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

2n – 1

2²⁻ⁿ

2ⁿ

2. 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 = 5/2, m =

p = 1/2, m = 6

p = – ½, m = 6

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

180

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

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

n > 2

n < 2

n ≤

n ≥ 2

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

7. The value of ¹⁵C₁₀ is equal to

15/10

15/11

5/10

5/11

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

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

-28/81

28/81

28/243

-28/243

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

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

27a³ + 36a²x

27a³ – 36a²x

81a⁴ – 36a²x

81a⁴ + 36a²x

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

13. 3 + 3 a + 3 a² + ………… ∞ is equal to 45/8, a > 0 then a is

7/8

7/15

15/7

15/23

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

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

1000

100000

10000

100

16.

17. (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

18. 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

3/2 – 48x/61

2/3 – 61x/48

1/2 – x/48

19. 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

69, 760

99, 784

20.

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

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

-2a²

-8a

-4a

12a

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

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

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

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

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

24. 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

None of these

p+q/r+q

p–r/p–q

25.

Page 2 of 4

26. The exponent in (a + b)⁷ is

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

|x|<1/2

|x|<2/3

|x|<1

|x|<1/3

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

None of these

-1

29. The middle term of (x + 1/x)¹⁰ is

¹⁰C₃

¹⁰C₅

¹⁰C₄

None of these

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

31. (x – 1)³ =

x³ – 3x + 3x – 1

x³ + 3x + 3x – 1

1 – 3x + 3x² – x³

x³ – x² + x + 1

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

n > 5

n ≥ 5

n > 3

n ≥ 3

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

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

(n+1)th term

None of these

n th term

N+2/3 th term

35. 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

36. (1 + 2x)⁴ =

1 – 8x + 24x² – 32x³ + 16x⁴

1 – 4x + 6x² – 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 + 4x + 6x² + 4x³ + x⁴

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

1024

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

n–1/2

n²–1/2

n–2/2

n²+1/2

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

4th and 5th

6th

4th

5th

40.

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

9th term

8th term

7th term

6th term

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

4th term

2nd term

3rd term

Seven term

43.

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

-1

-2

-1≤x≤1

-2≤x≤2

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

2ⁿ⁻²

2ⁿ

n²

2ⁿ⁻¹

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

-1

-2

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

-2≤x≤2

-1≤x≤1

-1

48. 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)

P (12, 2)

P (12, 10)

None of these

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 integers n

Integers n

Positive real numbers n

50.

Page 3 of 4

51. The number of terms in the binomial expansion is

Two less than the exponent

One less than the exponent

One more than the exponent

Equal to the exponent

52. (1 + x)⁷ =

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

53. 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

54. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/3! x³

n(n – 1)(n – 2)/2! x²

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

2nd term

3rd term

5th term

4th term

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

12th

13th

None of these

11th

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

58. (x – 1/x)³ =

None of these

x³ + x + 1/x + 1/x²

x³ – 3x + 3/x – 1/x³

x³ + 3x + 3/x + 1/x³

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

None of these

10 x 12

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

15th

14th

16th

13th

61. 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

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

63. 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

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

None of these

Odd

Prime

Even

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

None of these

An even number

Not a prime

Not an odd number

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

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

2891

1771

1563

3421

68. The exponent in (a-b)¹⁷ is

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. 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

2a b/2+b

a–b/a

a+b/2

71. 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.

72. 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

None of these

164

140

112

73.

74. 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)

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

n + 1

n – 1

None of these

Page 4 of 4

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

2ⁿ⁻¹

2(n – 1)

2ⁿ

77. 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

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

n/3(n–2)

n/2(n+1)

n/2(n–3)

n(n+3)

79. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

None of these

9998

10000

9999

80. 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 !

81.

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

(r + 1)th term

None of these

r th term

(r – 1)th term

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

-1024

-4/x²

- 27/1024x

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

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

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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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