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Mathematics Induction and Binomial Theorem Online Test

Maan AliLast Updated: October 15, 2025

Start your preparation for Mathematics Induction and Binomial Theorem Online Test. This online test contains important MCQs from past papers. Attempting this test will help you prepare for Annual Exams and Entry Tests. Read the questions carefully and select the correct option below to see your result.

Important Math Induction and Binomial Theorem Question and Answer

Total Questions:	84
Time Allowed:	40 Minutes
Total Marks:	84
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Induction and Binomial Theorem Practice Test Online With Explanation

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Page 1 of 4

Math

1. The sum of even co-efficient in the expansion (1+x)ⁿ is valid for

-2

-2≤x≤2

-1≤x≤1

-1

2. The middle tern in the expansion of (x + y)³⁰ us

16th

13th

14th

15th

3. If in the expansion of (1 + x)²⁰, then co-efficient of rth ad (r + 4)th term are equal, then r is

4. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

10000

None of these

9999

9998

5. The exponent in (a + b)⁷ is

6. If a+bx/a–bx = b+cx/b–cx = c+dx/c–dx (x ≠ 0), then a, b, c, d are in

None of these

A.P.

G.P.

H.P.

7. If n is any positive integer, then 1/1.2 + 1/2.3 + 1/3.4 + …….. + 1/n(n+1) =

n/n+2

n/n+1

n/2(n+1)

8. The term independent of x in the expansion of (x² – 1/3x)⁹ is equal to

28/243

28/81

-28/81

-28/243

9. If P, Q, R be the A.M., G.M., H.M. respectively between any two rational numbers a and b, then P – Q is

a–b/a

(√a – √b/√2)²

a+b/2

2a b/2+b

10. The no of terms in the expansion of (a-b)¹⁷ is

11. If n is any positive integer, then 4ⁿ > 3ⁿ + 4 is true for all

n > 2

n < 2

n ≥ 2

n ≤

12. The general term in the expansion (a + x)ⁿ is

(r + 1)th term

(r – 1)th term

None of these

r th term

13.

14. The greatest integer which divides the number 101¹⁰⁰ – 1 is

10000

100

1000

100000

15. pth term of an H.P. is qr and qth term is pr then a₅ is

-2

-1

16. The nth term of the series 1 + 1+2/2 + 1+2+3/3 + …………. Is

n–1/2

n–2/2

n²+1/2

n²–1/2

17. If ‘n’ is even them the middle term in the expansion of (a+b)ⁿ will be

N+2/3 th term

n th term

None of these

(n+1)th term

18. (x – 1)³ =

x³ – x² + x + 1

x³ + 3x + 3x – 1

1 – 3x + 3x² – x³

x³ – 3x + 3x – 1

19. The coefficient of 21st term in the expansion of (a + b)²³ is

1563

3421

2891

1771

20. If the middle term in the expansion (a + b)ⁿ is n/2 +1, then n is

None of these

Odd

Prime

Even

21.

22. The middle term in the expansion (a + b)¹²

7th term

9th term

6th term

8th term

23. If exponent I binomial expansion is 6, then the no. of terms are

Seven term

2nd term

3rd term

4th term

24.

25. The first three terms in the expansion of (1+ax)ⁿ (n ≠ 0) are 1, 6x and 16x², then the values of a and n are respectively

2 and 9

3/2 and 6

3 and 2

2/3 and 9

Page 2 of 4

26. The number of terms in the expansion (x² – 1/x²)⁷ is

27. The sum of exponents of a and b in every term of the expansion (a+b)ⁿ is

28.

29. If |x|<1, then the expansion of (1-x)½ up to two terms is

1 + x

1 + ½ x

1 – x

1 – ½ x

30. The number of diagonals in an n sides figure is equal to

n/2(n–3)

n/2(n+1)

n(n+3)

n/3(n–2)

31. The sum of co-efficient in (1 + x – 3x²)⁴¹⁶³ is

None of these

-1

32. A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is

164

140

None of these

112

33. The value of ¹⁵C₁₀ is equal to

5/11

15/10

15/11

5/10

34. Sum of odd coefficients in the binomial expansion is equal to ……….

2(n – 1)

2ⁿ

2ⁿ⁻¹

35. (1 + x)⁷ =

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

36. If in the expansion of (1 + x)ⁿ, co-efficients of 2nd, 3rd and 4th terms are in A.P., then x =

37. Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to number of heads is

120

38. If (1 + x – 2x²)⁴ = 1 + a₁x + a₂x² + a₃x³ + …… then the value of a₂ + a₄ + a₆ + ……. + a₁₂ will be

1024

39. The number of handshakes that can be exchanged among a party of 12 students if every student strikes hands once with every other student is

P (12, 2)

P (12, 10)

None of these

C (12, 2)

40. Digit in the unit place of the number 183!+3¹⁸³

41. The greatest term in the expansion of (3 + 2x)⁹, when x = 1 is

5th

6th

4th and 5th

4th

42. A family of 4 brothers and 3 sisters is to be arranged in a row for a photograph. In how many ways can they be seated if all sisters sit together?

5 (3 !)

5 !

4 ! 3 !

5 ! 3 !

43. The sum of the odd coefficients in the expansion (1+x)⁵ is

44. If C (n, 10) = C (n, 12), then n is equal to

10 x 12

None of these

45. If a statement P(n) is true for n = 1 and the truth of P(n) for n = k implies the truth of P(n) for n = k + 1, then P(n) is true for all

Integers n

Positive real numbers n

Positive integers n

Real numbers n

46. The nth term of the series 3, √3, 1, ……. Is 1/243, then n is:

47. If n is any positive integer, then 1²+2²+3²+…..+n² =

n(n + 1)(2n +)/6

(n + 1)(2n + 1)/3

n(n + 1)(2n +)/3

n(n + 1)(2n +)/2

48.

49. The middle term of (x + 1/x)¹⁰ is

¹⁰C₅

¹⁰C₃

¹⁰C₄

None of these

50. If n is not a natural number, then expansion of (1+x)³ is

-2≤x≤2

-1≤x≤1

-1

Page 3 of 4

51. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Taylor series

Binomial series

None of these

Binomial theorem

52. There are 4 letters and 4 direct envelopes. The number of ways in which every letter be put into a wrong envelope is

53. If ‘x’ be so small that is its square and higher powers may be neglected them (1 – x)½(9 – 4x)½/(8+3x)⅓

2/3 – 61x/48

3/2 – 48x/61

3/2 – 61x/48

1/2 – x/48

54. If the sum of co-efficient in the expansion of (a + b)ⁿ is 4096, then the greatest co-efficient in the expansion is

2924

924

1594

792

55. If exponent in the binomial expansion is 6, then the middle term is

3rd term

5th term

4th term

2nd term

56. The exponent in (a-b)¹⁷ is

57. The positive integer just greater than (1+0.0001)¹⁰⁰⁰⁰ is

58.

59. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/3! x³

n(n – 1)(n – 2)/2! x²

60. The sum of the coefficients in the expansion (1 + x)ⁿ is

61. If the 4th term is the expansion of (px + x⁻¹)ᵐ is 2.5 for all x ϵ R, then

p = 1/2, m = 6

p = 5/2, m =

p = – ½, m = 6

None of these

62. The number of terms in the binomial expansion is

One less than the exponent

One more than the exponent

Equal to the exponent

Two less than the exponent

63. If the pth, qth and rth terms of an A.P. are in G.P:., then the common ratio of the G.P. is

None of these

p–r/p–q

p+q/r+q

r–q/q–p

64. In a college examination, a candidate is required to attempt 6 out of 10 question, which are divided into two sections each containing 5 question. Further, the candidate is not permitted to attempt more than 4 questions from either of the section. The number of ways in which he can make up a choice of 6 questions is

100

200

65. The middle term in the expansion of (a + b)¹² is

11th

13th

None of these

12th

66. Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

None of these

30, 240

99, 784

69, 760

67. The expansion of (1 – 3x)⅔ is valid if

|x|<2/3

|x|<1/3

|x|<1/2

|x|<1

68. If n is any positive integer, then n! > 3ⁿ⁻¹ is true for all

n > 5

n > 3

n ≥ 5

n ≥ 3

69. The co-efficient of x⁴ in the expansion of (x/2 – 3/x²)¹⁰ is

504/259

450/263

405/256

None of these

70. The expansion of (3a – x/3a)⁴ up to two terms is

27a³ – 36a²x

81a⁴ – 36a²x

81a⁴ + 36a²x

27a³ + 36a²x

71. The 3rd term in the expansion of (1 + 6/x)⅓ = ?

-1024

- 27/1024x

-4/x²

72. 3 + 3 a + 3 a² + ………… ∞ is equal to 45/8, a > 0 then a is

7/8

15/23

15/7

7/15

73. The number of triangles that can be formed with 6 points on a circle is

74. (x – 1/x)³ =

None of these

x³ – 3x + 3/x – 1/x³

x³ + x + 1/x + 1/x²

x³ + 3x + 3/x + 1/x³

75. The number of ways in which a mixed double tennis game be arranged between 10 players consisting of 6 men and 4 women?

180

Page 4 of 4

76.

77. In the expansion of (a-22b)³ the co-efficient of b² is

-8a

12a

-4a

-2a²

78.

79. The number of term in the expansion of (a + b)ⁿ is

n + 1

n – 1

None of these

80. The sum of the coefficients in the expansion (1 + x)ⁿ is

2ⁿ⁻¹

2ⁿ

n²

2ⁿ⁻²

81. The number 11 ……………1 (91 times) is

None of these

Not an odd number

Not a prime

An even number

82. Sum of even coefficient is equal to ………. In the binomial expansion of (1 + x)ⁿ

2ⁿ

2n – 1

2²⁻ⁿ

83. (1 + 2x)⁴ =

1 + 8x + 24x² + 32x³ + 16x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 – 4x + 6x² – 4x³ + x⁴

1 – 8x + 24x² – 32x³ + 16x⁴

84. The sum of odd co-efficient in the expansion (1+x)⁴ is

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Maan AliLast Updated: October 15, 2025

3 Comments

Ummar says:

October 6, 2021 at 9:58 am

There must be reasons for every question that how this answer /why this answer, mention at the end of the tests.

Ayan Raza says:

September 21, 2017 at 7:28 pm

92%

umair ahmed says:

March 19, 2017 at 1:28 pm

80%

Important Math Induction and Binomial Theorem Question and Answer

Math Induction and Binomial Theorem Practice Test Online With Explanation

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