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11TH MATHEMATICS REVISION

Class 11 - Mathematics
Time Allowed: 2 hours and 30 minutes Maximum Marks: 75

Section A
1. Which of the following is a set? [1]
A. A collection of vowels in English alphabets is a set.
B. The collection of most talented writers of India is a set.
C. The collection of most difficult topics in Mathematics is a set.
D. The collection of good cricket players of India is a set.

a) B b) D

c) A d) C
2. If A ∪ B = B then [1]

a) B ⊂ A b) A ⊆ B

c) B = ϕ d) A ≠ ϕ

3. If A and B are two sets then A ∩ (A ∩ B ) = . . . .

′
[1]

a) ∈ b) A

c) ϕ d) B
4. Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second [1]
set. The values of m and n are, respectively,

a) 7, 7 b) 4, 4

c) 7, 4 d) 4, 7
5. If A = {1, 2, 3, 4, 5, 6} then the number of proper subsets is [1]

a) 63 b) 36

c) 64 d) 25

6. If A = {(x, y) : x2 + y2 = 25} and B = {(x, y) : x2 + 9y2 = 144} then A ∩ B contains [1]

a) three points b) two points

c) one point d) four points

7. If A ⊂ B, then [1]

a) A b)
c c c c
⊂ B B ⊄ A

c) A c
= B
c
d) B
c
⊂ A
c

8. If A = {x : x is a multiple of 3, x natural no., x < 30} and B = {x : x is a multiple of 5, x is natural no., x < 30} [1]

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 then A - B is

a) {3, 6, 9, 12, 15, 18, 21, 24, 27, 30} b) {3, 6, 9, 12, 18, 21, 24, 27}

c) {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 25, 27, d) {3, 6, 9, 12, 18, 21, 24, 27, 30}
30}
9. Let A = {a, b, c}, B = {a, b}, C = {a, b, d}, D = {c, d} and E = {d}. Then which of the following statement is not [1]
correct?

a) D ⊇ E b) C - B = E

c) B ∪ E = C d) C - D = E
10. If A = {1, 3, 5, B} and B = {2, 4}, then [1]

a) {4} ⊂ A b) None of these

c) B ⊂ A d) 4 ∈ A
11. Which of the following is a null set? [1]

a) C = ϕ b) B = {x : x + 3 = 3}

c) D = {0} d) A = {x : x > 1 and x < 3}

12. For any set A, (A')' is equal to [1]

a) ϕ b) A''

c) A d) A'
13. The set of all prime numbers is [1]

a) an infinite set b) a singleton set

c) a multi set d) a finite set

14. Given the sets A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, then A ∪ (B ∩ C) is [1]

a) {1, 2, 3} b) {3}

c) {1, 2, 3, 4, 5, 6} d) {1, 2, 3, 4}
15. Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the [1]
circle. If the triangle and circle intersect each other and are contained in a square. Then

a) S ∩ T = S ∩ C b) S ∩ T ∩ C = ϕ

c) S ∪ T ∪ C = C d) S ∪ T ∪ C = S
Section B
16. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. [1]

a) (6, 8) ∈ R b) (8, 7) ∈ R

c) (2, 4) ∈ R d) (3, 8) ∈ R
2

17. The domain of the function f given by f (x) = x +2x+1

2
[1]
x −x−6

a) R – {–3, 2} b) R – [3, – 2]

c) R – {-2, 3} d) R – (-3, - 2)
−−−−−−−−−
18. The domain of function f : R → R defined by f(x) 2
= √x − 3x + 2 is [1]

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 a) [2, ∞] b) (−∞, 1] ∪ [2, ∞)

c) (−∞, 1] d) [1, 2]
19. The domain and range of the function f given by f(x) = 2 − |x − 5| is [1]

a) Domain = R, Range = (−∞, 2) b) Domain = R+, Range = (−∞, 1]

c) Domain = R+, Range = (−∞, 2] d) Domain = R, Range = (−∞, 2]

20. If f (x) = x 3
−
1

x
3
, then f (x) + f ( ) is equal to
1

x
[1]

a) 2x3 b) 2 1

3
x

c) 1 d) 0
−−−−−
21. Let f(x) = log 2
(1 − x) + √x − 1 Then, dom (f) = ? [1]

a) (0, 1) b) [-1, 1)

c) (1, ∞) d) (−∞, −1]

−−−
22. Let f(x) √
x−1
then, dom f(x) = ? [1]
x−4

a) [1,4] b) (−∞, 4]

c) [1,4) d) (−∞, 1] ∪ (4, ∞)

23. Domain and range of f(x) =

|x−3|
are respectively. [1]
x−3

a) R, [-1, 1] b) R-, R

c) R - {3}, {1, -1} d) R+, R

24. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3. Then, R-1 is [1]

a) {(10,13),(12,10)} b) {(10,13), (8,11), (12,10)}

c) {(11,8), (13,10)} d) {(8,11), (10,13)}

25. Let f (x) = 1

2
Then, range (f) = ? [1]
(1−x )

a) [-1, 1] b) [1, -1]

c) (-∞, 1] d) [1, ∞)
−−−−−
26. The domain and range of real function f defined by f (x) = √x − 1 is given by [1]

a) Domain = [∞, ∞) , Range = [0, ∞) b) Domain = [1, ∞), Range = (∞, ∞)

c) Domain = [1, ∞) , Range = [0, ∞) d) Domain = (1, ∞) , Range = (0, ∞)

−−− −−−
27. The domain of definition of the function f(x) = √
x−2
+ √
1−x
is [1]
x+2 1+x

a) ϕ b) [1, -1]

c) [-1, 1] d) (−∞, −2] ∪ [2, ∞)

–
28. If f (x) = (25 − x 4 1/4
) for 0 < x <√5, then f (f ( 1

2
)) = [1]

a) 2-4 b) 2-3

c) 2-1 d) 2-2

29. If A = {x ∈ Z : 0 ≤ x ≤ 12} and R is the relation in A given by R = {(a, b) : |a - b| is a multiple of 4}. Then, the [1]

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 set of all elements related to 1 is

a) {2, 4, 6} b) {1, 3, 9}

c) {1, 4, 6} d) {1, 5, 9}
2

30. The range of the function f(x) = x −x

2
is [1]
x +2x

a) R - { - 1 / 2 ,1 } b) R - {1}

c) R d) R - { 1 / 2 ,-1 }

31. If A = {x : x2 - 5x + 6 = 0}, B = {2, 4}, C = {4, 5} then A × (B ∩ C ) is [1]

a) {(4, 2), (4, 3)} b) {(2, 2), (3, 3), (4, 4), (5, 5)}

c) {(2, 4), (3, 4), (4, 4)} d) {(2,4), (3, 4)}

32. The relation R defined on the set A = {1, 2, 3, 4, 5) by R = {(a, b) : |a2 - b2| < 7} is given by [1]

a) {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (1, 2), (2, b) {(3, 3), (4, 3), (5, 4), (3, 4)}
3)}

c) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} d) {(2, 2), (3, 2), (4, 2), (2, 4)}
33. If A is a finite set containing n distinct elements, then the number of relations on A is equal to [1]
2

a) 2 n
b) 2n

c) n2 d) 2× 2

34. If A = {1, 2, 4}, B = {2, 4, 5}, c = {2, 5}, then (A - B) × (B - C) is [1]

a) {(1, 4)} b) (2, 5)

c) {(1, 2), (1, 5), (2, 5)} d) (1, 4)

35. The domain of the function f(x) = log3+x(x2 - 1) is [1]

a) (-3, -2) ∪ (-2, -1) ∪ (1, ∞) b) [-3, -1) ∪ [1, ∞)

c) (-3, -1) ∪ (1, ∞) d) [-3, -2) ∪ (-2, -1) ∪ [1, ∞)

Section C

36. If 7 sin2θ + 3 cos2θ = 4, then tan θ = ? [1]

a) ± b)
1 1
±
√2 2

c) ± d)
1 1
±
√3 3

37. If sin θ = and , then (2 sec θ − 3 cot θ) = ? [1]

3 π
< θ < π
5 2

−13 −3
a) 2
b) 2

c) d)
13 3

2 2

sin 7x−sin 5x
38. cos 7x+cos 5x
=? [1]

a) tan x b) cot x

c) cot 2x d) tan 2x
1+sin 2x−cos 2x
39. 1+sin 2x+cos 2x
=? [1]

a) cot 2x b) cot x

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 c) tan 2x d) tan x
40. If tan A = a+1
a
and tan B = 1

2a+1
, then the value of A + B is [1]

a) 0 b) π

c) d)
π π

3 2

41. If the angles of a triangle are in A.P., then the measure of one of the angles in radians is [1]

a) b)
2π π

3 3

c) d)
π π

2 6

42. The minute hand of a watch is 1.4 cm long. How far does its tip move in 45 minutes? [1]

a) 6 cm b) 6.6 cm

c) 6.3 cm d) 7 cm

43.
cos(π+θ) cos(−θ)
=? [1]
π
cos(π−θ) cos( +θ)
2

a) cot θ b) - cot θ

c) tan θ d) - tan θ

44. If x = r cos α cos β ,y= r cos α sin β and z = r sin α , then x2 + y2 + z2 = ? [1]

a) r4 b) 1

c) r2 d) r3

45. If tan α = , tan β = , then cos 2α is equal to [1]

1 1

7 3

a) sin 2β b) sin 3β

c) sin 4β d) cos 2β
46. The value of tan 3A - tan 2A - tan A is equal to [1]

a) tan 3A tan 2A tan A b) – tan 3A tan 2A tan A

c) tan 3A tan 2A – tan A tan 3A – tan 3A tan d) tan A tan 2A – tan 2A tan 3A – tan 3A tan
2A A
47. cos 135° = ? [1]
−1
a) b)
1

√2 2

−1
c) 1

2
d)
√2

48. =? [1]
5π π
2 cos cos
12 12

a) b)
√3 1

2 √2

–
c) 1

2
d) √2

−−−−−
49. √
1+sin x
=? [1]
1−sin x

a) cot b)
x x
tan
2 2

c) tan( π

4
+
x

2
) d) cot(
π

4
+
x

2
)

(5 cos θ+4 cosec θ+3 tan θ)

50. If sin θ =
4
and
π
< θ < π , then =? [1]
5 2 (4 cot θ+3 sec θ+5 sin θ)

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 a) 1

2
b) -1

c) d) 1
−1

51. =? [1]
sin 2x

1−cos 2x

a) sec x b) cosec x

c) cot x d) tan x

52. sin (
31π
) =? [1]
3

−1
a) b)
√3

2 2

c) d)
1 −√3

2 2

−1
53. If sin x = 2
and x lies in quadrant III, then sin 2x = ? [1]

a) b)
1 1

2√3 2

–
c) d)
√3
√3
2

54. If sin θ + sin 2

θ = 1 , then (cos 2
θ + cos
4
θ) =? [1]

a) 3 b) 1

c) 2 d) 0
55. 2 sin
5π

12
cos
12
π
=? [1]

a) b)
(2+√3) √3

2 2

c) √3+1
d) 1

2
2

56. If α + β = , then the value of (1 + tan α) (1 + tan β) is [1]

π

a) 1 b) 2

c) -2 d) Not defined

57. ( 3 sin 40° - 4 sin340°) = ? [1]

–
a) b)
√3
3√3
2

–
c) 2√3 d)
3

58. sin 54° = ? [1]

a) b)
(√5+1)
√10+2√5

4
4

c) d)
(√5−1)
√10−2√5

4
4

If x sin 45° cos2 60° = [1]

2 ∘ ∘

59. , then x =
tan 60 cosec 30
∘ 2 ∘
sec 45 cot 30

a) 16 b) 2

c) 4 d) 8
∘ ∘
cos 10 +sin 10
60. ∘
cos 10 −sin 10
∘
is equal to [1]

a) -cot 35o b) cot 55o

c) -tan 35o d) tan 55o

Section D

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61. Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less [1]
than 23.

a) (3, 5), (5, 7), (7, 9) b) (6, 8),(8, 10), (10, 12)

c) (8, 6), (6, 4), (10, 6) d) (4, 6), (6, 8), (8, 10)
62. If x belongs to set of integers, A is the solution set of 2(x - 1) < 3x - 1 and B is the solution set of 4x - 3 ≤ 8 + x, [1]
find A ∩ B

a) {0, 2, 4} b) {1, 2, 3}

c) {0, 1, 2} d) {0, 1, 2, 3}
[1]
|x−2|
63. If x−2
≥ 0 , then

a) x ∈ (−∞, 2) b) x ∈ (−∞, 2]

c) x ∈ [2, ∞) d) x ∈ (2, ∞)

64. The solution set of the inequation: is: [1]

2x−1 3x
− + 1 < 0, x ∈ W
3 5

a) x ∈ S b) x ∈ N

c) null set d) x ∈ W
65. If |x + 2| ≤ 9 , then [1]

a) x ∈ ( - 7 , 11 ) b) x ∈ (−∞, −7) ∪ (11, ∞)

c) x ∈ [ - 11 , 7 ] d) x ∈ (−7, −∞) ∪ [∞, 11)

66. Solve the system of inequalities: x - 5 > 0, <2 [1]

2x−4

x+2

a) x > 5 b) x > -5

c) x > 2 d) x < -2
67. Solve the system of inequalities: [1]
x+7 2x+1
> 2, > 5
x−8 7x−1

a) (4, 8) b) (3, 6)

c) no solution d) (2, 5)
[1]
3(x−2)
68. Solve the system of inequalities: −15 < 5
≤ 0

a) -13 < x < 13 b) -23 < x ≤ 2

c) -23 < x < 23 d) -13 < x < 2

69. Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, [1]
then

a) x ∈ [– 3, 1] b) x ∈ (–∞, – 4) ∪ [3, ∞)

c) x ∈ [– 4, 3] d) x ∈ (– ∞, – 4] ∪ [3, ∞)
[1]
2(3−x)
70. The solution set for: ∣∣ ∣ 3
<
5 ∣ 5

a) ( 1

2
,
3

2
) b) (
3
,
9
)
4 4

c) ( 3

2
,
9

2
) d) (
1
,
3
)
4 4

71. If |x + 3| ≥ 10 , then [1]

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 a) b)

c) d)
72. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm [1]
longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for
the shortest board if the third piece is to be at least 5 cm longer than the second?

a) 3 ≤ x ≤ 91 b) 3 ≤ x ≤ 5

c) 5 ≤ x ≤ 91 d) 8 ≤ x ≤ 22
73. Solve the system of inequalities 4x + 3 ≥ 2x + 17 , 3x − 5 < − 2 , for the values of x, then [1]

a) no solution b) (−
3
,
2
)
2 5

c) (−4, 12) d) (-2, 2)

74. If a, b, c are real numbers such that a > b, c < 0 [1]

a) ac > bc b) ac < bc

c) ac ≥ bc d) ac ≠ bc
[1]
|x|−1
75. The solution set for: ≥ 0, x ≠ ±2
|x|−2

a) (-2, 2) b) (−∞, −2) ∪(−1, 1) ∪(2, ∞)

c) (−∞, −2) ∪(2, ∞) d) (−1, 2) ∪(3, ∞)

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