NCERT Class 11 MCQ Quiz Hub

1. If A, B and C are any three sets, then A – (B ∪ C) is equal to
(A – B) ∪ (A – C)
(A – B) ∪ C
(A – B) ∩ C
(A – B) ∩ (A – C)

2. (A’)’ = ?
∪ – A
A’
∪
A

3. A – B is read as?
Difference of A and B of B and A
None of the above
Difference of B and A
Both a and b

4. If A, B and C are any three sets, then A × (B ∪ C) is equal to
(A × B) ∪ (A × C)
(A ∪ B) × (A ∪ C)
(A × B) ∩ (A × C)
None of these

5. IF A = [5, 6, 7] and B = [7, 8, 9] then A ∪ B is equal to
[5, 6, 7, 8, 9]
[5, 6, 7]
[7, 8, 9]
None of these

6. Which of the following sets are null sets
{x: |x |< -4, x ?N}
2 and 3
Set of all prime numbers between 15 and 19
{x: x < 5, x > 6}

7. IF R = {(2, 1),(4, 3),(4, 5)}, then range of the function is?
Range R = {2, 4}
Range R = {1, 3, 5}
Range R = {2, 3, 4, 5}
Range R {1, 1, 4, 5}

8. The members of the set S = {x | x is the square of an integer and x < 100} is
{0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
{0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
{1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
{0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

9. In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?
19
41
21
57

10. { (A, B) : A² +B² = 1} on the sets has the following relation
reflexive
symmetric
none
reflexive and transitive

11. Two finite sets have N and M elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second test. Then the value of M and N are
7, 6
6, 4
7, 4
6, 3

12. The range of the function f(x) = 3x – 2‚ is
(- ∞, ∞)
R – {3}
(- ∞, 0)
(0, – ∞)

13. If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then,
B = C
A = C
A = B = C
A = B

14. In 2nd quadrant?
X < 0, Y < 0
X < 0, Y > 0
X > 0, Y > 0
X > 0, Y < 0

15. How many rational and irrational numbers are possible between 0 and 1?
0
Finite
Infinite
1

16. Empty set is a?
Finite Set
Invalid Set
None of the above
Infinite Set

17. If A = [5, 6, 7] and B = [7, 8, 9] then A U B is equal to
[5, 6, 7, 8, 9]
[5, 6, 7]
[7, 8, 9]
None of these

18. Which of the following two sets are equal
A = {1, 2} and B = {1}
A = {1, 2} and B = {1, 2, 3}
A = {1, 2, 3} and B = {2, 1, 3}
A = {1, 2, 4} and B = {1, 2, 3}

19. In a class of 50 students, 10 did not opt for math, 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science.
24
25
26
27

20. In last quadrant?
X < 0, Y > 0
X < 0, Y < 0
X > 0, Y < 0
X > 0, Y > 0

21. If f(x) = (a – x)1/n, a > 0 and n ∈ N, then the value of f(f(x)) is
1/x
x
x²
x1/2

22. The domain of the definition of the real function f(x) = √(log12 x² ) of the real variable x is
x > 0
|x| ≥ 1
|x| > 4
x ≥ 4

23. If f(x) = ex and g(x) = loge x then the value of fog(1) is
0
1
-1
None of these

24. Two functions f and g are said to be equal if f
the domain of f = the domain of g
the co-domain of f = the co-domain of g
f(x) = g(x) for all x
All of the above

25. A function f(x) is said to be an odd function if
f(-x) = f(x)
f(-x) = -f(x)
f(-x) = k * f(x) where k is a constant
None of these

26. If f(x) is an odd differentiable function on R, then df(x)/dx is a/an
Even function
Odd function
Either even or odd function
Neither even nor odd function

27. The function f(x) = sin (‎πx/2) + cos (πx/2) is periodic with period
4
6
12
24

28. If f(x) = log3 x and A = (3, 27) then f(A) =
(1, 1)
(3, 3)
(1, 3)
(2, 3)

29. The domain of tan-1 (2x + 1) is
R
R -{1/2}
R -{-1/2}
None of these

30. the function f(x) = x – [x] has period of
0
1
2
3

31. If f(x) =(3x – 2)/(2x – 3) then the value of f(f(x)) is
x
x²
x³
None of these

32. Let R be the set of real numbers. If f(x) = x² and g(x) = 2x + 1, then fog(x) is equal to
2x + 1
2x² + 1
(2x + 1)²
None of these

33. A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if x² + y² = 16 then the domain of R is
(0, 4, 4)
(0, -4, 4)
(0, -4, -4)
None of these

34. The number of binary operations on the set {a, b} are
2
4
8
16

35. If f is an even function and g is an odd function the fog is a/an
Even function
Odd function
Either even or odd function
Neither even nor odd function

36. The domain of the function f(x) = 1/(x² – 3x + 2) is
{1, 2}
R
R – {1, 2}
R – {1, -2}

37. The domain of the function f(x) = sin-1 (tan x) is
-π/4 ≤ x ≤ π/4
nπ – π/4 ≤ x ≤ nπ + π/4
nπ – π/3 ≤ x ≤ nπ + π/3
-π/3 ≤ x ≤ π/3

38. Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is
{7, -5, -3}
{-7, 5, -3}
{-7, -5, 3}
{-7, -5, -3}

39. The range of the function 7-xPx-3 is
{1, 2, 3, 4, 5}
{3, 4, 5}
{1, 2, 3}
None of these

40. The period of the function f(x) = sin4 3x + cos4 3x is
π/2
π/3
π/4
π/6

41. The value of cos² x + cos² y – 2cos x × cos y × cos (x + y) is
sin (x + y)
sin² (x + y)
sin³ (x + y)
sin4 (x + y)

42. If a×cos x + b × cos x = c, then the value of (a × sin x – b²cos x)² is
a² + b² + c²
a² – b² – c²
a² – b² + c²
a² + b² – c²

43. If cos a + 2cos b + cos c = 2 then a, b, c are in
2b = a + c
b² = a × c
a = b = c
None of these

44. The value of cos 5π is
0
1
-1
None of these

45. In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals
c/a
1
a/c
None of these

46. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is
4 : (√5 – 1)
5 : 4
(√5 – 1) : 4
None of these

47. The value of cos 180° is
0
1
-1
infinite

48. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is
30°
90°
60°
120°

49. If 3 × tan(x – 15) = tan(x + 15), then the value of x is
30
45
60
90

50. If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is
π/3
π/2
2π/3
3π/2

51. The value of tan 20 × tan 40 × tan 80 is
tan 30
tan 60
2 tan 30
2 tan 60

52. The general solution of √3 cos x – sin x = 1 is
x = n × π + (-1)n × (π/6)
x = π/3 – n × π + (-1)n × (π/6)
x = π/3 + n × π + (-1)n × (π/6)
x = π/3 – n × π + (π/6)

53. If tan² θ = 1 – e², then the value of sec θ + tan³ θ × cosec θ is
2 – e²
(2 – e²)1/2
(2 – e²)²
(2 – e²)3/2

54. The value of cos 20 + 2sin² 55 – √2 sin65 is
0
1
-1
None of these

55. If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is
2π/3
π/3
π/2
π/6

56. The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is
sin x
sin 2x
sin 3x
sin 4x

57. If tan A – tan B = x and cot B – cot A = y, then the value of cot (A – B) is
x + y
1/x + y
x + 1/y
1/x + 1/y

58. The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is
tan 6x
2 tan 6x
3 tan 6x
4 tan 6x

59. The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is
tan 6x
2 tan 6x
3 tan 6x
4 tan 6x

60. The sum of the series 1³ + 2³ + 3³ + ………..n³ is
{(n + 1)/2}²
{n/2}²
n(n + 1)/2
{n(n + 1)/2}²

61. If n is an odd positive integer, then an + bn is divisible by :
a² + b²
a + b
a – b
None of these

62. 1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}
n(n + 1)
n/(n + 1)
2n/(n + 1)
3n/(n + 1)

63. The sum of the series 1² + 2² + 3² + ………..n² is
n(n + 1)(2n + 1)
n(n + 1)(2n + 1)/2
n(n + 1)(2n + 1)/3
n(n + 1)(2n + 1)/6

64. {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =
1/(n + 1) for all n ∈ N.
1/(n + 1) for all n ∈ R
n/(n + 1) for all n ∈ N
n/(n + 1) for all n ∈ R

65. For any natural number n, 7n – 2n is divisible by
3
4
5
7

66. 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =
{n(n + 3)}/{4(n + 1)(n + 2)}
(n + 3)/{4(n + 1)(n + 2)}
n/{4(n + 1)(n + 2)}
None of these

67. The nth terms of the series 3 + 7 + 13 + 21 +………. is
4n – 1
n² + n + 1
n + 2
None of these

68. n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N
2
3
5
7

69. Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.
n(n+1)(n+2)/3
n(n+1)(n+2)/6
n(n+2)/6
(n+1)(n+2)/6

70. (n² + n) is ____ for all n ∈ N.
Even
odd
Either even or odd
None of these

71. For all n ∈ N, 3×52n+1 + 23n+1 is divisible by
19
17
23
25

72. (1 + x)n ≥ ____ for all n ∈ N,where x > -1
1 + nx
1 – nx
1 + nx/2 (
1 – nx/2

73. 102n-1 + 1 is divisible by ____ for all N ∈ N
9
10
11
13

74. For all n∈N, 72n − 48n−1 is divisible by :
25
2304
1234
26

75. {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =
n/(2n + 3)
n/{2(2n + 3)}
n/{3(2n + 3)}
n/{4(2n + 3)}

76. The value of √(-16) is
-4i
4i
-2i
2i

77. The value of √(-144) is
12i
-12i
±12i
None of these

78. The value of √(-25) + 3√(-4) + 2√(-9) is
13i
-13i
17i
-17i

79. if z lies on |z| = 1, then 2/z lies on
a circle
an ellipse
a straight line
a parabola