955

12)A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6kN/m andthe damping constant of the damper is 400Ns/m. If the mass is 50kg, then the damping factor (d) anddamped natural frequency ( ), respectively, are

[A]0.471 and 1.19Hz [B]0.471 and 7.48Hz[C]0.666 and 1.35Hz [D]0.666 and 8.50Hz

Gear/Gear trains



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13)An epicyclic gear train is shown schematically in the adjacent figureThe sun gear 2 on the input shaft is a 20 teeth external gear. The planet gear 3 is a 40 teeth external gear.The ring gear 5 is a 100 teeth internal gear. The ring gear 5 is fixed and the gear 2 is rotating at 50 rpmccw (ccw=counter-clockwise and cw=clockwise)The arm 4 attached to the output shaft will rotate at

[A]10 rpm ccw [B]10 rpm cw[C]12 rpm cw [D]12 rpm ccw

14)Match the followingType of gears Arrangement of shaftsP. Bevel gears 1. Non-parallel off-set shaftsQ. Worm gears 2. Non-parallel intersecting shaftsR. Herringbone gears 3. Non-parallel intersecting shaftsS. hypoid gears 4. Parallel shafts


15)Match the items in columns I and IIColumn I Column IIP. Addendum 1. CamQ. instantaneous center of velocity 2. BeamR. Section modules 3. LinkageS. Prime circle 4.Gear

[A]P-4, Q-2, R-3, S-1 [B]P-4, Q-3, R-2, S-1[C]P-3, Q-2, R-1, S-4 [D]P-3, Q-4; R-1, S-2.

16)A spur gear has a module of 3 mm, number of teeth 16, a face width of 36 mm and a pressure angle of .It is transmitting a power of 3 kW at 20 rev/s. Taking a velocity factor of 1.5, and a form factor of 0.3, thestress in the gear tooth is about


Gear/Gear trains



____________________________________________________________________________________________________________________ Pg.No.296




.

17)Match the type of gears with their most appropriate description.

[A]P-2, Q-4, R-1, S-6 [B]P-1, Q.4, R-5, S-6[C]P-2, Q-6, R-4, S-2 [D]P-6, Q-3, R-1, S-5.

18)One tooth of a gear having 4 module and 32 teeth is shown in the Figure. Assume that the gear tooth andthe corresponding tooth space make equal intercepts on the pitch circumference. The dimensions 'a' and'b', respectively, are closest to

[A]6.08 mm, 4 mm [B]6.48 mm, 4.2 mm[C]6.28 mm, 4.3 mm [D]6.28 mm, 4.1 mm.

Gear/Gear trains



____________________________________________________________________________________________________________________ Pg.No.297


Key Paper

1. B 2. B 3. C 4. B 5. D

6. B 7. B 8. B 9. C 10. B

11. A 12. A 13. A 14. B 15. B

16. B 17. A 18. D

Gear/Gear trains



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1)A flywheel of moment of inertia fluctuates by 30 rpm for a fluctation in enerfy of 1936 Joules. Themean speed of the flywheel is (in rpm)

[A]600 [B]900[C]968 [D]2940

2)A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a meanangular speed of 20 rad/s. If the total fluctuation of speed is not to exceed 2%, the mass moment ofinertia of the flywheel in kg- is

[A]25 [B]50[C]100 [D]125

3)Which of the following statement is correct ?

[A]Flywheel reduces speed fluctuations during acycle for a constant load but flywheel does notcontrol the meanspeed of the engine if the load changes

[B]Flywheel does not reduce speed fluctuationsduring a cycle for a constant load, but flywheeldoes control the mean speed of the engine if theload changes

[C]Governor control a speed fluctuations during acycle for a constant load,.but governor does notcontrol the mean speed of the engine if the loadchanges

[D]Governor controls speed fluctuations during acycle for a constant load, and governor alsocontrols the mean speed of the engine if the loadchanges.

4)For a certain engine having an average speed of 1200 rpm, a flywheel approximated as a solid disc, isrequired for keeping the fluctuation of speed within 2% about the average speed. The fluctuation of kineticenergy per cycle is found to be 2 kJ. What is the least possible mass of the flywheel if its diameter is not toexceed 1 m ?

[A]40 kg [B]51 kg[C]62 kg [D]73 kg

5)A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. Ifit rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is

[A]395 [B]790[C]1580 [D]3160

6)If is the coefficient of speed fluctuation of a flywheel then the ratio of will be

[A] [B]

[C] [D]

7)The speed of an engine varies from 210 rad/s to 190 rad/s. During a cycle the change in kinetic energy isfound to be 400 Nm. The inertia of the flywheel in is

[A]0.10 [B]0.20[C]0.30 [D]0.40

Fly wheels



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Key Paper

1. A 2. A 3. A 4. B 5. B

6. D 7. A

Fly wheels



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A uniform rigid slender bar of mass 10 kg, hinged at the left end is suspended with the help of spring anddamper arrangement as shown in Fig. where K = 2 kN/m, C = 500 Ns/m and the stiffness of the torsionalspring is 1 kN/m/rad. Ignore the hinge dimensions.

1)The un-damped natural frequency of oscillations of the bar about the hinge point is

[A]42.43 rad/s [B]30 rad/s[C]17.32 rad/s [D]14.14 rad/s

2)The damping coefficient in the vibration equation is given by

[A]500 Nms/rad [B]500 N/(m/s)[C]80 Nms/rad [D]80 N/(m/s)

3)Air flows through a venturi and into atmosphere. Air density is p; atmospheric pressure is ; throatdiameter is ; exit diameter is D and exit velocity is U. The throat is connected to a cylinder containing africtionless piston attached to a spring. The spring constant is k. The bottom surface of the piston isexposed to atmosphere. Due to the flow, the piston moves by distance x. Assuming incompressiblefrictionless flow, x is (See Figure)

[A] [B]

[C] [D]

4)The natural frequency of a spring-mass system on earth is . The natural frequency of this system on themoon ( = /6)

[A] [B]0.408 [C]0.204 [D]0.167

5)A mass m attached to a spring is subjected to a harmonic force as show in Fig.The amplitude of theforced motfon is observed to be 50 mm. The value of m (in kg) is

[A]0.1 [B]1.0[C]0.3 [D]0.5

Mechanical vibrations



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6)A concentrated mass m is attached at the centre of a rod of length 2L as shown in the figure. The rod iskept in a horizontal equilibrium position by a spring of stiffness k. For very small amplitude of vibration,neglecting the weights of the rod and spring, the undamped natural frequency of the system is

[A] [B]

[C] [D]

7)A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure.Under frictionless condition, the natural frequency of the system in Hz is close to

[A]32 [B]23[C]16 [D]11

8) A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls withoutslipping on a horizontal surface. The natural frequency of vibration of the system is

[A] [B][C] [D]

9)A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibrationof machine to the natural frequency of the isolation system is equal to 0.5, then transmissibility of ratio ofisolation is

[A]1/2 [B]3/4[C]4/3 [D]2

10)A mass M, of 2O kg is attached to the free end of a steel cantilever beam of length 1000 mm having across-section of 25 x 25 mm. Assume the mass of cantilever to be neglegible and , = 200 GPa. If thelateral vibration of this system is critically damped using a viscous damper, then damping constant of thedamper is(See Figure)

[A]1250 Ns/m [B]625 Ns/m[C]312.50 Ns/m [D]156.25 Ns/m




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11)An ejector mechanism consists of a helical compression spring having a spring constant of K = 981 x N/m. It is pre-compressed by 100 mm from its free state. If it is used to eject a mass of 100 kg held on it,the mass will move up through a distance of (See Figure)

[A]100 mm [B]500 mm[C]981 mm [D]1000 mm

12)There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz, respectively. Theyare mounted on test setups for conducting vibration experiments. If a loud pure note of frequency 144 Hzis produced by some instrument, which of the samples will show the most perceptible induced vibration?

[A]P [B]Q[C]R [D]S

13)The differential equation governing the vibrating system is (See Figure)

[A]m +c +k(x-y) = 0 [B]m( - ) + c( - ) + kx = 0[C]m +c( - )+kx= 0 [D]n( - ) + c( - ) + k(x -y) = 0.

14)In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1kN/m. By introducing adamper the frequency of oscillation is found to be 90% of the original value. What is the dampingcoefficient of the damper?

[A]1.2 N.s/m [B]3.4 N.s/m[C]8.7 N.s/m [D]12.0 N.s/m

15) A weighing machine consists of a 2 kg pan resting on spring. In this condition, with the pan resting on thespring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the un-deformed length and the spring constant k (stiffness)are

[A] = 220 mm, k=1862 N/m [B] = 210 mm, k=1960 N/m[C] = 200 mm, k=1960 N/m [D] = 200 mm, k=2156 N/m

16)A machine of 250 kg mass is supported on springs of total stiffness 100 kN/m. Machine has anunbalanced rotating force of 350 N at speed of 3600 rpm. Assuming a damping factor of 0.15, the value oftransnissibility ratio is

[A]0.0531 [B]0.9922[C]0.0162 [D]0.0028

17)The natural frequency of the spring mass system shown in the Figure is closest to




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[A]8 Hz [B]10 Hz[C]12 Hz [D]14 Hz

18)A uniform rigid rod of mass m = 1 kg and length L = 1 m is hinged at its center and laterally supported atone end by a spring of spring constant k = 300 N/m. The natural frequency in rad/s is

[A]10 [B]20[C]30 [D]40

19)A compression spring is made of music wire of 2 mm diameter having a shear strength and shear modulusof 800 MPa and 80 GPa respectively. The mean coil diameter is 20 mm, free length is 40 mm and thenumber of active coils is 10. If the mean coil diameter is reduced to 10 mm, the stiffrress of the spring isapproximately

[A]decreased by 8 times [B]decreased by 2 times[C]increased by 2 times [D]increased by 8 times.

20)For an underdamped harmonic oscillator resonance

[A]occurs when excitation frequency is greater thanundamped natural frequency

[B]occurs when excitation frequency is less thanundamped natural frequency

[C]occurs when excitation frequency is equal toundamped natural frequency [D]never occurs.

21)The natural frequency of the system shown below is

[A] [B][C] [D]

22)The equation of motion of a harmonic oscillator is given by , and The initialconditions at t=0 are x(0)=X , . The amplitude of x(t) after n completes cycles is.

[A] [B][C] [D]X.

23)

Mass of the beam is ‘m’ and spring stiffness is ‘k’. A hinge is attached with the beam as shown above.What will be the natural frequency of the system.

[A] [B][C] [D]

24)In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility (T)?

[A]T is nearly unity at small excitation frequencies [B]T can be always reduced by using higherdamping at any excitation frequency

[C]T is unity at the frequency ratio of 2 [D]T is infinity at resonance for undamped systems




____________________________________________________________________________________________________________________ Pg.No.304










25)What is the natural frequency of the spring mass system shown below? The contact between the blockand the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants aredenoted by k1 and k2 as shown below.

[A] [B]

[C] [D]

26)Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. Atresonance, the phase angle (in degree) of the displacement with respect to the exciting force is

[A]0 [B]45[C]90 [D]135

27)High damping reduces the transmissibility if the non-dimensional frequency ration ( = forcingfrequency, = natural frequency )

[A] is less than [B] is greater than [C]is less than [D]is greater than

28)For lightly damped heavy rotor systems, resonance occurs when the forcing w is equal to

[A]2 [B][C] [D]

29)A cantilver beam of negligible weight is carrying a mass M at its free end, and is also resting on an elasticsupport of stiffness as shown in the figure below. If represents the bending stiffness of the beam, thenatural frequency (rad/s) of the system is:

[A] [B]

[C] [D]

30)The earth can be assumed as a uniform sphere. Suppose the earth shrinks by 1% in diameter, the newday period

[A]will not change from 24 hrs [B]will reduce by about 2%[C]will reduce by about 1% [D]will increase by about 1%

31)A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected toan impulse force of magnitude 5 kN for seconds. The amplitude in mm of the resulting free vibration is

[A]0.5 [B]1.0[C]5.0 [D]10.0

32)The natural frequency of an undamped vibrating system is 100 rad./s. A damper with a damping factor of0.8 is introduced into the system. The frequency of vibration of the damped system, in rad/s, is

[A]60 [B]75[C]80 [D]100




____________________________________________________________________________________________________________________ Pg.No.305







33)Consider the system of two wagons shown in Fig. The natural frequencies of this system are

[A] [B][C] [D]

34)In the shown, the spring deflects by to position A (the equilibrium position) when a mass m is kept on it.During free vibration, the mass is at position B at some instant. The change in potential energy of thespring-mass system from position A to position B is

[A] [B][C] [D]

35)As shown in Figure, a mass of 100 kg is held between two springs. The natural frequency of vibration ofthe system, in cycles/s, is

[A] [B][C] [D]

36)Two helical tensile springs of the same material and also having identical mean coil diameter and weight,have wire diameter d and d/2 .the ratio of their stiffnesses is

[A]1 [B]4[C]64 [D]128

37)If the length of the cantilever beam is halved, then natural frequency of the mass M at the end of thiscantilever beam of negligible mass is increased by a factor of

[A]2 [B]4[C] [D]8




____________________________________________________________________________________________________________________ Pg.No.306






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38)The assembly shown in the Fig. is composed of two massless rods of length l with two particles each ofmass m. The natural frequency of this assembly for small oscillations is

[A] [B][C] [D]

39)Consider the arrangement shown in the Figure below where J is the combined polar mass moment ofinertia of the disc and the shafts. , , are the torsional stiffness of the respective shafts. The naturalfrequency of torsional oscillation of the disc is given by

[A] [B]

[C] [D]


40)A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dash pot withdamping coefficient of 15 Ns/m. The value of critical damping of the system is

[A]0.223 Ns/m [B]17.88 Ns/m[C]71.4 Ns/m [D]223.6 Ns/m

41)The value of logarithmic decrement is

[A]1.35 [B]1.32[C]0.68 [D]0.66




____________________________________________________________________________________________________________________ Pg.No.307


Key Paper

1. A 2. C 3. D 4. A 5. A

6. D 7. A 8. C 9. C 10. A

11. A 12. C 13. C 14. C 15. B

16. C 17. B 18. C 19. D 20. B

21. A 22. A 23. D 24. B 25. D

26. C 27. B 28. C 29. C 30. D

31. C 32. A 33. A 34. A 35. C

36. C 37. C 38. D 39. B 40. D

41. D




____________________________________________________________________________________________________________________ Pg.No.308






Index- IM & OR

Sl.No. Name of the Topic Pg.No.s 1. Linear programming 310-311 2. PERT & CPM 312-314 3. Queuing Theory 315-317 4. Inventory control 318-321 5. Transportation 322-323 6. Forecasting 324-325 7. Scheduling 326-327 8. Sequencing 328-329 9. Material requirement & planning 330-331 10. Motion & Work study 332-334









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One unit of product requires 3 kg of resource and 1 kg of resource . One unit of product requires 2kg of resource and 2 kg of resource . The profits per unit by selling product and are Rs. 2000 andRs. 3000 respectively . The manufacturer has 90 kg of resource and 100 kg of resource .

1) The unit worth of resource , i.e. dual price of resource in Rs. per kg is

[A]0 [B]1350[C]1500 [D]2000

2)The manufacturer can make a maximum profit of Rs.

[A]60000 [B]135000[C]150000 [D]200000

3)A company produces two types of toys : P and Q. Production time of Q is twice that of P and the companyhas a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per dayonly. The company makes a profit of Rs 3 and Rs 5 on type P and q respectively. For maximization ofprofits, the daily production quantities of P and @ toys should respectively be

[A]100 , 500 [B]500, 1000[C]800, 600 [D]1000, 1000

4)If at the optimum in a linear programming problem, a dual variable corresponding to a particular primalconstraint is zero, then it means that

[A] right hand side of the primal constraint can bealtered without affecting the optimum solution

[B]changing the right hand side of the primalconstraint will disturb the optimum solution

[C]the objective function is unbounded [D]the problem is degenerate.5)A linear programming problem is shown below.

Maximize 3x + 7y

Subject to 3x + 7y 104x + 6y 8x, y 0

It has

[A]an unbounded objective function [B]exactly one optimal solution.[C]exactly two optimal solutions. [D]infinitely many optimal solutions.

6)A manufacturer produces two types of products, 1 and 2, at production levels and respectively. Theprofit is given is . The production constraints are

The maximum profit which can meet the constraints is

[A]29 [B]38[C]44 [D]75

7)Simplex method of solving linear programming problem uses

[A]all the points in the feasible region [B]only the corner points of the feasible region[C]intermediate points within the infeasible region [D]only the interior points in the feasible region.

Linear programming



____________________________________________________________________________________________________________________ Pg.No.310


Key Paper

1. A 2. B 3. C 4. C 5. B

6. A 7. B

Linear programming



____________________________________________________________________________________________________________________ Pg.No.311


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Consider the following PERT network:

The optimistic time, most likely time and pessimistic time of all the activities are given in the table below

1)The critical path duration of the network (in days) is

[A]11 [B]14[C]17 [D]18

2)The standard deviation of the critical path is

[A]0.33 [B]0.55[C]0.77 [D]0.88

3)In PERT analysis a critical activity has

[A]maximum Float [B]zero Float[C]maximum Cost [D]minimum Cost.

4)A project has six activities (A to F) with respective activity durations 7, 5, 6, 6, 8,4 days. The network hasthree paths A-B, C-D and E-F. All the activities can be crashed with the same crash cost per day. Thenumber of activities that need to be crashed to reduce the project duration by 1 day is

[A]1 [B]2[C]3 [D]6

5)For the network shown in Figure below, the objective is to find the length of the shortest path from node Pto node G. Let be the length of directed arc from node i to node j.

Let be the length of the shortest path from P to node j. Which of the following equations can be used tofind ?

PERT & CPM



____________________________________________________________________________________________________________________ Pg.No.312









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[A] [B][C] [D]

6)In PERT, the distribution of activity times is assumed to be

[A]Normal [B]Gamma[C]Beta [D]Exponential

7)A dummy activity is used in PERT network to describe

[A]precedence relationship [B]necessary time delay[C]resource restriction [D]resource idleness.

8)A project consists of three parallel paths with durations and variances of (10, 4),(12,4) and (12, 9)respectively. According to the standard PEBT assumptions, the distribution of the project duration is

[A]Beta with mean 10 and standard deviation 2 [B]Beta with mean 12 and standard deviation 2[C]Normal with mean 10 and standard deviation 3 [D]Normal with mean 12 and standard deviation 3.

9)A Project consists of activities A to M shown in the net in the following Fig. the duration of the activitiesmarked in days

The project can be completed

[A]Between 18 , 19 days [B]between 20,22 days[C]between 24,26 days [D]between 60, 70 days.

10)The project activities, precedence relationships and durations are described in the table. The critical pathof the project is

Activity precedence duration(in days)

P -- 3Q -- 4R P 5S Q 5

T R,S 7 U R,S 5 V T 2

W U 10

[A] P-R-T-V [B]Q-S-T-V[C]P-R-U-W [D]Q-S-U-W

11)The expected time ( ) of a PERT activity in terms of optimistic time ( ), pessimistic time ( ) and most likelytime ( ) is given by

[A] [B][C] [D]

PERT & CPM



____________________________________________________________________________________________________________________ Pg.No.313


Key Paper

1. D 2. D 3. B 4. C 5. C

6. C 7. A 8. B 9. C 10. D

11. A

PERT & CPM



____________________________________________________________________________________________________________________ Pg.No.314


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1)The cost of providing service in a queuing system increases with

[A] increased mean time in the queue [B] increased arrival rate[C]decreased mean time in the queue [D]decreased arrival rate.

2)Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival.The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poissonprocess and service times are exponentially distributed, the average waiting time in queue in min is

[A]3 [B]4[C]5 [D]6

3)At a production machine, parts arrive according to a Poisson process at the rate of 0.35 parts per minute.Processing time for parts have exponential distribution with mean of 2 minutes. What is the probability thata random part arrival finds that there are already 8 parts in the system (in machine + in queue) ?

[A]0.0247 [B]0.0576[C]0.0173 [D]0.082

4)In a single serve infinite population queuing model, arrivals follows a Poisson distribution with mean = 4per hour. The service times are exponential with mean service time equal to 12 minutes. The expectedlength of the queue will be

[A]4 [B]3.2[C]1.25 [D]5

5)Little's law is a relationship between

[A]stock level and lead time in an inventory system [B]waiting time and length of the queue in a queuingsystem

[C]number of machines and job due dates in ascheduling problem

[D]uncertainty in the activity time and projectcompletion time

6) Cars arrive at a service station according to Poisson's distribution with a mean rate of 5 per hour. Theservice time per car is exponential with a mean of 10 minutes. At steady state, the average waiting timein the queue is

[A]10 minutes [B]20 minutes[C]25 minutes [D]50 minutes

7)An electronic equipment manufacturer has decided to add a component sub-assembly operation that canproduce 80 units during a regular 8-hour shift. This operation consists of three activities as below.Activity Standard time(min.)M. Mechanical assembly 12E. Electric wiring 16T. Test 3For line balancing the number of work stations required for the activities M, E and T would respectively be

[A]2,3,1 [B]3,2,1[C]2,4,2 [D]2,1,3

8)A maintenance service facility has Poisson arrival rates, negative exponential service time and operateson a first come first served queue discipline. Breakdowns occur on an average of 3 per day with a range ofzero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero toseven. The mean waiting time for an item to be serviced would be

[A]1/6 day [B]1/3 day[C]1 day [D]3 days

9)Consider a single server queuing model with Poisson arrivals and exponential service .The number in the system is restricted to a maximum of 10. The probability that a person who comes inleaves without joining the queue is

Queuing theory



____________________________________________________________________________________________________________________ Pg.No.315





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[A]1/11 [B]1/10[C]1/9 [D]1/2

10)The number of customers arriving at a railway reservation counter is Poisson distributed with an arrivalrate of eight customers per hour. The reservation clerk at this counter takes six minutes per customer onan average with an exponentially distributed service time. The average number of the customers in thequeue will be

[A]3 [B]3.2[C]4 [D]4.2

11)In an M/M/1 queuing system, the number of arrivals in an interval of length T is a Poisson random variable

(i.e., the probability of there being n arrivals in an interval of length T is ). The probability densityfunction f(t) of the inter-arrival time is given by

[A] [B][C] [D]

Queuing theory



____________________________________________________________________________________________________________________ Pg.No.316


Key Paper

1. C 2. C 3. C 4. B 5. B

6. D 7. A 8. A 9. A 10. B

11. B

Queuing theory



____________________________________________________________________________________________________________________ Pg.No.317


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1)If the demand for an item is doubled and the ordering cost halved, the economic order quantity

[A] remains unchanged [B] increases by a factor of [C]is doubled [D]is halved.

2)Set up costs do not include

[A] labour cost of setting up machines [B]ordering cost of raw material[C]maintenance cost of the machines [D]cost of processing the work piece.

3)One of the following statements about PRS (Periodic Reordering System) is not true. Identify.

[A]PRS requires continuous monitoring of inventorylevels [B]PRS is useful in control of perishable items

[C]PRS provides basis for adjustments to accountfor variations in demand

[D]In PRS, inventory holding costs are higher than inFixed Recorder Quantity system

4)In inventory planning, extra inventory is unnecessarily carried to the end of the planning period when usingone of the following lot size decision policies :

[A]Lot - for - lot production [B]Economic Order Quantity (EOQ) lot size[C]Period Order Quantity (POQ) lot size [D]Part Period total cost balancing .

5)In computing Wilson's economic lot size for an item, by mistake the demand rate estimate used was 40%higher than the true demand rate. Due to this error in the lot size computation, the total cost of setups plusinventory holding per unit time would rise above the true optimum by approximately

[A]1.4% [B]6.3 %[C]18.3 % [D]8.7 %

6)An item can be purchased for Rs 100. The ordering cost is Rs 200 aud the inventory carrying cost is 10%of the item cost per annum. If the annual demand is 4000 units, then economic order quantity (in units) is

[A]50 [B]100[C]200 [D]400

7)Market demand for springs is 8,00,000 per annum. A company purchases these springs in lots aud sellsthem. The cost of making a purchase order is Rs 1,200. The cost of storage of springs is Rs 120 perstored piece per annum. The economic order quantity is

[A]400 [B]2828[C]4000 [D]8000

8)Two machines of the same production rate are available for use. On machine 1, the fixed cost is t 100 andthe variable cost is Rs 2 per piece produced. The corresponding numbers for the machine 2 are Rs 200and Rs 1 respectively. For certain strategic reasons both the machines are to be used concurrently. Thesale price of the first 800 units is Rs 3.50 per unit and subsequeatly it is only Rs 3.00. The breakevenproduction rate for each machine is

[A]75 [B]100[C]150 [D]600

9)Annual demand for window frames is 1000. Each frame costs rs 200 and ordering cost is rs 300 perorder. Inventory holding cost is rs 40 per frame per year. The supplier is willing to offer 2% discount if theorder quantity is 1000 or more, and 4% if order quantity is 2000 or more. Ifthe total cost is to beminimized, the retailer should

[A]order 200 frames every time [B]accept 2% discount[C]accept 4% discount [D]order Economic Order Quantity

10)The word kanban is most appropriately associated with

[A]econimic order quantity [B] just-in-time production

Inventory control



____________________________________________________________________________________________________________________ Pg.No.318







[C]capacity planning [D]product design11)There are two products P and Q with the following characteristics

The economic order quantity (EOQ) of products P and Q will be in the ratio

[A]1 : 1 [B]1 : 2[C]1 : 4 [D]1 : 8

12)A standard machine tool and an automatic machine tool are being compared. for the production of acomponent. Following data.refers to the two machines.

The breakeven production batch size above which the automatic machine tool will be economical to use,will be

[A]4 [B]5[C]24 [D]225

13)A company has an annual demand of 1000 units, ordering cost of Rs 100/ order and carrying cost of Rs100/ unit-year. If the stock-out costs are estimated to be nearly 400 each time the company runs out-of-stock, then safely stock justified by the carrying cost will be

[A]4 [B]20[C]40 [D]100

14)A component can be prod ced by any of the four processes I, II, III and IV. Process I has a fixed costof 20 and variable cost of RS. 3 per piece. Process II has a fixed cost of 50 and variable cost of Re 1 perpiece. Process III has a fixed cost of RS 40 and variable cost of RS 2 per piece. Process IV has a fixedcost of 10 and variable cost of Rs 4 per piece. If the company wishes to produce 100 pieces of thecomponent, from economic point of view it should choose

[A]process I [B]process II[C]process III [D]process IV

15)The distribution of lead time demand for an item is as follows:Lead time demand probability80 0.20100 0.25120 0.30140 0.25The reorder level is 1.25 times the expected value of the lead time demand. The service level is

[A]25 % [B]50 %[C]75 % [D]100 %

Inventory control



____________________________________________________________________________________________________________________ Pg.No.319







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16)Consider the following data for an item.Annual demand : 2500 units per year, Ordering cost Rs.100 per order Inventory holding rate:25% of unitprice.Price quoted by supplier

The optimum order quantity (in units) is

[A]447 [B]471[C]500 [D] 600

17)A stockist wishes to optimize the number of perishable items he needs to stock in any month in his store.The demand distribution for this perishable items is

The stockist pays Rs. 70 for each item and he sells each at Rs. 90. If the stock is left unsold in any month,he can sell the item at Rs. 50 each. There is no penalty for unfulfilled demand. To maximize the expectedprofit, the optimal stock level is

[A]5 units [B]4 units[C]3 units [D]2 units

18)The maximum level of inventory of an item is 100 and it is achieved with infinite replenishment rate. Theinventory becomes zero over one and half month due to consumption at a uniform rate. This cyclecontinues throughout the year. Ordering cost is Rs 100 per order and inventory carrying cost is Rs 10 permonth. Annual cost (in Rs) of the plan, neglecting material cost is

[A]1000 [B]2800[C]4800 [D]6800

19)The net requirements of an item over 5 consecutive weeks are 50-0-15-20-20. The inventory carrying costand ordering cost are Rs 1 per item week and Rs 100 per order respectively. Starting inventory is zero.use "Least Unit Cost Technique" for developing the plan. The cost of the plan (in RS) is

[A]200 [B]250[C]255 [D]260

20)In a machine shop, pins of 15 mm diameter are produced at a rate of 1000 per month and the same isconsumed at a rate of 500 per month. The production and consumption continue simultaneously till themaximum inventory is reached. Then inventory is allowed to reduce to zero due to consumption. The lostsize of production is 1000. If backlog is not allowed, the maximum inventory level is

[A]400 [B]500[C]600 [D]700

Inventory control



____________________________________________________________________________________________________________________ Pg.No.320


Key Paper

1. A 2. B 3. A 4. B 5. C

6. D 7. C 8. A 9. D 10. B

11. C 12. B 13. C 14. B 15. C

16. A 17. B 18. D 19. B 20. B

Inventory control



____________________________________________________________________________________________________________________ Pg.No.321


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.

1)The principles of motion economy are mostly used while conducting

[A]a method study on an operation [B]a time study on an operation

[C]a financial appraisal of an operation [D]a feasibility study of the proposed manufacturingplant.

2)The supply at three sources is 50, 40 and 60 units respectively whilst the demand at the four destinationsis 20, 30, 10 and 50 units. In solving this transportation problem

[A]dummy source of capacity 40 units is needed [B]a dummy destination of capacity 40 units isneeded

[C]no solution exists as the problem is infeasible [D]no solution exists as the problem is degenerate.3)The symbol used for Transport in work study is

[A] [B]T[C] [D]

4)A company has two factories S1, S2 and two warehouses D1, D2. The supplies from S1 and S2 are 50and 40 units respectively. Warehouse D1 requires a minimum of 20 units and a maximum of 40 units. Warehouse D2 requires a minimum of 20 units and, over and above, it can take as much as can besupplied. A balanced transportation problem is to be formulated for the above situation. The number ofsupply points, the number of demand points, and the total supply (or total demand) in the balancedtransportation problem respectively are

[A]2,4,90 [B]2,4,110[C]3,4,90 [D]3,4,110

5)A firm is required to procure three items (P, Q and R). The prices quoted for these items (in Rs). bysuppliers , ,and , are given in table. The management policy requires that each item has to besupplied by only one supplier and one supplier supply only one item. The minimum total cost (in Rs) ofprocurement to the firm is

[A]350 [B]360[C]385 [D]395

6)For the standard transportation linear program-me with m sources and n destinations and total supplyequaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero values(amounts from source i to destination j) is desired. The best upper bound for this number is

[A]mn [B]2( m + n )[C]m + n [D]m + n - 1

Transportation



____________________________________________________________________________________________________________________ Pg.No.322


Key Paper

1. A 2. B 3. A 4. C 5. C

6. D

Transportation



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1)In a forecasting model, at the end of period 13, the forecasted value for period 14 is 75. Actual value in theperiods 14 to 16 are constant at 100. If the assumed simple exponential smoothing parameter is 0.5, thehthe MSE at the end of period 16 is

[A]820.31 [B]273.44[C]43.75 [D]14.58

2)In simple exponential smoothing forecasting, to give higher weightage to recent demand information, thesmoothing constant must be close to

[A] -1 [B]zero[C]0.5 [D]1.0

3)In a time series forecasting model, the demand for five time periods was 10, 13, 15, 18 and 22. A linearregression fit resulted in an equation F = 6.9 + 2.9 t where F is the forecast for period t. The sum ofabsolute deviations for the five data is

[A]2.2 [B]0.2[C]-1.2 [D]24.3

4)The sale of cycles in a shop in four consecutive months are given as 70, 68, 82, 95. Exponentiallysmoothing average method with a smoothing factor of 0.4 is used in forecasting. The expected number ofsales in the next month is

[A]59 [B]72[C]86 [D]136

5)The demand and forecast for February are 12000 and 10275, respectively. Using single exponentialsmoothening method (smoothening coefficient = 0.25), forecastfor the month of March is

[A]431 [B]9587[C]10706 [D]11000

6)For a product, the forecast and the actual sales for December 2OO2 were 25 and 20 respectively. If theexponential smoothing constant ( ) is taken as 0.2, then forecast sales for January 2003 would be

[A]21 [B]23[C]24 [D]27

7)The sales of a product during the last four years wdre 860, 880, 870 and 890 units. The forecast for thefourth year was 876 units. If the forecast for the fifth year, using simple exponential smoothing, is equal tothe forecast using a three period moving average, the value of the exponential smoothing constant is

[A]1/7 [B]1/5[C]2/7 [D]2/5

8)A moving average system is used for forecasting weekly demand. and are sequences of forecastswith parameters and , respectively, where , and , ( > ) denote the numbers of weeks over whichthe moving averages are taken. The actual demand shows a step increase from to at a certain time.Subsequently,

[A]Neither nor will catch up with the value , [B]both sequences and will reach in the sameperiod

[C] will attain the value , before [D] will attain the value , before .

Forecasting



____________________________________________________________________________________________________________________ Pg.No.324


Key Paper

1. B 2. D 3. A 4. B 5. C

6. C 7. C 8. A

Forecasting



____________________________________________________________________________________________________________________ Pg.No.325


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Four jobs are to be processed on a machine as per data listed in the table.

Job Processing time Due date(in days)

1 4 6 2 7 9 3 2 19 4 8 17

1)If the Earliest Due Data (EDD) rule is used to sequence the jobs, the number of jobs delayed is

[A]1 [B]2[C]3 [D]4

2)Using the Shortest Processing Time (SPT) rule, total tardiness is

[A]0 [B]2[C]6 [D]8

3)Which one of the following is NOT a decision taken during the aggregate production planning stage?

[A]Scheduling of machines [B]Amount of labour to be committed[C]Rate at which production should happen [D]Inventory to be carried forward

4)A set of 5 jobs is to be processed on a single machine. The processing time (in days) is given in the tablebelow. The holding cost for each job is Rs. K per day.

A schedule that minimizes the total inventory cost is

[A]T-S-Q-R-P [B]P-R-S-Q-T[C]T-R-S-Q-P [D]P-Q-R-S-Z.

Scheduling



____________________________________________________________________________________________________________________ Pg.No.326


Key Paper

1. C 2. D 3. A 4. A

Scheduling



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1)A manufacturing shop processes sheet metal jobs, where in each job must pass through two machines (and , in that order). The processing time (in hours) for these jobs is

The optimal make-span(in hours) of the shop is

[A]120 [B]115[C]109 [D]79

Sequencing



____________________________________________________________________________________________________________________ Pg.No.328


Key Paper

1. B

Sequencing



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1)In a MRP system, component demand is

[A] forecasted [B]established by the master production schedule[C]calculated by the MRP system from the master

production schedule [D]ignored.

Material requirement & planning



____________________________________________________________________________________________________________________ Pg.No.330


Key Paper

1. C

Material requirement & planning



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1)The actual observed time for an operation was 1 minute per piece. If the performance rating of theoperator was 120 and a 5 percent personal time is to be provided, the standard time in minutes per pieceis:

[A]1.000 [B]1.200[C]1.250 [D]1.263

2)Statistical quality control was developed by

[A]Frederick Taylor [B]Water Shewhart[C]George Dantzig [D]W.E. Deming.

3)A stop watch time study on an operator with a performance rating of 120 yielded a time of 2 minutes. Ifallowances of 10% of the total available time are to be given, the standard time of the operation is

[A] 2 minutes [B]2.4 minutes[C]2.64 minutes [D]2.67 minutes.

4)The individual human variability in time studies to determine the production standard is taken care of by

[A]personal allowances [B]work allowances[C]rating factor [D]none of the above

5)In a weaving operation, the parameter to be controlled is the number of defects per 10 square yards ofmaterial. Control chart appropriate of this task is

[A]P-chart [B]C-chart[C]R-chart [D]

6)Which one of the following forecasting techniques is not suited for making forecasts for planningproduction schedules in the short range ?

[A]Moving average [B]Exponential moving average[C]Regression [D]Delphi

7)Analysis of variance is concerned with

[A]determining change in a dependent variable perunit change in an independent variable

[B]determining whether a qualitative factor affectsthe mean of an output variable

[C]determining whether significant correlation existsbetween an output variable and input variable

[D]determining whether variances in two or morepopulations are significantly different.

8)The first algorithm for Linear Programming was given by

[A]Bellman [B]Dantzing[C]Kulm [D]von Neumann

9)In a time study exercise, the time observed for an activity was 54 seconds. The operator had aperformance rating of 120. A personal time allowance of 107a is given. The standard time for the activity,in seconds, is

[A]54 [B]60.8[C]72 [D]58.32

10)The standard time of an operation while conducting a time study is

[A]mean observed time + allowances [B]normal time + allowances[C]mean observed time x rating factor + allowances [D]normal x rating factor + allowances.

11)Production flow analysis (PFA) is a method of identifying part families that uses data from

[A]engineering drawings [B]production schedule[C]bill of materials [D]route sheets

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12)A residential school stipulates the study hours as 8.00 pm to 10.30 pm. Warden makes random checks ona certain student 11 occasions a day during the study hours over a period of 10 days and observes that heis studying on 71 occasions. Using 95% confidence interval the estimated minimum hours of his studyduring that 10 day period is

[A]8.5 hours [B]13.9 hours[C]16.1 hours [D]18.4 hours

13)Vehicle manufacturing assembly line is an example of

[A]Product layout [B]process layout[C]manual layout [D]fixed layout.

14)An assembly activity is represented on an operation Process Chart by the symbol

[A]AA [B]A[C]D [D]O

15)The table gives details of an assembly line.

What is the line efficiency of the assembly line ?

[A]70% [B]75%[C]80% [D]85%

Motion & Work study



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Key Paper

1. D 2. B 3. C 4. C 5. B

6. D 7. D 8. B 9. C 10. B

11. D 12. C 13. A 14. D 15. C

Motion & Work study



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Index- Heat-Transfer

Sl.No. Name of the Topic Pg.No.s 1. Conduction 336-341 2. Fins/Transient hat conduction 342-343 3. Convection 344-346 4. Radiation 347-349 5. Heat Exchanger 350-352









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Heat is being transferred by convection from water at to a glass plate whose surface that is exposed tothe water is at . The thermal conductivity of water is 0.6 W/mK and the thermal conductivity of glass is1.2 W/mK. The spatial gradient of temperature in the water at the water-glass interface is

1)The value of the temperature gradient in the glass at the water-glass interface in K/m is

[A] [B]0.0[C] [D]

2)The heat transfer coefficient h in is

[A]0.0 [B]4.8[C]6 [D]750

3)A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder andsurroundings is 5 . It is proposed to reduce the heat loss from the pipe by adding insulation

having a thermal conductivity of 0.05 W/mK. Which one of the following statements is TRUE?

[A]The outer radius of the pipe is equal to the criticalradius. [B]The outer radius of the pipe is less than the

critical radius.

[C]Adding the insulation will reduce the heat loss. [D]Adding the insulation will increase the heat loss.4)Consider steady-state heat conduction across the thickness in a plane composite wall (as shown in the

figure) exposed to convection conditions on both sides.

Given

Assuming negligible contact resistance between the wall surfaces, the interface temperature, T (in ), ofthe two walls will be

[A] -0.50 [B]2.75[C]3.75 [D]4.50

5)One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate of 'q'can be written as

[A] [B][C] [D]

Conduction



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6)A stainless steel tub ( = 19 W/mK) of 2 cm ID and 5 cm OD is insulated with 3 cm thick asbestos ( = 0.2W/mK). If the temperature difference between the innermost and outermost surfaces is C, the heattransfer rate per unit length is

[A]0.94 W/m [B]9.44 W/m[C]944.72 W/m [D]9447.21 W/m

7)In a case of one-dimensional heat conduction in a medium with constant properties, T is the temperatureat position r, at time t. Then is proportional to

[A] [B][C] [D]

8)In a composite slab, the temperature at the interface (Tinter) between two materials is equal to theaverage of the temperatures at the two ends. Assuming steady one-dimensional heat conduction,which ofthe following statements is true about the respective thermal conductivities? (See Figure)

[A]2 = [B] = [C]2 = 3 [D] = 2

9)Heat flows through a composite slab, as shown below in Fig. The depth of the slab is 1 m. The k valuesare in W/mK. The overall thermal resistance in K/W is

[A]17.2 [B]21.9[C]28.6 [D]39.2

10)A 100 W electric bulb was switched on in a 2.5 m x 3 m x 3 m size thermally insulated room having atemperature of C. The room temperature at the end of 24 hours will be

[A] [B][C] [D]

11)With an increase in the thickness of insulation around a circular pipe, heat loss to surroundings due to

[A]convection increases, while that due toconduction decreases

[B]convection decreases, while that due toconduction increases

[C]convection and conduction decreases [D]convection and conduction increases.

Conduction



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12)For the three-dimensional object shown in the Figure below, five faces are insulated. The sixth face(PQRS), which is not insulated, interacts thermally with the ambient, with a convective heat transfercoefficient of l0 W/ .K. The ambient temperature is C. Heat is uniformly generated inside the object atthe rate of 100 W/ . Assuming the face PQRS to be at uniform temperature, its steady state temperatureis

[A] [B][C] [D]

13)Steady two-dimensional heat conduction takes place in the body shown in the Figure below. The normaltemperature gradients over surfaces P and Q can be considered to be uniform. The temperaturegradient at surface Q is equal to 10 K/m. Surfaces P and Q are maintained at constant temperatures asshown in the figure, while the remaining part of the boundary is insulated. The body has a constant thermal

conductivity of 0.1 W/m.K. The values of and at surface P are

[A] [B][C] [D]

14)A building has to be maintained at (dry bulb) and (wet bulb). The dew point temperature underthese conditions is . The outside temperature is (dry bulb) and the internal and external surfaceheat transfer coefficients are and respectively. If the building wall has a thermalconductivity of 1.2 W/m.K, the minimum thickness (in m) of the wall required to prevent condensation is

[A]0.471 [B]0.407[C]0.321 [D]0.125

15)A silicon sample is uniformly doped with phosphorous atoms/ and 2× boron atoms/ . If all thedopants are fully ionized, the material is

[A]n-type with carrier concentration of / [B]p-type with carrier concentration of /[C]p-type with carrier concentration of 2× / [D] will get damaged and will be safe

16)For a current carrying wire of 20 mm diameter exposed to air (h = 25 W/ K), maximum heat distributionoccurs when the thickness of insulation (k = 0.5 W/m K), is:

[A]20 mm [B]10 mm[C]2.5 mm [D]0 mm

17)Two insulating materials of thermal conductivity K and 2K are available for logging a pipe carrying a hotfluid. If the radial thickness of each material is the same.

[A]material with higher thermal conductivity shouldbe used for the inner layer and one with lowerthermal conductivity for the outer.

[B]material with lower thermal conductivity should beused for the inner layer and one with higherthermal conductivity for the outer.

[C] it is immaterial in which sequence the insulatingmaterials are used

[D]it is not possible to judge unless numerical valuesof dimensions are given

18)The one dimensional heat condition partial differential equation , is

Conduction



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[A]parabolic [B]hyperbolic[C]elliptic [D]mixed

19)For a current wire of 20 mm diameter exposed to air (h =2OW/ K), maximum heat dissipation occurswhen thickness of insulation (k = 0.5 W/mK) is

[A]20 mm [B]25 mm[C]20 mm [D]10 mm

20)The temperature variation under steady heat conduction across a composite slab of two materials withthermal conductivities and is shown in Fig. Then, which one of the following statements holds ?

[A] [B][C] [D]

21)Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; withboundary conditions as shown in the figure below. The conductivity of the wall is given by k = + bT ;where and b are positive constants, and T is temperature.

As x increases, the temperature gradient ( dT/dx ) will

[A] remain constant [B]be zero[C]increase [D]decrease

22)Consider one-dimensional steady state heat conduction along x-axis (0 x L), through a plane wall withthe boundary surfaces (x=0 and x=L) maintained at temperatures of and . Heat is generateduniformly throughout the wall. Choose the CORRECT statement.

[A]The direction of heat transfer will be from thesurface at to the surface at .

[B]The maximum temperature inside the wall mustbe greater than .

[C]The temperature distribution is linear within thewall.

[D]The temperature distribution is symmetric aboutthe mid-plane of the wall.

23)In a pulverized-fuel-fired large power boiler, the heat transfer from the burning fuel to the walls of thefurnace is

[A]by conduction only [B]by convection only[C]by conduction and convection [D]predominantly by radiation

24)It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1W/mK) to increase heat transfer withair. If the air side heat transfer coefficients is , then optimum thickness of enamel paint should be

[A]0.25 mm [B]0.5 mm[C]1 mm [D]2 mm

25)In descending order of magnitude, the thermal conductivity of (o) pure iron, (D) liquid water, (c) saturatedwater vapour, and (d) pure aluminum can be arranged as

Conduction



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.

[A]a b c d [B]b c a d[C]d a b c [D]d c b a

Conduction



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Key Paper

1. C 2. D 3. C 4. C 5. B

6. C 7. D 8. D 9. C 10. C

11. A 12. D 13. D 14. B 15. A

16. B 17. B 18. A 19. B 20. A

21. D 22. B 23. C 24. B 25. C

Conduction



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1)A steel ball of diameter 60 mm is initially in thermal equilibrium at in a furnace. It is suddenlyremoved from the furnace and cooled in ambient air at , with convective heat transfer coefficient h = 20W/ K. The thermo-physical properties of steel are: density ρ = 7800 kg/ , conductivity k = 40 W/mK andspecific heat c = 600 J/kgK. The time required in seconds to cool the steel ball in air from to is

[A]519 [B]931[C]100 [D]125

2)A steel steam pipe 10 cm inner diameter and 11 cm outer diameter is covered with an insulation having athermal conductivity of 1 WmK. If the convective heat transfer coefficient between the surface of insulationand the surrounding air is 8 W/ X, then critical radius of insulation is

[A]10 cm [B]11 cm[C]12.5 cm [D]15 cm

3)Lumped heat transfer analysis of a solid object suddenly exposed to a fluid medium at a differenttemperature is valid when

[A]Biot number <0.1 [B]Biot number >0.1[C]Fourier number <0.1 [D]Fourier number >0.1

4)The value of Biot number is very small (less than 0.01) when

[A] the convective resistance of the fluid is negligible [B] the conductive resistance of the fluid is negligible[C]the conductive resistance of the solid is negligible [D]none of these.

5)A fin has 5 mm diameter and 100 mm length. The thermal conductivity of fin material is 400 W.One end of the fin is maintained at 130° and its remaining surface is exposed to ambient air at

30°C. If the convective transfer coefficient is 40 W the heat loss (in W) from the fin is

[A]0.08 [B]5.0[C]7.0 [D]7.8

6)Which one of the following configurations has the highest fin effectiveness?

[A]Thin, closely spaced fins [B]Thin, widely spaced fins[C]Thick, widely spaced fins [D]Thick, closely spaced fins

7)A spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300 K.The heat transfer coefficient between the steel ball and the surrounding is . The thermalconductivity of steel is 20 W/mK. The temperature difference between the centre and the surface of thesteel ball is

[A] large because conduction resistance is far higherthan the convective resistance

[B] large because conduction resistance is far lessthan the convective resistance.

[C]small because conduction resistance is far higherthan the convective resistance.

[D]small because conduction resistance is far lessthan the convective resistance.

8)A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement oftemperature of a gas stream. The convective heat transfer co-efficient on the bead surface is 400 W/ KThermophysical properties of thermocouple material are k = 20 W/mK C = 400 J/kg K and p = 8500 kg/ .If the thermocouple initially at C is placed in a hot stream of C, then time taken by the bead to reach

, is

[A]2.35 s [B]4.9 s[C]14.7 s [D]29.4 s

Fins/Transient hat conduction



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Key Paper

1. A 2. C 3. A 4. B 5. B

6. A 7. D 8. B

Fins/Transient hat conduction



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1)A fluid flowing over a flat plate has the following properties:Dynamic viscosity: 25 kg /msSpecific heat : 2.0 kJ/kgKThermal conductivity : 0.05 W/mkThe hydrodynamic boundary layer thickness is measured to be 0.5 mm. The thickness of thermalboundary layer would be

[A]0.1 mm [B]0.5 mm[C]1.0 mm [D]None of the above

2)Heat transfer coefEcients for free convection in gases, forced convection in gases and vapours, and forboiling water lie, respectively in the ranges of

[A] [B][C] [D]

3)If there are m physical quantities and n fundamental dimensions in a particular process, the number ofnon-dimensional parameters is

[A]m + n [B]m x n[C]m - n [D]m / n

4)The properties of mercury at 300 K are : density = 18529 kg/ , specific heat at constant pressure = 0.1393kJ/kg-K dynamic viscosity = 0.1523 x N.s/ and thermal conductivity = 8.540 W/m-K. The Prandtlnumber of the mercury at 300 K is

[A]0.0248 [B]2.48[C]24.8 [D]248

5)Water (Prandtl number - 6) flows over a flat plate which is heated over the entire length. Which one of thefollowing relationship between the hydrodynamic boundary layer thickness and the thermal boundarylayer thickness is true ?

[A] [B][C] [D]can not be predicted

6)Consider a laminar boundary layer over a heated flat plate. The free stream velocity is tL. At somedistance x from the leading edge the velocity boundary layer thickness is , and the thermal boundarylayer thickness is . If the Prandtl number is greater than 1, then

[A] [B][C] [D]

7)A phenomenon is modelled using n dimensional variables with k primary dimensions. The number of nondimensional variables is

[A]k [B]n[C]n-k [D]n+k

8)Match the following :P : Compressible flow U : Reynolds numberQ : Free surface flow V : Nusselt numberR : Boundary layer flow W : Weber numberS : Pipe flow X : Froude numberT : Heat convection Y : Mach number Z : Skin friction coefficient

[A]P-U; Q-X; R-V; S-Z; T-W [B]P-W; Q-X; R-Z; S-U; T-V[C]P-Y; Q-W; R-Z; S-U; T-X [D]P-Y; Q-W; R-Z; S-U; T-V

Convection



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9)A coolant fluid at C flows over a heated flat plate maintained at a constant temperature of C. Theboundary layer temperature distribution at a given location on the plate may be approximated as T = 30 +70exp (−y) where y (in m) is the distance normal to the plate and T is in . If thermal conductivity of thefluid is 1.0W/mK, the local convective heat transfer coefficient (in W/ K) at that location will be

[A]0.2 [B]1[C]5 [D]10

10)The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness offlows of two fluids P and Q on a flat plate are 1/2 and 2 respectively. The Reynolds number based on theplate length for both the flows is . The Prandtl and Nusselt numbers for P are and 35 respectively. ThePrandtl and Nusselt numbers for Q are respectively


11)In a two-dimensional velocity field with velocities u and v along the x and y directions respectively, theconvective acceleration along the x-direction is given by

[A] [B]

[C] [D]

12)A small copper ball of 5 mm diameter at 500 K is dropped into an oil bath whose temperature is 300 K.The thermal conductivity of copper is 400 W/m.K its density and its specific heat 385 J/kg.K If theheat transfer coefficient is and lumped analysis is assumed to be valid, the rate of fall of thetemperature of the ball at the beginning of cooling will be, in K/s.

[A]8.7 [B]13.9[C]17.3 [D]27.7

13)For flow of fluid over a heated plate, the following fluid properties are known viscosity = 0.001 Pa.s ;specific heat at constant pressure = 1 kJ/kg.K ; thermal conductivity = 1W/m.K. The hydrodynamicboundary layer thickness at a specified location on the plate is 1 mm. The thermal boundary layerthickness at the same location is

[A]0.001 mm [B]0.01 mm[C]1 mm [D]1000 mm

14)The average heat transfer co-efficient on a thin hot vertical plate suspended in still air can be determinedfrom observations of the change in plate temperature with time as it cools. Assume the plate ' temperatureto be uniform at any instant of time and radiation heat exchange with the surroundings negligible. Theambient temperature is the plate has a total surface area of and a mass of 4 kg. The specific heatof the plate material is 2.5 kJ/kg.K. The convective heat transfer co-efficient in , at the instant whenthe plate temperature is and the change in plate temperature with time , is

[A]200 [B]20[C]15 [D]10


15)An un-insulated air conditioning duct of rectangular cross-section 1 m x 0.5 m, carrying air at with avelocity of 10 m/s, is exposed to an ambient of . Neglect the effect of duct construction material. For airin the range of 20 - , data are as follows: thermal conductivity = 0.025 W/m.K: viscosity = 18 Pa.s;Prandtl number = 073; density = 1.2 . The laminar flow Nusselt number is 3.4 for constant walltemperature conditions and, for turbulent flow, . The Reynolds number for the flow is

[A]4.44 [B]890[C] [D]

16)The heat transfer per metre length of the duct, in watts, is

[A]3.8 [B]5.3[C]89 [D]769

Convection



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Key Paper

1. B 2. A 3. C 4. A 5. B

6. A 7. C 8. D 9. B 10. A

11. A 12. C 13. C 14. D 15. C

16. D

Convection



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Radiative heat transfer is intended between the inner surfaces of two very large isothermal parallel metalplates. While the upper plate (designated as plate 1) is a black surface and is the warmer one beingmaintained at , the lower plate (plate 2) is a diffuse and gray surface with an emissivity of 0.7 and iskept at . Assume that the surfaces are sufficiently large to form a two-surface enclosure and steadystate conditions to exist. Stefan Boltzmann constant is given as 5.67× W/

1)The irradiation (in kW/ ) for the upper plate (plate 1) is

[A]2.5 [B]3.6[C]17.0 [D]19.5

2)If plate 1 is also a diffuse and gray surface with an emissivity value of 0.8, the net radiation heat exchange(in kW/ ) between plate 1 and plate 2 is

[A]17.0 [B]19.0[C]23.0 [D]31.7

3)The following Fig. was generated from experimental data relating spectral black body emissive power towavelength at three temperatures .

The conclusion is that the measurements are

[A]correct because the maxima in . show thecorrect trend [B]correct because Planck's law is satisfied

[C]wrong because the Stefan Boltzmann law is notsatisfied.

[D]wrong because Wien's displacement law is notsatisfied.

4)A solid cylinder (surface 2) is located at the centre ofa hollow sphere (surface 1). The diameter of thesphere is 1 m, while the cylinder has a diameter and length of 0.5 m each. The radiation configurationfactor is

[A]0.375 [B]0.625[C]0.75 [D]1

5)A hollow enclosure is formed between two infinitely long concentric cylinders of radii 1 m and 2 m,respectively. Radiative heat exchange takes place between the inner surface of the larger cylinder(surface-2) and the outer surface of the smaller cylinder (surface-1). The radiating surfaces are diffusedand the medium in the enclosure is nonparticipating. The fraction of the thermal radiation leaving the largersurface and striking itself is (See Figure)

[A]0.25 [B]0.5[C]0.75 [D]1

6)The radiative heat transfer rate per unit area (W/ ) between two plane parallel grey surfaces (emissivity =0.9) maintained at 400 K and 300 K is:

[A]992 [B]812[C]464 [D]567

Radiation



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7)In radio-active heat transfer, a gray surface is one

[A]which appears gray to the eye [B]whose emissivity is independent of wavelength[C]which has reflectivity equal to zero [D]which appears equally bright from all directions.

8)Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 Kand 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67 × W/ , the net radiation heat exchange rate in kW/ between the two plates is

[A]0.66 [B]0.79[C]0.99 [D]3.96

9)Global warming is caused by

[A]ozone [B]carbon dioxide[C]nitrogen [D]carbon monoxide

10)For the circular tube of equal length and diameter shown below, the view factor is 0.17. The viewfactor in this case will be.

[A]0.17 [B]0.21[C]0.79 [D]0.83

11)What is the value of the view factor for two inclined flat plates having common edge of equal width, andwith an angle of 20 degrees ?

[A]0.83 [B]1.17[C]0.66 [D]1.34

12)A plate having 10 c area each side is hanging in the middle of a room of 100 m2 total surface area. Theplate temperature and emissivity are respectively 800 K and 0.6. The temperature and emissivity valuesfor the surfaces of the room are 300 K and 0.3 respectively. Boltzmann's constant = 5.67 x W/ .The total heat loss from the two surfaces of the plate is

[A]13.66 W [B]27.32 W[C]27.87 W [D]13.66 MW

13)For an opaque surface, the absorptivity ( ) , transmissivity ( ) and reflectivity ( ) are related by theequation:

[A] + = [B] + + = 0[C] + = 1 [D] + = 0

14)Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If andare the diameters of the inner and outer tubes respectively, then the view factor is given by

[A] [B]zero[C] [D]

Radiation



____________________________________________________________________________________________________________________ Pg.No.348


Key Paper

1. A 2. D 3. D 4. B 5. D

6. B 7. B 8. A 9. B 10. D

11. A 12. B 13. C 14. D

Radiation



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Water (specific heat, cp = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of . Thepipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux in W/ :

1)If = 5000 and the convection heat transfer coefficient at the pipe outlet is 1000 W/ K, the temperaturein at the inner surface of the pipe at the outlet is

[A]71 [B]76[C]79 [D]81

2)If = 2500x, where x is in m and in the direction of flow (x = 0 at the inlet), the bulk mean temperature ofthe water leaving the pipe in is

[A]42 [B]62[C]74 [D]104

3)Air enters a counterflow heat exchanger at C aud leaves at C. Water enters at C and leaves atC. The LMTD in degree C is

[A]5.65 [B]4.43[C]19.52 [D]20.17

4)For the same inlet and outlet temperatures of hot and cold fluids, the Log Mean Temperature Difference(LMTD) is

[A]greater for parallel flow heat exchanger than forcounter flow heat exchanger.

[B]greater for counter flow exchanger than forparallel flow heat exchanger.

[C]same for both parallel and counter flow heatexchangers. [D]dependent on the properties of the fluids.

5)In a counter flow heat exchanger, for the hot fluid the heat capacity = 2 kJ/kg K mass flow rate = 5 kg/s,inlet temperature = , outlet temperature = . For the cold fluid, heat capacity = C kJ/kg K mass flowrate = 10 kg/s, inlet temperature = . Neglecting heat transfer to the surroundings, the outlettemperature of the cold fluid in is

[A]7.5 [B]32.5[C]45.5 [D]70.0

6)In a condenser of a power plant, the steam condenses at a temperature of 60 °C. The cooling water entersat 30 °C and leaves at 45 °C. The logarithmic mean temperature difference (LMTD) of the condenser is

[A]16.2 °C [B]21.6 °C[C]30 °C [D]37.5 °C

7)Water ( = 4.18 kJ/kg.K) at C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air( = 1 kJ/kg.K) enters at C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchangeris 0.8, the LMTD (in ) is

[A]40 [B]20[C]10 [D]5

8)In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specificheat at constant pressure and mass flow rate) of the hot and cold fluid are equal. The hot fluid, flowing at1kg/s with = 4kJ/kgK, enters the heat exchanger at C while the cold fluid has an inlet temperature of

C. The overall heat transfer coefficient for the heat exchanger is estimated to be 1kW/ K and thecorresponding heat transfer surface area is 5 . Neglect heat transfer between the heat exchanger and theambient. The heat exchanger is characterized by the following relation:2 = 1 − exp (−2NTU) .The exit temperature (in ) for the cold fluid is

[A]45 [B]55[C]65 [D]75

Heat exchanger



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9)Hot oil is cooled from 80°C to 50°C in an oil cooler which uses air as the coolant. The air temperature risesfrom 30°C to 40°C. The designer uses a LMTD value of 26°C. The type of heat exchanger is

[A]parallel [B]double pipe[C]counter flow [D]cross flow

10)The logarithmic mean temperature difference (LMTD) of a counterflow heat exchanger is C. The coldfluid enters at C and the hot fluid enters at C. Mass flow rate of the cold fluid is twice that of the hotfluid. Specific heat at constant pressure of the hot fluid is twice that of the cold fluid. The exit temperatureof the cold fluid

[A] is C [B] is C[C]is C [D]cannot be determined

11)In a counter flow heat exchanger, hot fluid enters at and cold fluid leaves at . Mass flow rate of thehot fluid is 1 kg/s and that of the cold fluid is 2 kg/s. Specific heat of the hot fluid is 10 kJ/kg.K and that ofthe cold fluid is 5 kJ/kg.K. The Log Mean Temperature Difference (LMTD) for the heat exchanger in is

[A]15 [B]30[C]35 [D]45

12)The practice to use steam on the shell side and cooling water on the tube side in condensers of steampower plant is because

[A] to increase overall heat transfer coefficient aswater side velocity can be increased if water is onthe tube side.

[B]condenser can act as a storage unit forcondensed steam

[C]rate of condensation of steam is invariablysmaller than the mass flow rate of cooling water.

[D]it is easier to maintain vacuum on the shell sidethan on the tube side.

13)In a certain heat exchanger, both the fluids have identical mass flow rate-specific heat product. The hotfluid enters at and leaves at and the cold fluid entering at leaves at . The effectiveness ofthe heat exchanger is

[A]0.16 [B]0.58[C]0.72 [D]1.0

Heat exchanger



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Key Paper

1. D 2. B 3. B 4. B 5. B

6. B 7. C 8. B 9. D 10. A

11. C 12. A 13. D

Heat exchanger



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