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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 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)

None of these

C (12, 2)

P (12, 2)

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

3. 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

30, 240

None of these

69, 760

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

A.P.

G.P.

None of these

H.P.

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

-28/81

-28/243

28/243

28/81

6. The number of terms in the binomial expansion is

Two less than the exponent

Equal to the exponent

One less than the exponent

One more than the exponent

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

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

81a⁴ + 36a²x

81a⁴ – 36a²x

27a³ + 36a²x

27a³ – 36a²x

9. The middle term of (x + 1/x)¹⁰ is

¹⁰C₄

¹⁰C₅

None of these

¹⁰C₃

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

5th

6th

4th

4th and 5th

11. The exponent in (a-b)¹⁷ is

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

2891

1771

1563

3421

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

n/2(n–3)

n/3(n–2)

n/2(n+1)

n(n+3)

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

r th term

(r – 1)th term

(r + 1)th term

None of these

15.

16.

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

18. 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

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

|x|<2/3

|x|<1/2

|x|<1/3

|x|<1

20.

21. 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 and 2

2/3 and 9

3/2 and 6

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

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

n > 5

n ≥ 5

n > 3

n ≥ 3

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

3rd term

5th term

2nd term

4th term

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

3rd term

Seven term

2nd term

4th term

Page 2 of 4

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

n/n+1

n/2(n+1)

n/n+2

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

-1

-2≤x≤2

-1≤x≤1

-2

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

-1

-2

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

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

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

32. 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

924

2924

1594

33. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

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

16th

13th

15th

14th

35. 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

140

112

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

100

100000

10000

1000

38.

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

(n+1)th term

N+2/3 th term

None of these

n th term

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

-1≤x≤1

-1

-2≤x≤2

41. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

10000

9999

9998

None of these

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

n²+1/2

n–2/2

n–1/2

n²–1/2

43. 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

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

n ≤

n ≥ 2

n < 2

n > 2

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

None of these

-1

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

180

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

1024

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

-1024

- 27/1024x

-4/x²

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

Real numbers n

Positive real numbers n

Integers n

Positive integers n

50.

Page 3 of 4

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

405/256

504/259

450/263

None of these

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

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

2ⁿ

2(n – 1)

2ⁿ⁻¹

54. 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 !

4 ! 3 !

5 ! 3 !

5 (3 !)

55.

56. The value of ¹⁵C₁₀ is equal to

15/10

5/10

5/11

15/11

57. 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

58. (x – 1)³ =

x³ – x² + x + 1

1 – 3x + 3x² – x³

x³ – 3x + 3x – 1

x³ + 3x + 3x – 1

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

13th

12th

None of these

11th

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

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

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

n + 1

n – 1

None of these

63. (1 + 2x)⁴ =

1 – 4x + 6x² – 4x³ + x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 – 8x + 24x² – 32x³ + 16x⁴

64. 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

3/2 – 61x/48

1/2 – x/48

2/3 – 61x/48

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

2ⁿ

2n – 1

2²⁻ⁿ

66.

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

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

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

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

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

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

69. 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–r/p–q

r–q/q–p

None of these

p+q/r+q

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

6th term

8th term

9th term

7th term

71. 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

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

-8a

-4a

12a

-2a²

73. (1 + x)⁷ =

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

74. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

None of these

Binomial series

Taylor series

Binomial theorem

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

2ⁿ

2ⁿ⁻²

2ⁿ⁻¹

n²

Page 4 of 4

76.

77. The exponent in (a + b)⁷ is

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

None of these

10 x 12

79. (x – 1/x)³ =

x³ + 3x + 3/x + 1/x³

x³ – 3x + 3/x – 1/x³

None of these

x³ + x + 1/x + 1/x²

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

An even number

Not a prime

Not an odd number

None of these

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

Odd

Even

Prime

None of these

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

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

p = 5/2, m =

None of these

p = 1/2, m = 6

p = – ½, m = 6

84. 3 + 3 a + 3 a² + ………… ∞ is equal to 45/8, a > 0 then a is

15/23

7/15

15/7

7/8

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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