NCERT Class 11 MCQ Quiz Hub

1. If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equalsx
128 ω
-128 ω
128 ω²
-128 ω²

2. The least value of n for which {(1 + i)/(1 – i)}n is real, is
1
2
3
4

3. Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =
-2√3 + 2i
2√3 + 2i
2√3 – 2i
-√3 + i

4. The value of i-999 is
1
-1
i
-i

5. Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Further assume that the origin, z1 and z1 form an equilateral triangle. Then
a² = b
a² = 2b
a² = 3b
a² = 4b

6. The complex numbers sin x + i cos 2x are conjugate to each other for
x = nπ
x = 0
x = (n + 1/2) π
no value of x

7. The curve represented by Im(z²) = k, where k is a non-zero real number, is
a pair of striaght line
an ellipse
a parabola
a hyperbola

8. The value of x and y if (3y – 2) + i(7 – 2x) = 0
x = 7/2, y = 2/3
x = 2/7, y = 2/3
x = 7/2, y = 3/2
x = 2/7, y = 3/2

9. Find real θ such that (3 + 2i × sin θ)/(1 – 2i × sin θ) is imaginary
θ = nπ ± π/2 where n is an integer
θ = nπ ± π/3 where n is an integer
θ = nπ ± π/4 where n is an integer
None of these

10. If {(1 + i)/(1 – i)}n = 1 then the least value of n is
1
2
3
4

11. If arg (z) < 0, then arg (-z) – arg (z) =
π
-π
-π/2
π/2

12. if x + 1/x = 1 find the value of x2000 + 1/x2000 is
0
1
-1
None of these

13. If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are
-1, -1 + 2ω, – 1 – 2ω²
– 1, -1, – 1
– 1, 1 – 2ω, 1 – 2ω²
– 1, 1 + 2ω, 1 + 2ω²

14. (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to
2n
22n
23n
24n

15. The modulus of 5 + 4i is
41
-41
√41
-√41

16. Sum of two rational numbers is ______ number
rational
irrational
Integer
Both 1, 2 and 3

17. if x² = -4 then the value of x is
(-2, 2)
(-2, ∞)
(2, ∞)
No solution

18. Solve: (x + 1)² + (x² + 3x + 2)² = 0
x = -1, -2
x = -1
x = -2
None of these

19. If (x + 3)/(x – 2) > 1/2 then x lies in the interval
(-8, ∞)
(8, ∞)
(∞, -8)
(∞, 8)

20. The region of the XOY-plane represented by the inequalities x ≥ 6, y ≥ 2, 2x + y ≤ 10 is
unbounded
a polygon
exterior of a triangle
None of these

21. The interval in which f(x) = (x – 1) × (x – 2) × (x – 3) is negative is
x > 2
2 < x and x < 1
2 < x < 1 and x < 3
2 < x < 3 and x < 1

22. If -2 < 2x – 1 < 2 then the value of x lies in the interval
(1/2, 3/2)
(-1/2, 3/2)
(3/2, 1/2)
(3/2, -1/2)

23. The solution of the inequality |x – 1| < 2 is
(1, ∞)
(-1, 3)
(1, -3)
(∞, 1)

24. If | x − 1| > 5, then
x∈(−∞, −4)∪(6, ∞]
x∈[6, ∞)
x∈(6, ∞)
x∈(−∞, −4)∪(6, ∞)

25. The solution of |2/(x – 4)| > 1 where x ≠ 4 is
(2, 6)
(2, 4) ∪ (4, 6)
(2, 4) ∪ (4, ∞)
(-∞, 4) ∪ (4, 6)

26. If (|x| – 1)/(|x| – 2) ‎≥ 0, x ∈ R, x ‎± 2 then the interval of x is
(-∞, -2) ∪ [-1, 1]
[-1, 1] ∪ (2, ∞)
(-∞, -2) ∪ (2, ∞)
(-∞, -2) ∪ [-1, 1] ∪ (2, ∞)

27. The solution of the -12 < (4 -3x)/(-5) < 2 is
56/3 < x < 14/3
-56/3 < x < -14/3
56/3 < x < -14/3
-56/3 < x < 14/3

28. Solve: |x – 3| < 5
(2, 8)
(-2, 8)
(8, 2)
(8, -2)

29. The graph of the inequations x ≥ 0, y ≥ 0, 3x + 4y ≤ 12 is
interior of a triangle including the points on the sides
in the 2nd quadrant
exterior of a triangle
None of these

30. If |x| < 5 then the value of x lies in the interval
(-∞, -5)
(∞, 5)
(-5, ∞)
(-5, 5)

31. Solve: f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0
(-∞, 1] ∪ (2, ∞)
(-∞, 1] ∪ (2, 3)
(-∞, 1] ∪ (3, ∞)
None of these

32. If x² = 4 then the value of x is
-2
2
-2, 2
None of these

33. The solution of the 15 < 3(x – 2)/5 < 0 is
27 < x < 2
27 < x < -2
-27 < x < 2
-27 < x < -2

34. Solve: 1 ≤ |x – 1| ≤ 3
[-2, 0]
[2, 4]
[-2, 0] ∪ [2, 4]
None of these

35. There are 12 points in a plane out of which 5 are collinear. The number of triangles formed by the points as vertices is
185
210
220
175

36. The number of combination of n distinct objects taken r at a time be x is given by
n/2Cr
n/2Cr/2
nCr/2
nCr

37. Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is
1296
671
625
585

38. Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is
1296
671
625
585

39. If repetition of the digits is allowed, then the number of even natural numbers having three digits is
250
350
450
550

40. The number of ways in which 8 distinct toys can be distributed among 5 children is
58
85
8P5
5P5

41. The value of P(n, n – 1) is
n
2n
n!
2n!

42. In how many ways can 4 different balls be distributed among 5 different boxes when any box can have any number of balls?
54 – 1
54
45 – 1
45

43. The number of ways of painting the faces of a cube with six different colors is
1
6
6!
None of these

44. Out of 5 apples, 10 mangoes and 13 oranges, any 15 fruits are to be distributed among 2 persons. Then the total number of ways of distribution is
1800
1080
1008
8001

45. 6 men and 4 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is
604800
17280
120960
518400

46. The number of ways can the letters of the word ASSASSINATION be arranged so that all the S are together is
152100
1512
15120
151200

47. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon on n sides. If Tn+1 – Tn = 21, then n equals
5
7
6
4

48. How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order?
120
240
360
480

49. How many factors are 25 × 36 × 52 are perfect squares
24
12
16
22

50. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
40
196
280
346

51. In how many ways in which 8 students can be sated in a line is
40230
40320
5040
50400

52. The number of squares that can be formed on a chess board is
64
160
224
204

53. How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS, if repetition of letters is not allowed
720
420
5040
None of these

54. The coefficient of y in the expansion of (y² + c/y)5 is
10c
10c²
10c³
None of these

55. The coefficient of y in the expansion of (y² + c/y)5 is
10c
10c²
10c³
None of these

56. (1.1)10000 is _____ 1000
greater than
less than
equal to
None of these

57. The fourth term in the expansion (x – 2y)12 is
-1670 x9 × y³
-7160 x9 × y³
-1760 x9 × y³
-1607 x9 × y³

58. If n is a positive integer, then (√3+1)2n+1 + (√3−1)2n+1 is
an even positive integer
a rational number
an odd positive integer
an irrational number

59. If the third term in the binomial expansion of (1 + x)m is (-1/8)x² then the rational value of m is
2
1/2
3
4

60. The greatest coefficient in the expansion of (1 + x)10 is
10!/(5!)
10!/(5!)²
10!/(5! × 4!)²
10!/(5! × 4!)

61. The coefficient of xn in the expansion of (1 – 2x + 3x² – 4x³ + ……..)-n is
(2n)!/n!
(2n)!/(n!)²
(2n)!/{2×(n!)²}
None of these

62. The value of n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively is
2
4
6
8

63. If α and β are the roots of the equation x² – x + 1 = 0 then the value of α2009 + β2009 is
0
1
-1
10

64. The general term of the expansion (a + b)n is
Tr+1 = nCr × ar × br
Tr+1 = nCr × ar × bn-r
Tr+1 = nCr × an-r × bn-r
Tr+1 = nCr × an-r × br

65. The coefficient of xn in the expansion (1 + x + x² + …..)-n is
1
(-1)n
n
n+1

66. If n is a positive integer, then (√5+1)2n + 1 − (√5−1)2n + 1 is
an odd positive integer
not an integer
an even positive integer
none of these

67. In the expansion of (a + b)n, if n is even then the middle term is
(n/2 + 1)th term
(n/2)th term
nth term
(n/2 – 1)th term

68. In the expansion of (a + b)n, if n is odd then the number of middle term is/are
0
1
2
More than 2

69. if n is a positive ineger then 23nn – 7n – 1 is divisible by
7
9
49
81

70. In the binomial expansion of (71/2 + 51/3)37, the number of integers are
2
4
6
8

71. The number of ordered triplets of positive integers which are solution of the equation x + y + z = 100 is
4815
4851
8451
8415

72. In the binomial expansion of (a + b)n, the coefficient of fourth and thirteenth terms are equal to each other, then the value of n is
10
15
20
25

73. If a, b, c are in G.P., then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a, e/b, f/c are in
AP
GP
HP
None of these

74. If a, b, c are in AP then
b = a + c
2b = a + c
b² = a + c
2b² = a + c

75. If a, b, c are in AP then
b = a + c
2b = a + c
b² = a + c
2b² = a + c

76. Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is
2 + √3
2 – √3
2 ± √3
None of these

77. The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is
n/(n+1)
1/(n+1)
1/n
None of these

78. If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then
a, b, c are in AP
a², b², c² are in AP
1/1, 1/b, 1/c are in AP
None of these