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1

General Aptitude

Q. No. 1 – 5 Carry One Mark Each

1. Based on the given statements, select the appropriate option with respect to grammar and

usage. Statements

(i) The height of Mr. X is 6 feet.

(ii) The height of Mr. Y is 5 feet.

(A) Mr. X is longer than Mr. Y.

(B) Mr. X is more elongated than Mr. Y.

(C) Mr. X is taller than Mr. Y.

(D) Mr. X is lengthier than Mr. Y.

Key: (C)

2. The students the teacher on teachers’ day for twenty years of dedicated teaching.

(A) facilitated (B) felicitated (C) fantasized (D) facillitated

Key: (B)

3. After India’s cricket world cup victory in 1985, Shrotria who was playing both tennis and

cricket till then, decided to concentrate only on cricket. And the rest is history.

What does the underlined phrase mean in this context?

(A) history will rest in peace (B) rest is recorded in history books

(C) rest is well known (D) rest is archaic

Key: (C)

4. Given 1/2 1/2

9 inches 0.25yards , which one of the following statements is TRUE?

(A) 3 inches = 0.5 yards (B) 9 inches = 1.5 yards

(C) 9 inches = 0.25 yards (D) 81 inches = 0.0625 yards

Key: (C)

5. S, M, E and F are working in shifts in a team to finish a project. M works with twice the

efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in a

day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to

contribution of E in the project?

(A) 1:1 (B) 1:2 (C) 1:4 (D) 2:1

Key: (B)




2

Q. No. 6 – 10 Carry Two Marks Each

6. The Venn diagram shows the preference of the student population for leisure activities.

From the data given, the number of students who like to read books or play sports is .

(A) 44 (B) 51 (C) 79 (D) 108

Key: (D)

Exp: From Venn diagram

n(A) no of persons reading books 13 44 12 7 76

n(B) no of persons playing 15 44 7 17 83

n(A B) 51

n(A B) n(A) n(B) n(A B) 76 83 51 108

7. Social science disciplines were in existence in an amorphous form until the colonial period

when they were institutionalized. In varying degrees, they were intended to further the colonial

interest. In the time of globalization and the economic rise of postcolonial countries like India,

conventional ways of knowledge production have become obsolete.

Which of the following can be logically inferred from the above statements?

(i) Social science disciplines have become obsolete.

(ii) Social science disciplines had a pre-colonial origin.

(iii) Social science disciplines always promote colonialism.

(iv) Social science must maintain disciplinary boundaries.

(A) (ii) only (B) (i) and (iii) only

(C) (ii) and (iv) only (D) (iii) and (iv) only

Key: (A)

8. Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without

number markings seemed to show 1:30. What is the actual current time shown by the clock?

(A) 8:15 (B) 11:15 (C) 12:15 (D) 12:45

Key: (D)

Exp: If reflection is seen as Actual will be

Thus present time will be 10:30 2:15 12:45

1:3010:30

29




3

9. M and N start from the same location. M travels 10 km East and then 10 km North-East. N

travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between

M and N at the end of their travel?

(A) 18.60 (B) 22.50 (C) 20.61 (D) 25.00

Key: (C)

10. A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a

square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of

the side of the square (in mm) such that the combined area of the square and the rectangle is a

MINIMUM?

(A) 30 (B) 40 (C) 120 (D) 180

Key: (B)

Exp: x y 340

Perimeter of rectangle x 2x

2 2x3 3

Perimeter of square 340 2x

Length of square340 2x

4

2

2340 2x 2Totalarea x f (x)

4 9

4 2x 340

f '(x) x 09 4

4 1

x 340 2x x 909 4

Length of square340 2x

40mm4

Mechanical Engineering

Q. No. 1 – 25 Carry One Mark Each

1 A real square matrix A is called skew-symmetric if

(A) AT

= A

(B) AT

= A-1

(C) AT

= A

(D) AT

= A+A-1

Key: (C)

2 e

3xx 0

log (1 4x)l t is equal to

e 1

(A) 0 (B) 1

12 (C)

4

3 (D) 1

Key: (C)

x/ 3

Square Rectangle

x

x

2x/ 3




4

Exp: e

3xx 0

log (1 4x) 0lim

e 1 0

3x 0x 0

1.4

4 41 4xlime .3 (1 4.0)e .3 3

3. Solutions of Laplace’s equation having continuous second-order partial derivatives are called

(A) biharmonic functions

(B) harmonic functions

(C) conjugate harmonic functions

(D) error functions

Key: (B)

4. The area (in percentage) under standard normal distribution curve of random variable Z within

limits from −3 to +3 is _____

Key: 99.74

Exp:

5. The root of the function f(x) = x3+x1 obtained after first iteration on application of Newton-

Raphson scheme using an initial guess of x0=1 is

(A) 0.682 (B) 0.686 (C) 0.750 (D) 1.000

Key: (C)

Exp: We have

n

n 1 n

n

f xx x

f x

For n=0,

0

1 0

0

f xx x

f x

3 2

0

0 0

1

f (x) x x 1 f (x) 3x 1

given x 1

f x f (1) 1, f x f (1) 4

1 3x 1 0.75

4 4

3 99.74%

1 68.4%

2 95.45%

0




5

6. A force F is acting on a bent bar which is clamped at one end as shown in the figure.

The CORRECT free body diagram is

(A) (B)

(C) (D)

Key: (A)

7. The cross-sections of two solid bars made of the same material are shown in the figure. The

square cross-section has flexural (bending) rigidity I1, while the circular cross-section has

flexural rigidity I2. Both sections have the same cross-sectional area. The ratio I1/I2 is

(A) 1/

(B) 2 /

(C) / 3

(D) / 6

Key: (C)

Exp: Flexural rigidity = EI

Both have same cross-section area

2 2a d4

Where a is side of square and d is diameter of circle.

2

4 4a d16

2 44

11

442

2

daE

I 12 1612

I 3d dE6464

( 1 2E E because of same material)




6

8. The state of stress at a point on an element is shown in figure (a). The same state of stress is

shown in another coordinate system in figure (b).

The components (xx,yy,xy) are given by

(A) p / 2, p / 2, 0

(B) (0,0,p)

(C) p, p,p / 2

(D) 0,0, p / 2

Key: (B)

Exp: We know,

x y x y

xycos2 sin 22 2

Where, is the location of any oblique plane which making an angle in CCW direction.

o

xx x yWhen 45 , , p, p

o

xx

p p p pcos90 0

2 2

When o45 , yy

op p p p

cos90 02 2

When o45 , xy

We know x y

xysin 2 cos22

xy

p psin90 p

2

xx yy xy, , is 0, 0,p

9. A rigid link PQ is undergoing plane motion as shown in the figure (VP and VQ are non-zero). VQP

is the relative velocity of point Q with respect to point P.

Which one of the following is TRUE?

(A) VQP has components along and perpendicular to PQ

(B) VQP has only one component directed from P to Q

(C) VQP has only one component directed from Q to P

(D) VQP has only one component perpendicular to PQ

Key: (D)

a b




7

Exp: Let P QV & V make an angle and with axis of link PQ respectively.

Since link PQ is rigid, so the distance between P & Q will never change. Hence relative

velocity between P & Q along axial direction should be zero.

p QV cos V sin

Relative velocity between P & Q

r

P

r

Q

r

P Q

V sin PQ to PQ

V sin PQ to PQ

V sin V sin PQ to PQ

10. The number of degrees of freedom in a planar mechanism having n links and j simple hinge

joints is

(A)3(n 3) 2j (B) 3(n 1) 2j (C) 3n 2j (D) 2j 3n 4

Key: (B)

Exp: DOF F 3 n 1 2j

Where, n total number of links

j = Effective number of binary points

11. The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1

mm. Assume the acceleration due to gravity g =10 m/s2. The natural frequency of this spring-

mass system (in rad/s) is ______

Key: (100)

Exp: 3

st

n 3

st

10 m

g 10100 rad/sec

10

12. Which of the bearings given below SHOULD NOT be subjected to a thrust load?

(A) Deep groove ball bearing

(B) Angular contact ball bearing

(C) Cylindrical (straight) roller bearing

(D) Single row tapered roller bearing

Key: (C)

QV sin

PV sin

PV sin

PV cos

QV cos

QV sin

PV cos

PV sin

PV

QV

QV cos

P

Q

QV sin




8

13. A channel of width 450 mm branches into two sub-channels having width 300 mm and 200

mm as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible

flow through the main channel is 0.9 m3/s and the velocity in the sub-channel of width 200

mm is 3 m/s, the velocity in the sub-channel of width 300 mm is m/s.

Assume both inlet and outlet to be at the same elevation.

Key: 1

Exp: Apply Mass conservation and taking incompressibility

We have

3

1 1 2 2 3 3 1 1

2

2

2

A V A V A V Given A V 0.9m /s

0.9 0.3V 0.2 3

0.9 0.6 0.3V

V 1m / s

14. For a certain two-dimensional incompressible flow, velocity field is given by 2ˆ ˆ2xyi y j . The

streamlines for this flow are given by the family of curves

(A) 2 2x y constant (B) 2xy constant

(C) 22xy y = constant (D) xy constant

Key: (B)

Exp: 2ˆ ˆv 2xyi y j

u vy x

2xydy d

2

2 2

2 2

2

On integrating

= xy f x

y f ' x yx

y f ' x y

f ' x 0 f x constant

=xy constant

1

2

3

2V ?

3V 3m/s

30.9m /s

300mm

450mm

200mm




9

15. Steady one-dimensional heat conduction takes place across the faces 1 and 3 of a composite

slab consisting of slabs A and B in perfect contact as shown in the figure, where kA , kB denote

the respective thermal conductivities. Using the data as given in the figure, the interface

temperature T2 (in °C) is .

Key: 67.5

Exp: 2 31 2

A B

A B

2 2

T TT T

L L

k A k A

130 T T 30

0.1 0.3

20 100

2 2

2

o

2

390 3T 5T 150

8T 540

T 67.5 C

Interface temperature o67.5 C

16. Grashof number signifies the ratio of

(A) inertia force to viscous force

(B) buoyancy force to viscous force

(C) buoyancy force to inertia force

(D) inertia force to surface tension force

Key: (B)

Exp: Grashof number 2

Inertia force Buoyant force(Gr)

(Viscous force)

17. The INCORRECT statement about the characteristics of critical point of a pure substance is

that

(A) there is no constant temperature vaporization process

(B) it has point of inflection with zero slope

(C) the ice directly converts from solid phase to vapor phase

(D) saturated liquid and saturated vapor states are identical

Key: (C)

Exp: The process of conversion from solid phase to vapour phase is called sublimation and this

does not happen at critical point. All the other statements are true at Critical point.




10

18. For a heat exchanger, ∆Tmax is the maximum temperature difference and ∆Tmin is the minimum

temperature difference between the two fluids. LMTD is the log mean temperature difference.

Cmin and Cmax are the minimum and the maximum heat capacity rates. The maximum possible

heat transfer (Qmax) between the two fluids is

(A) Cmin LMTD (B) Cmin ∆Tmax (C) Cmax ∆Tmax (D) Cmax ∆Tmin

Key: (B)

Exp: In a heat exchanger, maximum possible heat transfer will be.

max min maxQ C T

19. The blade and fluid velocities for an axial turbine are as shown in the figure.

The magnitude of absolute velocity at entry is 300 m/s at an angle of 65 to the axial direction,

while the magnitude of the absolute velocity at exit is 150 m/s. The exit velocity vector has a

component in the downward direction. Given that the axial (horizontal) velocity is the same at

entry and exit, the specific work (in kJ/kg) is _____

Key: 52.80

Exp: Given: o90 65 25 .

Let ‘1’ & ‘2’ denotes inlet & outlet of vane.

Vane velocity (u) = 1 2u u 150m / s.

Inlet:

Velocity of whirling 1w 1V V cos

300cos25 271.89m / s

Velocity of flow 1f 1V V sin

300sin25 126.7854m / s

Absolute velocity of Inlet =1 1w fV V

It is given that horizontal velocity is same at entry & exit.

So,

1 2f fV V

2

1 o

126.7859 V cos

126.7854cos 32.3

150

2w 2V V sin(32.3) 80.16m / s




11

Absolute velocity at outlet

2 22 f wV V V

Specific work done on the fluid per unit weight sp( w )

2 1sp w ww u. V V

Let j unit vector positive toward upward.

ˆ ˆ ˆw ( 150 j). (271.89 j) ( 80.16 j) 52.8075kJ / kg

20. Engineering strain of a mild steel sample is recorded as 0.100%. The true strain is

(A) 0.010% (B) 0.055% (C) 0.099% (D) 0.101%

Key: (C)

Exp: 0.1

100

We know,

T ln 1 , where T is True strain and is Engineering strain

T

0.1ln 1 0.0009995

100

T % 0.0009995 100 0.099%

2wV 80.16

1wV 271.89m / sec

( )Ve

( )Ve

u 150m / sec

( )Ve

2rV

2wV

2fV

1V1wV

1fV

1rV

65

u 150m / s

2u

2V

1u




12

21. Equal amounts of a liquid metal at the same temperature are poured into three moulds made of

steel, copper and aluminum. The shape of the cavity is a cylinder with 15 mm diameter. The

size of the moulds are such that the outside temperature of the moulds do not increase

appreciably beyond the atmospheric temperature during solidification. The sequence of

solidification in the mould from the fastest to slowest is

(Thermal conductivities of steel, copper and aluminum are 60.5, 401 and 237 W/m-K,

respectively. Specific heats of steel, copper and aluminum are 434, 385 and 903 J/kg-K,

respectively.

Densities of steel, copper and aluminum are 7854, 8933 and 2700 kg/m3, respectively.)

(A) Copper - Steel - Aluminum

(B) Aluminum - Steel – Copper

(C) Copper - Aluminum - Steel

(D) Steel - Copper - Aluminum

Key: (C)

Exp: steel steel steel

copper copper copper

A1 A1 Al

K 60.5; 7854; C 434 J/kg K

K 401; 8933; C 385 J/kg K

K 237; 2700; C 903 J/kg K

c

3

steel

3

copper

3

A1

Heat capacity

c 3408.636 kJ/m K

c 3439.205 kJ/m K

c 2438.100 kJ/m K

3 3 2

steel

steel

3 3 2

copper

copper

3 3 2

A1

A1

k 60.510 0.0177 10 m /s

c 3408

k 40110 0.1166 10 m /s

c 3439

k 23.710 0.1119 10 m /s

c 2438

So, cooling rates would be copper, Aluminium, steel

22. In a wire-cut EDM process the necessary conditions that have to be met for making a

successful cut are that

(A) wire and sample are electrically non-conducting

(B) wire and sample are electrically conducting

(C) wire is electrically conducting and sample is electrically non-conducting

(D) sample is electrically conducting and wire is electrically non-conducting

Key: (B)

Exp: In this process, a thin metallic wire is fed on to the conducting workpiece, which is submerged

in a tank of dielectric fluid such as de-ionized water. Wire is fed in the programmed path &

material is cut from the workpiece accordingly. Material removal takes place by a series of

discrete discharges between the wire electrode & workpiece in the presence of a dielectric

fluid. The di-electric fluid gets ionized in between the tool electrode gap thereby creating a




13

path for each discharge. The area wherein discharge takes place gets heated to very high

temperature such that the surface get melted & removed. The cut particles (debris) get flushed

away by continuous flowing dielectric fluid.

Generally, wire-cut EDM is used for cutting Aluminium, brass, etc. & wire material used for

quicker cutting action is zinc coated brass wires.

23. Internal gears are manufactured by

(A) hobbing (B) shaping with pinion cutter

(C) shaping with rack cutter (D) milling

Key: (B)

24. Match the following part programming codes with their respective functions

Part Programming Codes Functions

P. G01 I. Spindle stop

Q. G03 II. Spindle rotation, clockwise

R. M03 III. Circular interpolation,

anticlockwise

S. M05 IV. Linear interpolation

(A) P – II, Q – I, R – IV, S – III

(B) P – IV, Q – II, R – III, S – I

(C) P – IV, Q – III, R – II, S – I

(D) P – III, Q – IV, R – II, S – I

Key: (C)

25. In PERT chart, the activity time distribution is

(A) Normal (B) Binomial (C) Poisson (D) Beta

Key: (D)

Q. No. 26 – 55 carry Two Marks Each

26. The number of linearly independent eigenvectors of matrix

2 1 0

A 0 2 0

0 0 3

is ____ .

Key: 2

Exp: Here 2,2,3

For 2, No. of L.I eigen vectors

3 rank of A 2I 3 2 1

For 3, No. of L.I eigen vectors =1

∴ Total L.I eigen vectors = 2




14

27. The value of the line integral C

F.r ds, where C is a circle of radius 4

units is .

Here, ˆ ˆF(x,y) yi 2xj and r is the UNIT tangent vector on the curve C at an arc length s

from a reference point on the curve. i and j are the basis vectors in the x-y Cartesian

reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise

direction.

Key: 16

Exp: By Green’s theorem,

c c

2

F.r ' ds ydx 2xdy 2 1 dxdy

416

28. 2

xlim x x 1 x is

(A) 0 (B) ∞ (C) 1/2 (D) −∞

Key: (C)

Exp: 2

2

2x

2 2

2x

x

2

x x 1 xlim x x 1 x

x x 1 x

x x 1 xlim

x x 1 x

1x 1

1 0 1xlim

21 1 1 0 0 1x 1 1

x x

29. Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen,

and a jack is

(A) 16

5525 (B)

64

2197 (C)

3

13 (D)

8

16575

Key: (A)

Exp: Required probability

4 4 4

1 1 1

52

3

C C C 64 16

C 22100 5525

30. An inextensible massless string goes over a frictionless pulley. Two

weights of 100 N and 200 N are attached to the two ends of the

string. The weights are released from rest, and start moving due to

gravity. The tension in the string (in N) is .

Key: 133.33

100N

200N




15

Exp: From F.B.D

200

200 T ag

…(1)

100

T 100 ag

…(2)

Adding equations (1) and (2)

300

100 a a g/3g

From equation (1)

200 2 200200 T

g 3 3

200T 200 133.33N

3

31. A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without

slipping down a curved path as shown in figure. The speed v of the disc when it reaches

position B is m/s.

Acceleration due to gravity g = 10 m/s2.

Key: 20

Exp: According to energy conservation principle

Total K.E + P.E = constant

A A B B

2 2

2 2

2

2

K.E P.E K.E P.E

1 10 mg.30 m v I 0

2 2

1 1 130 10 1 v 1 v

2 2 2

mr vI and

2 r

330 10 v v 20m/s

4

TT

a

a

100

200

F.B.D

T

100

a

F.B.D

T

200

a




16

32. A rigid rod (AB) of length L 2 m is undergoing translational as well as rotational motion

in the x-y plane (see the figure). The point A has the velocity 1ˆ ˆV i 2 jm / s. The end B is

constrained to move only along the x direction.

The magnitude of the velocity V2 (in m/s) at the end B is

Key: 3

Exp: 1

x y

2 2

1

v i 2j

v 1 and v 2

v 1 2 5

Let ϕ is angle between v1 and x-axis.

tan 2 63.43

45 63.43 18.43

Since, the rod is rigid

1 2

2 2

v cos v cos45

5 cos18.43 v cos45 v 3m/s

33. A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on

its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E =

200 GPa.

The deformed shape is a square of dimension L 2 . If L 2 m and 0.001 m, the

Poisson’s ratio of the plate material is ______

Key: 0.2

Exp: According to Hooke’s Law

yx

xE E

Where,

x y x

5

2p and

2 p p

E E

2 1 p 2501 1 0.2

2000 E 2 10

1V 5

1

2

=α+45°

45

1V sin

1V

1V cos

2V

2V cos45

45

2V sin 45




17

34. Two circular shafts made of same material, one solid (S) and one hollow (H), have the same

length and polar moment of inertia. Both are subjected to same torque. Here, S is the twist

and S is the maximum shear stress in the solid shaft, whereas H is the twist and H is the

maximum shear stress in the hollow shaft. Which one of the following is TRUE?

(A) s H s Hand (B) s H s Hand

(C) s H s Hand

(D) s H s Hand

Key: (D)

Exp: According to pure torsion equation

T G

J R

Let ds and d1 are diameter of solid shaft and outer diameter of hollow shaft

s s

s s s h

h h s h

h h

s shs h

s 1 1

T

J R

T R R

J R

d.

d d d

Since, s hJ J

1d must be greater than ds

s

1

d

d must be less than 1 s h and

s s s

s ss h

h h h

h h

T G

JT G

T GJ

J

35. A beam of length L is carrying a uniformly distributed load w per unit length. The flexural

rigidity of the beam is EI. The reaction at the simple support at the right end is _____ .

(A)

wL

2 (B)

3wL

8 (C)

wL

4 (D)

wL

8 Key: (B)

Exp:

A B

BR

A B

1

2

BR




18

34

B1 2

R;

8EI 3EI

Since, net vertical deflection at B is zero

1 2

34

BB

R 3R

8EI 3EI 8

36. Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane.

Another pair of equal masses m1 is attached to the opposite sides of the shaft in the vertical

plane as shown in figure. Consider m = 1 kg, e = 50 mm, e1 = 20 mm, b = 0.3 m, a = 2 m and

a1 = 2.5 m. For the system to be dynamically balanced, m1 should be kg.

Key: 2

Exp: Couple due to m = couple due to m1

1 1 1

1

mea m e a

50 2m 1 2kg

20 2.5

37. A single degree of freedom spring-mass system is subjected to a harmonic force of constant

amplitude. For an excitation frequency of 3k

,m

the ratio of the amplitude of steady state

response to the static deflection of the spring is .

Key: 0.5

Exp:

2

n

1 1 1M.F 0.5

1 3 21




19

38. A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt

is 25 mm2. A torque T = 200 N-m is acting on the joint. Neglecting friction due to clamping

force, maximum shear stress in a bolt is MPa.

Key: 40

Exp: Let the resisting force in each bolt = F Newton

Net resisting torque (TR) = 34F 50 10 N-m

Applied torque (T) = Resisting Torque

3T 4F 50 10

200F 1000 1000N

4 50

Let shear stress developed in each bolt = MPa

It is given that resisting area (AR) = 25mm2

RF A

100040MPa

25

39. Consider a fully developed steady laminar flow of an incompressible fluid with viscosity µ

through a circular pipe of radius R. Given that the velocity at a radial location of R/2 from the

centerline of the pipe is U1, the shear stress at the wall is kµU1/R, where K is

Key: 2.667

Exp: 1

wall 1

Given, ,R u at R/2 U ,

y k u /R

K=?

Velocity profile in horizontal pipe flow is

2

max 2

2

1 max 2

1 max max 1

wall

r R

ru u 1

R

Ru u 1

4R

3 4u u u u

4 3

uy

r

maxmax max 12

1

2 u2r 2 2 4u u

R R R R 3

u8 8k 2.667

3 R 3




20

40. The water jet exiting from a stationary tank

through a circular opening of diameter 300 mm

impinges on a rigid wall as shown in the figure.

Neglect all minor losses and assume the water

level in the tank to remain constant. The

net horizontal force experienced by the

wall is kN.

Density of water is 1000 kg/m3.

Acceleration due to gravity g = 10 m/s2

Key: 8.76

Exp: Force exerted by a jet of water striking fixed wall is 2av N where a is area of jet.

3 2 2

3 2

10 0.3 v v 2gh 2 10 6.24

10 0.3 2 10 62 8.76kN4

41. For a two-dimensional flow, the velocity field is 2 2 2 2

x yˆ ˆ ˆ û i j,where i and j arex y x y

the

basis vectors in the x-y Cartesian coordinate system. Identify the CORRECT statements from

below.

(1) The flow is incompressible.

(2) The flow is unsteady.

(3) y-component of acceleration,

y 2

2 2

ya

x y

(4) x-component of acceleration,

x 2

2 2

x ya

x y

(A) (2) and (3) (B) (1) and (3) (C) (1) and (2) (D) (3) and (4)

Key: (B)

Exp: 2 2 2 2

x yu ; v

x y x y

Given flow is independent of time of flow is steady

Density ‘ρ’ is not present in velocity components, so flow is incompressible

Acceleration along x direction

x

u ua u v

x y

2 2

2 2 2 2

2 2 22 2 2 2 2 2

xu

x y

x y x2xu y x u 2xy

x yx y x y x y




21

2 2 2 3

2 32 22 2 2 2

y xu x xy xu

x x y x y x y

…(a)

2

2 32 2 2 2 2 2

u y 2xy 2xyv

y x y x y x y

…(b)

2 3 2 2 2

x 3 3 22 2 2 2 2 2

xy x 2xy x x y xa a b

x y x y x y

So, only statement 1 & 3 are correct.

42. Two large parallel plates having a gap of 10 mm in between them are maintained at

temperatures.

T1 = 1000 K and T2 = 400 K. Given emissivity values, 1 0.5, 2 0.25 and Stefan-

Boltzmann constant = 5.67 × 10−8 W/m

2-K

4, the heat transfer between the plates (in

kW/m2) is

Key: 11.049

Exp:

4 4

1 2

1 2

1 2

8 4 4

2 2

T TQ

1 11

5.67 10 1000 400

1 11

0.5 0.25

W kW11049.696 11.049m m

43. A cylindrical steel rod, 0.01 m in diameter and 0.2 m in length is first heated to 7500

C and

then immersed in a water bath at 1000C. The heat transfer coefficient is 250 W/m

2-K. The

density, specific heat and thermal conductivity of steel are =7801 kg/m3, c = 473

J/kg-K, and k = 43 W/m-K, respectively. The time required for the rod to reach 3000C is

____ seconds.

Key: 43.49

Exp: d = 0.01 m

L = 0.2m, R=7801 kg/m3.

o

i

o

t 750 C, C 473J / kgK

t 100 C, k 43 W / mK

2

2

c

dV d4h 250W / m K, LA d 4

i c

t t hA hln

t t Vc cL

i

t t h 4ln

t t c d

300 100 250 4ln 43.49s

750 100 7801 473 0.01

1T 1000K2T 400K

1 0.5 2 0.25




22

44. Steam at an initial enthalpy of 100 kJ/kg and inlet velocity of 100 m/s, enters an

insulated horizontal nozzle. It leaves the nozzle at 200 m/s. The exit enthalpy (in kJ/kg)

is .

Key: 85

Exp: 1

1

2

h 100kJ / kg

C 100m / s

C 200m / s

2 2

1 21 2

2 2

2

C Ch h

2000 2000

100 200h 100 85kJ / kg

2000 2000

45. In a mixture of dry air and water vapor at a total pressure of 750 mm of Hg, the partial

pressure of water vapor is 20 mm of Hg. The humidity ratio of the air in grams of water vapor

per kg of dry air (gw/kgda) is ____ .

Key: 17

Exp: t

v

P 750 mm of Hg

P 20 mm of Hg

Humidity ratio (or) specific Humidity

V

t V

w.v w.v

Pw 0.622

P P

200.622

750 20

kg g0.017 17

kg d.a kg d.a

46. In a 3-stage air compressor, the inlet pressure is 1p , discharge pressure is 4p and the

intermediate pressures are p2 and 3 2 3p p p . The total pressure ratio of the compressor is 10

and the pressure ratios of the stages are equal. If 1p 100 kPa, the value of the pressure 3p (in

kPa) is .

Key: 464.16

Exp: 3 stage compressor, P1= 100 kPa

Pressure ratios of all stages are equal

32 4

1 2 3

PP P

P P P

Overall pressure ratio 4

1

P10

P

332 4p

1 2 3

PP Pr 10 2.154

P P P

2

3 p 1

3

P (r ) P

P 2.514 2.514 100 464.16kPa

12

2

2

C

h1

1

C

h




23

47. In the vapour compression cycle shown in the figure, the

evaporating and condensing temperatures are 260 K and 310 K,

respectively. The compressor takes in liquid-vapour mixture (state

1) and isentropically compresses it to a dry saturated vapour

condition (state 2). The specific heat of the liquid refrigerant is

4.8kJ/kg-K and may be treated as constant. The enthalpy of

evaporation for the refrigerant at 310 K is 1054 kJ/kg.

The difference between the enthalpies at state points 1 and 0 (in kJ/kg) is

Key: 1103.51

Exp: pdQ C dT

3p fg

2 0

0

C dT hs s

T 310

1 0 1 2

310 1054s s 4.8ln ( s s )

260 310

1 0

1 0

h h 310 10544.8ln

260 260 310

h h 1103.51kJ kg

48. Spot welding of two steel sheets each 2 mm thick is carried out successfully by passing 4 kA

of current for 0.2 seconds through the electrodes. The resulting weld nugget formed between

the sheets is 5 mm in diameter. Assuming cylindrical shape for the nugget, the thickness of the

nugget is mm.

Key: 2.91

Exp: st 2mm

n

3

I 4kA; t 0.2

d 5mm; t ?

L.H 1400

R 200

8000kg m

Energy supplied = 2I Rt …(a)

2

3 64 10 200 10 0.2 640J

Energy required for melting = V L.H … (b)

3 2 6

n1400 10 8000 5 10 t4

n219911.4858t

Equating (a) & (b)

640 = n219911.4858t

nt 2.91mm

Latent heat of fusion for steel 1400 kJ/kg

Effective resistance of the weld joint 200

Density of steel 8000 kg/m3

s

T

3 2

40

1




24

49. For an orthogonal cutting operation, tool material is HSS, rake angle is 22°, chip thickness is

0.8 mm, speed is 48 m/min and feed is 0.4 mm/rev. The shear plane angle (in degrees) is

(A) 19.24 (B) 29.70 (C) 56.00 (D) 68.75

Key: (B)

Exp: oGiven 22

Thickness of chip = 20.8mm t

Feed = 0.4 mm/rev

Speed = 48m/min

In orthogonal cutting = feed = thickness of uncut chip. 1t

2

1

o

o

1

t 0.8K 2

t 0.4

cos cos22tan 0.57

K sin 2 sin 22

tan 0.57 29.7

50. In a sheet metal of 2 mm thickness a hole of 10 mm diameter needs to be punched. The yield

strength in tension of the sheet material is 100 MPa and its ultimate shear strength is 80 MPa.

The force required to punch the hole (in kN) is

Key: 5.0265

Exp: Given

s

yt

t 2mm

d 10mm

80MPa

S 100MPa

sF dt 10 2 80 5026.5N 5.0265kN

51. In a single point turning operation with cemented carbide tool and steel work piece, it is found

that the Taylor’s exponent is 0.25. If the cutting speed is reduced by 50% then the tool life

changes by ____ times

Key: 16

Exp: n = 0.25

12

VV

2

n n

1 1 2 2V T V T

n n1

1 1 2

VV T T

2

0.25

2

1

T2

T

4

2 1T T 2

2 1T 16 T

Tool life changes by 16 times




25

52. Two optically flat plates of glass are kept at a small angle as shown in the figure.

Monochromatic light is incident vertically.

If the wavelength of light used to get a fringe spacing of 1 mm is 450 nm, the wavelength of

light (in nm) to get a fringe spacing of 1.5 mm is _______.

Key: 675

Exp: Fringe space by (d1) = 1mm

1

2 2

450nm

d 1.5mm, ?

1 2

1 2

2

tan2d 2d

1.5450 675nm

1

53. A point P (1, 3, −5) is translated by ˆ ˆ ˆ2i 3j 4k and then rotated counter clockwise by 90

about the z-axis. The new position of the point is

(A) (−6, 3, −9) (B) (−6, −3, −9) (C) (6, 3, −9) (D) (6, 3, 9)

Key: (A)

Exp: We can write vector ˆ ˆ ˆ2i 3j 4k

as coordinate form as 2, 3, 4 .

ˆ ˆ ÔP i 3j 5k

ˆ ˆ ÔP 3i 6j 9k

Now rotate OP'

vector about z axis through 90°

in counter clockwise direction.

Since, it is rotated about z-axis, therefore z-

coordinate remains same.

n o o

n o o

x x cos y sin

y x sin y cos

Where o ox , y are co-ordinates corresponding

to old values

n nx , y are co-ordinates corresponding to new values

After rotating vector OP

through an angle θ in counter clockwise

n

n

n

n

x 3 cos90 6sin90

x 6

y 3sin90 6cos90

y 3

Hence the new coordinate is 6, 3, 9

h

L

x

t

0

z

x

y

P 1,3, 5 P' 3,6, 9




26

54. The demand for a two-wheeler was 900 units and 1030 units in April 2015 and May

2015, respectively. The forecast for the month of April 2015 was 850 units. Considering a

smoothing constant of 0.6, the forecast for the month of June 2015 is

(A) 850 units (B) 927 units

(C) 965 units (D) 970 units

Key: (D)

Exp:

JuneF 970 units

55. A firm uses a turning center, a milling center and a grinding machine to produce two parts.

The table below provides the machining time required for each part and the maximum

machining time available on each machine. The profit per unit on parts I and II are Rs. 40 and

Rs. 100, respectively. The maximum profit per week of the firm is Rs. .

Type of machine

Machining time required for

the machine part (minutes) Maximum machining time

available per week (minutes)

I II

Turning Center 12 6 6000

Milling Center 4 10 4000

Grinding Machine 2 3 1800

Key: 40,000

Exp: Linear program formulation is

1 2max z 40x 100x

Constraints are

1 2

1 2

1 2

1 2

12x 6x 6000

4x 10x 4000

2x 3x 1800

x , x 0

At 0,400 , z 40,000

At 375, 250 ,z 40,000

At 500,0 ,z 20,000

∴ Maximum profit per week is Rs. 40,000.

Month Demand t 1 t 1Forecast D 1 F

April 900 850

May 1030 0.6 900 0.4 850 880

June 0.6 1030 0.4 880 970

375, 250

0, 1000

0, 600

0, 400

500,0 900,0 1000,01x

2x

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ME GATE-2016-PAPER-03d1zttcfb64t0un.cloudfront.net/gatepapers/GATE2016/ME...Q. No. 1 – 5 Carry One Mark Each 1. Based on the given statements, select the appropriate option with