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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

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

4. The number of terms in the binomial expansion is

Equal to the exponent

One more than the exponent

Two less than the exponent

One less than the exponent

5. 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

C (12, 2)

None of these

P (12, 2)

P (12, 10)

6. (x – 1)³ =

x³ + 3x + 3x – 1

1 – 3x + 3x² – x³

x³ – 3x + 3x – 1

x³ – x² + x + 1

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

n²–1/2

n–1/2

n–2/2

n²+1/2

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

None of these

p = – ½, m = 6

p = 5/2, m =

p = 1/2, m = 6

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

n/2(n+1)

n/n+2

n/n+1

11. The exponent in (a-b)¹⁷ is

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

180

13. The middle term of (x + 1/x)¹⁰ is

¹⁰C₄

¹⁰C₅

None of these

¹⁰C₃

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

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

5th

4th

4th and 5th

6th

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

n + 1

n – 1

None of these

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

Prime

Even

None of these

Odd

18. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Binomial series

Taylor series

Binomial theorem

None of these

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

2ⁿ⁻¹

2ⁿ

2(n – 1)

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

n ≥ 3

n > 3

n ≥ 5

n > 5

21. 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/√2)²

a+b/2

2a b/2+b

a–b/a

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

1024

23. 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 !

5 (3 !)

4 ! 3 !

5 ! 3 !

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

13th

12th

None of these

11th

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

1771

3421

1563

2891

Page 2 of 4

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

27. (1 + 2x)⁴ =

1 – 8x + 24x² – 32x³ + 16x⁴

1 – 4x + 6x² – 4x³ + x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

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

405/256

450/263

504/259

None of these

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

N+2/3 th term

(n+1)th term

n th term

None of these

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

31. 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

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

33. 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

99, 784

None of these

30, 240

69, 760

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

2n – 1

2ⁿ

2²⁻ⁿ

35. 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

3/2 – 48x/61

2/3 – 61x/48

1/2 – x/48

3/2 – 61x/48

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

1 – x

1 + ½ x

1 – ½ x

1 + x

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

None of these

(r + 1)th term

(r – 1)th term

r th term

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

-4a

-8a

12a

-2a²

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

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

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

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

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

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

2nd term

3rd term

5th term

4th term

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

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

43. 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

140

None of these

112

164

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

9th term

6th term

7th term

8th term

45. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

46. 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

200

100

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

None of these

10 x 12

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

49. 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

Positive real numbers n

Real numbers n

Integers n

Positive integers n

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

-1

-2≤x≤2

-1≤x≤1

Page 3 of 4

51.

52. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

10000

9999

9998

None of these

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

n > 2

n < 2

n ≥ 2

n ≤

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

81a⁴ – 36a²x

27a³ + 36a²x

81a⁴ + 36a²x

27a³ – 36a²x

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

|x|<1/2

|x|<1/3

|x|<1

|x|<2/3

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

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

n²

2ⁿ⁻²

2ⁿ

2ⁿ⁻¹

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

r–q/q–p

p+q/r+q

p–r/p–q

None of these

59. 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

3 and 2

3/2 and 6

2 and 9

2/3 and 9

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

None of these

-1

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

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

14th

16th

13th

15th

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

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

65. The value of ¹⁵C₁₀ is equal to

5/11

5/10

15/11

15/10

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

1000

100000

10000

100

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

792

1594

924

2924

68. (1 + x)⁷ =

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

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

-2

-1

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

71.

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

15/7

15/23

7/15

7/8

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

Seven term

3rd term

2nd term

4th term

74. The exponent in (a + b)⁷ is

75.

Page 4 of 4

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

28/243

28/81

-28/243

-28/81

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

n/2(n–3)

n(n+3)

n/2(n+1)

n/3(n–2)

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

-2

-2≤x≤2

-1≤x≤1

-1

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

A.P.

H.P.

None of these

G.P.

80.

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

Not an odd number

None of these

An even number

Not a prime

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

- 27/1024x

-4/x²

-1024

83. (x – 1/x)³ =

x³ + 3x + 3/x + 1/x³

x³ – 3x + 3/x – 1/x³

x³ + x + 1/x + 1/x²

None of these

84.

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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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