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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. 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 integers n

Positive real numbers n

Real numbers n

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

None of these

N+2/3 th term

(n+1)th term

n th term

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

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

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

p+q/r+q

p–r/p–q

r–q/q–p

None of these

6. (x – 1/x)³ =

x³ + x + 1/x + 1/x²

x³ – 3x + 3/x – 1/x³

None of these

x³ + 3x + 3/x + 1/x³

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

5th

6th

4th

4th and 5th

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

n²+1/2

n²–1/2

n–2/2

n–1/2

9. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/3! x³

n(n – 1)(n – 2)/2! x²

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

-8a

-2a²

-4a

12a

11.

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

-1

None of these

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

4th term

2nd term

3rd term

Seven term

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

n > 5

n > 3

n ≥ 5

n ≥ 3

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

2ⁿ⁻²

n²

2ⁿ⁻¹

2ⁿ

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

n/2(n–3)

n/3(n–2)

n(n+3)

n/2(n+1)

17. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

None of these

10000

9999

9998

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

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

1024

20. 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, 10)

C (12, 2)

P (12, 2)

None of these

21. The number of terms in the binomial expansion is

One more than the exponent

Equal to the exponent

One less than the exponent

Two less than the exponent

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

Odd

Even

None of these

Prime

23. 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

None of these

p = – ½, m = 6

p = 5/2, m =

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

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

Page 2 of 4

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

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

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

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

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

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

-1

-2

-1≤x≤1

-2≤x≤2

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

1594

792

924

2924

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

2nd term

5th term

4th term

3rd term

30.

31. 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

(√a – √b/√2)²

a–b/a

2a b/2+b

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

H.P.

G.P.

None of these

A.P.

33. (x – 1)³ =

x³ – 3x + 3x – 1

1 – 3x + 3x² – x³

x³ – x² + x + 1

x³ + 3x + 3x – 1

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

None of these

n + 1

n – 1

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 – 61x/48

2/3 – 61x/48

1/2 – x/48

3/2 – 48x/61

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

37. 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

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

3421

1771

2891

1563

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

8th term

6th term

9th term

7th term

40.

41.

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

2(n – 1)

2ⁿ⁻¹

2ⁿ

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

44.

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

15/7

7/15

15/23

7/8

46. 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

3/2 and 6

2 and 9

2/3 and 9

3 and 2

47. (1 + 2x)⁴ =

1 – 8x + 24x² – 32x³ + 16x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 – 4x + 6x² – 4x³ + x⁴

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

180

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

50. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Taylor series

Binomial theorem

Binomial series

None of these

Page 3 of 4

51. The value of ¹⁵C₁₀ is equal to

5/11

15/11

15/10

5/10

52. The exponent in (a-b)¹⁷ is

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

|x|<1/2

|x|<1/3

|x|<2/3

|x|<1

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

1 – ½ x

1 + x

1 + ½ x

1 – x

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

504/259

405/256

450/263

None of these

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

57. 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

None of these

112

140

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

n > 2

n < 2

n ≥ 2

n ≤

59. 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 !)

5 ! 3 !

4 ! 3 !

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

1000

10000

100000

100

61. The exponent in (a + b)⁷ is

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

-1≤x≤1

-2≤x≤2

-1

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

-1024

- 27/1024x

-4/x²

64. (1 + x)⁷ =

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

65. 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

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

-1

-2

67.

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

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

(r + 1)th term

None of these

(r – 1)th term

r th term

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

2n – 1

2ⁿ

2²⁻ⁿ

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

10 x 12

None of these

72. 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

30, 240

69, 760

None of these

99, 784

73. The middle term of (x + 1/x)¹⁰ is

¹⁰C₅

¹⁰C₃

None of these

¹⁰C₄

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

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

27a³ – 36a²x

81a⁴ – 36a²x

81a⁴ + 36a²x

27a³ + 36a²x

Page 4 of 4

76.

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

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

n/n+1

n/n+2

n/2(n+1)

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

-28/81

28/81

-28/243

28/243

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

None of these

Not a prime

Not an odd number

An even number

81.

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

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

14th

13th

15th

16th

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

None of these

13th

11th

12th

How to Score High in Mathematics Induction and Binomial Theorem Online Test?

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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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