Bt0063 mathematics fot it

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Model Question Paper

Subject Code: BT0063

Subject Name: Mathematics for IT

Credits: 4 Marks: 140

Part A (One mark questions)

1. In ------------------ form an element is not generally repeated, i.e., all the elements are taken

as distinct.

A) Set roster

B) Set builder

C) Roster

D) set tabular

2.�If every element of a set A is also an element of a set B, then A is called a subset of B or A

is contained in B. It is written as_________

A) A ⊂ B.

B) A � B

C)�A x B

D) A ∩ B

3. Let A = {1, 2, 3, 4, } and B = {3, 1, 4, 2) Then.

A) A≠ B

B) A=B

C) A ⊂ B

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D) A ⊄B

4. Let A and B be two sets. If A ⊂ B and A ≠ B, then B is called a _______ of A

A) Power set

B) Subset

C) Superpower set

D) Superset

5. Which of the following sentence is not a statement?

1. New Delhi is in India.

2. Two plus two is four.

3. Two plus two is five.

4. Switch on the fan.

A) 1

B) 2

C) 3

D) 4

��New statements that can be formed by combining two or more simple statements are called

__________

A) Simple statement

B) Compound statement

C)�Complex statement

D) Logical statement

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7. Which of the following sentence is optative?

A) Open the door.

B) Where are you going?

C) Hurrah! We have won the match.

D) May God bless you!

8. Which of the following sentence is open sentence?

A) Open the door.

B) He is a college Student

C) Hurrah! We have won the match.

D) May God bless you!

9. Which of the following equation represents Closure Law

A) a, b ∈ G, a * b ∈ G

B) a * (b * c) = (a * b) * c

C) a * e = e * a = a

D) a * b = b * a = e

10.�Find�7 + 5 10 =?

A) 17

B) 3

C)�2

D) 1

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11. Let e and e′ be the two identity elements of a group G and a ∈ G

Then ae =?

A) 1

B) e

c) e’

D) a

12. Find (ab) (b–1a–1)

A) a

B) b

C) e

D) 1

13. 1+ tan2=______

A) sec2

B) sin2

C) cos2

D) cosec2

14.�If 2

3BandA

2,

5

4Bcos,

13

5Asin

πππ

π<<<<

−== then the value of Sin (A+B) is

A) 63/65

B) 16/65

C) 56/65

D) 65/53

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15. Express 2.53 radians in degrees

A) °9.142 �

B) °9.143

C) °9.144

D) °9.141 �

� � � ��

�� Express 792° in radians

A)� ( )5/22 π �

�� ( )5/21 π

C) ( )15/22 π

D) ( )5/23 π

17. If a > b, then isba −

A) Positive

B) Negative

C) Zero

D) None of the Above

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18. Choose the right answer

abba −+− is equal to

A) 2 (b – a)

B) 0

C) 2 (a – b)

D) ba2 −

19. Evaluate ( )6x2It3x

−→

A) 2

B) 1

C) -1

D) 0

20. Evaluate ( )1x2It 2

0x+

→

A) 2

B) 1

C) -1

D) 0

21.If y = tan x, then dx

dy is

A) x2sin �

B) x2cos �

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C) x2sec

D) x2cot

22. If y = cot x evaluate =dx

dy

A) cos2 x

B) x2sin−

C) xec2cos− �

D) cos

23. If f(x) = k find ( )xf ′ .

A) 0

B) ��

C) ��

D) -1

24. f(x) = log x x > 0, Find ( ) =′ xf

A) log x

B) 1/x

C) 1

D) log (log x)

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25. Solve � =xdxec2cos

A) ��

B) - cos x+ C�

C) –cosec x +C

D) –sin x +C

26. Solve � =−dxx

4

A) cx

+−

2

2

B) cx

+−

−

2

2

C) cx

+−

−

5

5

D) cx

+−

−

3

3

27. If f(x) = x2 and g(x) = x2 + 2, then

A) ( ) ( ).xgxf ′≤′

B) ( ) ( )xgxf ′=′ 2

C) ( ) ( ).xgxf ′≠′

D) ( ) ( )xgxf ′=′

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28. Solve 3

2

x

cbxax ++

A) kx

c

x

bx +−−=

2log

B) kx

c

x

bx +−−=

222log

C) kx

c

x

bx +−−=

22log

D) kx

c

x

bx +−−=

222log

29. What is the order and degree of the equation? dx/dy

x

dx

dy.xy +=

A) Second order, second degree�

B) First order, second degree�

C) First order, First degree�

D)�Second order, First degree�

30. Solve y22y2x3 exedx

dy −− +=

A) cxee

xy

++=332

322

B) cxee

xy

++=332

33

C) cxee

xy

++=332

332

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D) cxee

xy

++=332

232

31. For all z1, z2 ∈ C. ?. 21 =zz

A) 22 zz + �

B) 22 zz − �

C) 22 . zz �

D) 22 / zz �

32.�If z = x + iy is a complex number then ______ is called the modulus or absolute value of z.

A) 22 yx +

B) yx +

C)� yx +2

D) 2

yx +

33. ��

��

�=

765

432A and �

�

��

�=

321

987B then 2A + 3B=?

A) ��

��

�=

231825

353013�

B) ��

��

�=

231813

353025�

C) ��

��

�=

232813

353125�

� ��

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D) ��

��

�=

351813

233025�

34.�If ��

��

�=�

�

��

�

−+

−+

1014

26

dcdc2

b2a2b2a2 then a, b, c, =?

A) a = 3. b = 1 c = 8

B) a = 2. b = 1 c = 8

C)�a = 2. b = 4 c = 8

D) a = 2. b = 1 c = 9

35. For the expression ........2

1.........

8

1

4

1

2

11

1n

+�

��

++++

−

1

2

12

−

�

��

−=

n

nS = ?

A)

n

nS �

��

−=

2

12 �

B)

n

nS

2

2

12 �

��

−= �

C)

1

2

12

−

�

��

−=

n

nS �

D)

1

2

12

+

�

��

−=

n

nS �

36.�For the series 1+2+3+4+5+6+……… Sn= ?

A) ( )

�

��

+=

2

1nSn

B) ( )

�

��

+=

2

1nnSn

� ��

��

C)� ( )�

��

−=

2

1nnSn

D) ( )

�

��

−=

2

1nSn

37.For the expression ........2

1.........

8

1

4

1

2

11

1n

+�

��

++++

−

1

2

12

−

�

��

−=

n

nS = ?

A)

n

nS �

��

−=

2

12 �

B)

n

nS

2

2

12 �

��

−= �

C)

1

2

12

−

�

��

−=

n

nS �

D)

1

2

12

+

�

��

−=

n

nS �

38.�The mean of marks scored by 30 girls of a class is 44%. The mean for 50 boys is 42%.

Find the mean for the whole class.

A) %75.32

B) %75.22

C) %75.42

D) %75.52

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39. Heights of six students are 163, 173, 168, 156, 162 and 165 cms. Find the arithmetic mean.

A) .5.164 cms �

B) .5.163 cms �

C) .164 cms �

D) .5.165 cms �

40.�In an office there are 84 employees. Their salaries are as given below:

Salary

(Rs.) 2430 2590 2870 3390 4720 5160

Employees 4 28 31 16 3 2

Find the mean salary of the employees

A) 16.2975.Rs

B) 26.2975.Rs

C)� 46.2975.Rs

D) 36.2975.Rs

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Part B (Two mark questions)

41. Let U = {1,2,3,4,5,6,7,8,9,10} and A= {1,3,5,7,9} Find�A′.

A) {2, 4, 6, 8, 10}.

B {2, 3, 6, 8, 10}.

C) {2, 4, 5, 8, 10}.

D) {2, 4, 6, 9, 10}.

42. Let A = {2, 4, 6, 8} and B = {6, 8, 10, 12}. Find A ∪ B.

A) {2, 4, 6, 8, 10, 12}.

B) {2, 6, 8, 12}.

C) {2, 4, 6, 10, 12}.

D) {2, 6, 8, 10, 12}.

43. Which of the following is not a negation of the statement: New Delhi is a city

A) New Delhi is not a city

B) it is not the case that new delhi is a city

C) it is false that New Delhi is a city

D) New delhi is capital of india

44. If a statement is true for all logical possibilities it is said as ________

A) Tautologies

B) negatition

C) conjuction

D) compound

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45. Fill the empty spaces in the composition table

A) 1,1,1

B) 2,2,2

C) 3,3,3

D) 4,4,4

46. _______and ________are the properties to be satisfied for non-empty set G is said to be a

semi group w.r.t. the binary operation

A) Inverse, identity

B) Closure, inverse

C) Identity, Associative

D) Closure, Associative

47. ��°°+°°

°+°−°

03cos60cos90sin45sin2

30sec45tan260tan22

222

is

A) 3/4

B) 4/3

C) 1/2

D) 1

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48. Simplify AA

AA

2sin2cos1

2sin2cos1

++

+−

A) Cos A

B) tan A

C) Cosec A

D) Sec A

49. E�� n2

1n2It

n

+

∞→� is

A) 1

B) -1

C) 1/2

D) -1/2

50. E�� 2

2

n n2n35

7n4n3It

++

++

∞→

A) 3/2

B) 2/3

C) -2

D) +2

51. If �

��

+= −

2

1

x1

x2siny find =

dx

dy

A) 21

3

x+

B) 21

1

x+

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C) 21

2

x+

D) 21

4

x+

52. Find dx

dy when taytax

33 sin,cos ==

A) ��

B) - tan t

C) cot t

D) cos t

53. Integrate Sin 10x Sin 2x w.r.t. x

A) cx

x

x+−

24

2sin.

2

18sin

B) cx

x

x+−

24

12sin.

2

18sin

C) cx

x

x+−

24

12sin.

2

14sin

D) cx

x

x+−

24

12sin.

2

12sin

54. Evaluate ( )� −≠+ .1n,dxbaxn

A) ( )

( )c

na

ban

+−

+−

1

1

B) ( )

( )c

na

ban

++

++

1

1

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C) ( )

( )c

na

ban

++

D) ( )

( )c

na

ban

++

++

2

2

55. Solve ( ) xydy2dxyx 22 =−

A) ( ) 123 cyxx =−

B) ( ) 122 cy3xx =−

C) ( ) 123 3 cyxx =−

D) ( ) 132 3 cyxx =−

56. Solve ( ) ( )2x3 1xeydx

dy1x +=−+

A) ( )13

1 2 +�

��

+= xcey

x

B) ( )23

1 3 +�

��

+= xcey

x

C) ( )12

1 3 +�

��

+= xcey

x

D) ( )13

1 3 +�

��

+= xcey

x

57._________ form of a complex number is called the polar form or the trigonometric form.

A) ( ).sinicosr θθ +

B) ( ).sincos θθ +r

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C) ( ).sincos θθ i+

D) ( ).sincos θθ +

58. For every z1, z2 ∈ C, z1z2 ∈ C. represents _______Property

A) Associative law

B) Commutative law

C) Closure law

D) Distributive law

59. ��

��

�

−=

101

102A and

��

�

�

��

�

�

=

10

64

21

B then AB = ?

A) ��

��

�

−

−=

51

12AB

B) ��

��

�

−

−=

12

51AB

C) ��

��

�

−−=

11

25AB

D) ��

��

�

−−=

11

52AB

60.

��

�

�

��

�

�

−=

043

312

210

A and

��

�

�

��

�

�

=

100

010

001

B find BA

� ��

��

A)

��

�

�

��

�

�

−=

043

310

212

B)

��

�

�

��

�

�

−=

343

212

010

C)

��

�

�

��

�

�

−=

043

312

210

D)

��

�

�

��

�

�

−=

013

312

241

Part C (Four mark questions)

61. Match the following

Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find

a) A × B i) {(1, 4), (2, 4), (3, 4)}.

b) A × C ii) {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5),

(2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.

c) (A × B) ∩ (A × C) iii) {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

d) (A × B) ∪ (A × C) iv) {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5),

(3, 6)}

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A) a-iv, b-ii, c-iii, d-i

B) a-i, b-i, c-iv, d-iii

C) a-iii, b-iv, c-i, d-ii

D) a-i, b-iii, c-iv, d-ii

62. State whether the following statements are True or False

A) a-True, b-False, c-True, d-False

B) a-True, b-False, c-False, d-False

C) a-True, b-True, c-True, d-True

D) a-False, b-False, c-True, d-False

63. The following lines are the proof� ��Theorem, Theorem: In a group G the inverse of

an element is unique. Find the missing statements

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A) ca,cb,ba,e �

B) ba,ca,ba,c �

C) ca,ca,ab,c �

D) ab,ac,ba,e


1. Sin 2A a. 2 Sin A Cos A

2. Cos 2A b. 1-2sin2A

3. Sin 3A c. 3 Sin A - 4 sin3A

4. Cos 3A d. 4cos3A-3 Cos A

A) 1-a,2-c,3-b,4-d �

B) 1-d,2-c,3-b,4-a

C) 1-b, 2-a,3-c,4-d

D) 1-b,2-d,3-a,4-c �


1. ( )2

1xxx1It ++

→ a. 4

2. 21x xx1

1It

++→ b. 2

3. 2

0xx4x32It ++

→ c. 1/3

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4. 2x

4xIt

2

2x −

−

→ d. 3

A) 1-a,2-c,3-b,4-d �

B) 1-d,2-b,3-c,4-a

C) 1-b, 2-a,3-c,4-d

D) 1-d,2-c,3-b,4-a


Y dy/dx

1. 9x3x4

12 +−

a. ( )2

2

1x2

5x4x4

+

−+

2. 1x2

1x3x2 2

+

+− b. sec2 x

3. xcos

xcosxsin + c.

( )22 9x3x4

3x8

+−

+−

4. 1x

xsinxcosx2 +

+ d.

( )( )22

3

1x

xsinx3xxcos2

+

+−

A) 1-a, 2-c,3-b,4-d �

B) 1-d, 2-b, 3-c,4-a

C) 1-c 2-a, 3-b,4-d

D) 1-d, 2-c,3-b,4-a

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67. State TRUE or FALSE

1. A partial differential equation is that in which there are two or more independent

variables and partial coefficients with respect to any of them.

2. An ordinary differential equation is that in which all the differential coefficients have

reference to two independent variable.

3. The order of a differential equation is the order of the highest derivative appearing in it.

4. The degree of a differential equation is the total number of variables occurring in it

A) 1-T, 2-F, 3-F, 4-T �

B) 1-F, 2-F, 3-T, 4-F

C) 1-T, 2-F, 3-T, 4-F

D) 1-F, 2-F, 3-F,4-T

68. Match the following complex numbers in polar form

a) i3 + i) ��

��

��

��

−+�

��

−

4sin

4cos2

ππi

b) 1 – i ii) �

��

+

3

2sin

3

2cos2

ππi

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c) 3i1 +− iii) �

��

+

6sin

6cos2

ππi

A) a-i, b-ii, c-iii,

B) a-iii, b-i, c-ii,

C) a-iii, b-ii, c-i

D) a-ii, b-i, c-iii

69. Match the following determinants

a)

25169

1694

941

i) -9

b)

2100

4111

2130

1210

ii) -8

c)

1111

0110

1010

1100

iii) 2



C) a-iii, b-ii, c-i

D) a-ii, b-i, c-iii

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a) �∞

=−−

+++++=

1n2n21n

......2

1......

2

1

2

11

2

1 i) series is divergent.

b) .........43211

++++++=�∞

=

nun

n ii) The given series oscillates between 2

finite values

c) ( ) .....1111111n

n−+−+−=−�

∞

=

iii) series is a convergent series.



C) a-iii, b-ii, c-i

D) a-ii, b-i, c-iii

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a) �∞

=−−

+++++=

1n2n21n

......2

1......

2

1

2

11

2

1 i) series is divergent.

b) .........43211

++++++=�∞

=

nun

n ii) The given series oscillates between 2

finite values

c) ( ) .....1111111n

n−+−+−=−�

∞

=

iii) series is a convergent series.



C) a-iii, b-ii, c-i

D) a-ii, b-i, c-iii

72. 10 students of B.Com class of a college have obtained the following marks in statistics out

of 100. Calculate the standard deviation

S. No : 1 2 3 4 5 6 7 8 9 10

Marks : 5 10 20 25 40 42 45 48 70 80

A) 23.07

B) 22.77

C) 21.07

D) 24.07

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73. Solve the following: .........150.100.50

33.18.3

100.50

18.3

50

3+++

A) 17

10 5

1

−�

��

=S

B) 5

1

7

10�

��

=S

C) 17

10 5

1

+�

��

=S

D) 27

10 5

1

+�

��

=S

74. Solve ∞+++ to..........!7

6

!5

4

!3

2

A) S=1

B) S=1/e

C) S=e

D) S=- 1

75. Integrate the following functions w.r.t. x. Match them.

a) 2

x

1

x

e6 i) �

�

��

�

−

5

xsin1xsin2

2

b) x2

x

e94

e

+ ii)

( )nxtanxsecn

1

+

� ��

��

c) ( )

0nxtanxsec

xsecn

>+

iii) ��

��

�

−

2

e3tan

6

1 x1

d) xsin

xcos3

iv) x

1

e6−

A) a-iv, b-ii, c-iii, d-i

B) a-i, b-iv, c-iii, d-ii

C) a-iii, b-i, c-ii ,d-iv

D) a-iv, b-iii, c-ii, d-i

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Answer Keys

Part - A Part - B Part - C

Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key

1 C 21 C 41 A 61 C

2 A 22 C 42 A 62 C

3 B 23 A 43 D 63 B

4 D 24 B 44 A 64 C

5 D 25 A 45 A 65 D

6 B 26 D 46 D 66 C

7 D 27 D 47 B 67 C

8 B 28 C 48 B 68 B

9 A 29 B 49 A 69 D

10 C 30 C 50 A 70 B

11 D 31 C 51 C 71 B

12 C 32 A 52 B 72 A

13 A 33 B 53 B 73 A

14 B 34 B 54 B 74 B

15 C 35 C 55 B 75 D

16 A 36 B 56 D

17 A 37 C 57 A

18 D 38 C 58 C

19 D 39 A 59 D

20 B 40 D 60 C

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Bt0063 mathematics fot it