This model question paper contains 55 questions divided into two parts for the subject Mathematics for IT. Part A contains one mark questions in multiple choice format covering topics like sets, relations, functions, limits, derivatives, integrals and mathematical statements. Part B contains 2 mark questions involving concepts like sets, logic, trigonometry, limits, derivatives and integrals that need to be solved. The question paper tests the understanding of core mathematical concepts required for an IT program through multiple choice and theoretical questions.

1. 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

2. 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

3. 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

4. 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
5 −4 π 3π
14. If sin A = , cos B = , < A < π and π < B < then the value of Sin (A+B) is
13 5 2 2
A) 63/65
B) 16/65
C) 56/65
D) 65/53

5. 15. Express 2.53 radians in degrees
A) 142.9°
B) 143.9°
C) 144.9°
D) 141.9°
Express 792° in radians
A) (22 π / 5)
(21 π / 5)
C) (22 π / 15)
D) (23 π / 5)
17. If a > b, then a − b is
A) Positive
B) Negative
C) Zero
D) None of the Above

6. 18. Choose the right answer
a − b + b − a is equal to
A) 2 (b – a)
B) 0
C) 2 (a – b)
D) 2 a − b
19. Evaluate It (2 x − 6 )
x →3
A) 2
B) 1
C) -1
D) 0
20. Evaluate It
x →0
(2 x 2
+1 )
A) 2
B) 1
C) -1
D) 0
dy
21.If y = tan x, then is
dx
A) sin 2 x
B) cos 2 x

7. C) sec 2 x
D) cot 2 x
dy
22. If y = cot x evaluate =
dx
A) cos2 x
B) − sin 2 x
C) − cos ec 2 x
D) cos
23. If f(x) = k find f ′(x ) .
A) 0
B)
C)
D) -1
24. f(x) = log x x > 0, Find f ′( x ) =
A) log x
B) 1/x
C) 1
D) log (log x)

8. 25. Solve cos ec 2 xdx =
A)
B) - cos x+ C
C) –cosec x +C
D) –sin x +C
26. Solve x −4 dx =
x −2
A) +c
2
x −2
B) +c
−2
x −5
C) +c
−5
x −3
D) +c
−3
27. If f(x) = x2 and g(x) = x2 + 2, then
A) f ′( x ) ≤ g ′( x ).
B) f ′( x ) = 2 g ′( x )
C) f ′( x ) ≠ g ′(x ).
D) f ′( x ) = g ′( x )

9. ax 2 + bx + c
28. Solve
x3
b c
A) = log x − − +k
x 2x
b c
B) = log x − − 2 +k
2x 2x
b c
C) = log x − − 2 +k
x 2x
b c
D) = log 2 x − − 2 +k
x 2x
dy x
29. What is the order and degree of the equation? y = x. +
dx dy / dx
A) Second order, second degree
B) First order, second degree
C) First order, First degree
D) Second order, First degree
dy
30. Solve = e 3 x −2 y + x 2 e −2 y
dx
e2 y e2x x3
A) = + +c
2 3 3
e y e3x x 3
B) = + +c
2 3 3
e 2 y e3 x x 3
C) = + +c
2 3 3

10. e 2 y e3x x 2
D) = + +c
2 3 3
31. For all z1, z2 ∈ C. z1 . z 2 = ?
A) z 2 + z 2
B) z 2 − z 2
C) z 2 . z 2
D) z 2 / z 2
32. If z = x + iy is a complex number then ______ is called the modulus or absolute value of z.
A) x2 + y 2
B) x +y
C) x2 + y
D) x + y2
2 3 4 7 8 9
33. A = and B = then 2A + 3B=?
5 6 7 1 2 3
13 30 35
A) =
25 18 23
25 30 35
B) =
13 18 23
25 31 35
C) =
13 28 23

11. 25 30 23
D) =
13 18 35
2a + 2 b 2a − 2 b 6 2
34. If = then a, b, c, =?
2c + d c −d 14 10
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
n −1 n −1
1 1 1 1 1
35. For the expression 1 + + + + ......... + ........ Sn = 2 − =?
2 4 8 2 2
n
1
A) S n = 2 −
2
2n
1
B) S n = 2 −
2
n −1
1
C) S n = 2 −
2
n +1
1
D) S n = 2 −
2
36. For the series 1+2+3+4+5+6+……… Sn= ?
A) S n =
(n + 1)
2
n(n + 1)
B) S n =
2

12. n(n − 1)
C) S n =
2
D) S n =
(n − 1)
2
n −1 n −1
1 1 1 1 1
37.For the expression 1 + + + + ......... + ........ Sn = 2 − =?
2 4 8 2 2
n
1
A) S n = 2 −
2
2n
1
B) S n = 2 −
2
n −1
1
C) S n = 2 −
2
n +1
1
D) S n = 2 −
2
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) 32.75%
B) 22.75%
C) 42.75%
D) 52.75%

13. 39. Heights of six students are 163, 173, 168, 156, 162 and 165 cms. Find the arithmetic mean.
A) 164.5 cms.
B) 163.5 cms.
C) 164 cms.
D) 165.5 cms.
40. In an office there are 84 employees. Their salaries are as given below:
Salary
2430 2590 2870 3390 4720 5160
(Rs.)
Employees 4 28 31 16 3 2
Find the mean salary of the employees
A) Rs. 2975.16
B) Rs. 2975.26
C) Rs. 2975.46
D) Rs. 2975.36

14. 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

15. 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
tan 2 60° − 2 tan 2 45° + sec 2 30°
47. is
2 sin 2 45° sin 90° + cos 2 60° cos 3 0°
A) 3/4
B) 4/3
C) 1/2
D) 1

16. 1 − cos 2 A + sin 2 A
48. Simplify
1 + cos 2 A + sin 2 A
A) Cos A
B) tan A
C) Cosec A
D) Sec A
2n + 1
49. E It is
n →∞ 2 n
A) 1
B) -1
C) 1/2
D) -1/2
3n 2 + 4n + 7
50. E It
n →∞ 5 + 3n + 2n 2
A) 3/2
B) 2/3
C) -2
D) +2
2x dy
51. If y = sin −1 2
find =
1+ x dx
3
A)
1 + x2
1
B)
1 + x2

17. 2
C)
1+ x2
4
D)
1 + x2
dy
52. Find when x = a cos 3 t , y = a sin 3 t
dx
A)
B) - tan t
C) cot t
D) cos t
53. Integrate Sin 10x Sin 2x w.r.t. x
sin 8 x 1 sin 2 x
A) − . +c
x 2 24
sin 8 x 1 sin 12 x
B) − . +c
x 2 24
sin 4 x 1 sin 12 x
C) − . +c
x 2 24
sin 2 x 1 sin 12 x
D) − . +c
x 2 24
54. Evaluate (ax + b )n dx , n ≠ −1.
A)
(a + b )n−1 + c
a(n − 1)
B)
(a + b )n+1 + c
a(n + 1)

18. C)
(a + b )n + c
a(n )
D)
(a + b )n+2 + c
a(n + 2)
( )
55. Solve x 2 − y 2 dx = 2 xydy
( )
A) x x − 3 y 2 = c1
( )
B) x x 2 − 3 y 2 = c 1
( )
C) x x 3 − 3 y 2 = c1
( )
D) x x 2 − 3 y 3 = c1
dy
56. Solve (x + 1) − y = e 3 x (x + 1)2
dx
1 2x
A) y = e +c (x + 1)
3
1 3x
B) y = e +c (x + 2)
3
1 3x
C) y = e +c (x + 1)
2
1 3x
D) y = e +c (x + 1)
3
57._________ form of a complex number is called the polar form or the trigonometric form.
A) r (cos θ + i sin θ ).
B) r (cos θ + sin θ ).

19. C) (cos θ + i sin θ ).
D) (cos θ + sin θ ).
58. For every z1, z2 ∈ C, z1z2 ∈ C. represents _______Property
A) Associative law
B) Commutative law
C) Closure law
D) Distributive law
1 2
2 0 1
59. A = and B = 4 6 then AB = ?
−1 0 1
0 1
2 −1
A) AB =
−1 5
−1 5
B) AB =
2 −1
5 2
C) AB =
−1 −1
2 5
D) AB =
−1 −1
0 1 2 1 0 0
60. A = 2 − 1 3 and B = 0 1 0 find BA
3 4 0 0 0 1

20. 2 1 2
A) = 0 −1 3
3 4 0
0 1 0
B) = 2 −1 2
3 4 3
0 1 2
C) = 2 − 1 3
3 4 0
1 4 2
D) = 2 −1 3
3 1 0
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)}

21. 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

22. A) ca,cb,ba,e
B) ba,ca,ba,c
C) ca,ca,ab,c
D) ab,ac,ba,e
64. Match the following
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
65. Match the following
x →1
(
1. It 1 + x + x 2 ) a. 4
1
2. It b. 2
x →1 1 + x + x2
3. It 2 + 3 x + 4 x 2 c. 1/3
x →0

23. x2 − 4
4. It d. 3
x →2 x − 2
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
66. Match the following
Y dy/dx
1 4x2 + 4x − 5
1. a.
4x2 − 3x + 9 (2 x + 1)2
2x2 − 3x +1
2. b. sec2 x
2x +1
sin x + cos x − 8x + 3
3. c.
cos x (4 x 2
− 3x + 9 )
2
4.
x cos x + sin x
d.
(
2 cos x − x 3 + 3 x sin x )
2
x +1 (x 2
+1 )
2
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

24. 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
π π
a) 3 +i i) 2 cos − + i sin −
4 4
2π 2π
b) 1 – i ii) 2 cos + i sin
3 3

25. π π
c) − 1 + i 3 iii) 2 cos + i sin
6 6
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
1 4 9
a) 4 9 16 i) -9
9 16 25
0 1 2 1
0 3 1 2
b) ii) -8
1 1 1 4
0 0 1 2
0 0 1 1
0 1 0 1
c) iii) 2
0 1 1 0
1 1 1 1
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

26. 70. Match the following determinants
∞
1 1 1 1
a) n −1
=1+ + 2 + ...... + n −2 + ...... i) series is divergent.
n =1 2 2 2 2
∞
b) u n = 1 + 2 + 3 + 4 + ....... + n + .. ii) The given series oscillates between 2
n =1
finite values
∞
c) (− 1)n = −1 + 1 − 1 + 1 − 1..... iii) series is a convergent series.
n =1
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

27. 71. Match the following determinants
∞
1 1 1 1
a) n −1
=1+ + 2 + ...... + n −2 + ...... i) series is divergent.
n =1 2 2 2 2
∞
b) u n = 1 + 2 + 3 + 4 + ....... + n + .. ii) The given series oscillates between 2
n =1
finite values
∞
c) (− 1)n = −1 + 1 − 1 + 1 − 1..... iii) series is a convergent series.
n =1
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
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

28. 3 3.18 3.18.33
73. Solve the following: + + + .........
50 50.100 50.100.150
1
10 5
A) S = −1
7
1
10 5
B) S =
7
1
10 5
C) S = +1
7
1
10 5
D) S = +2
7
2 4 6
74. Solve + + + ..........to ∞
3! 5! 7!
A) S=1
B) S=1/e
C) S=e
D) S=- 1
75. Integrate the following functions w.r.t. x. Match them.
1
6e x sin 2 x
a) i) 2 sin x 1 −
x2 5
ex 1
b) 2x
ii)
4 + 9e n (sec x + tan x )n

29. sec x 1 3e x
c) n >0 iii) tan −1
(sec x + tan x )n 6 2
1
cos 3 x
d) iv) − 6e x
sin x
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

30. 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