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

3. 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

r–q/q–p

p+q/r+q

p–r/p–q

4. 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

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

n ≤

n > 2

n ≥ 2

n < 2

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

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

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

9. The number of terms in the binomial expansion is

One more than the exponent

Two less than the exponent

Equal to the exponent

One less than the exponent

10. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

11. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

9998

10000

9999

None of these

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

-1024

- 27/1024x

-4/x²

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

14. 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

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

924

792

1594

2924

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

n > 3

n > 5

n ≥ 5

n ≥ 3

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

n/n+2

n/2(n+1)

n/n+1

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

9th term

7th term

6th term

8th term

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

None of these

Prime

Odd

Even

20. 3 + 3 a + 3 a² + ………… ∞ is equal to 45/8, a > 0 then a is

7/15

15/23

15/7

7/8

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

n–2/2

n²+1/2

n²–1/2

n–1/2

22. 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

112

None of these

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

1024

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

81a⁴ – 36a²x

27a³ + 36a²x

81a⁴ + 36a²x

27a³ – 36a²x

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

None of these

(r – 1)th term

(r + 1)th term

r th term

Page 2 of 4

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

-1

None of these

27. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

None of these

Binomial theorem

Taylor series

Binomial series

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

-2

-1≤x≤1

-1

-2≤x≤2

29. 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?

4 ! 3 !

5 (3 !)

5 ! 3 !

5 !

30. The exponent in (a + b)⁷ is

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

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

-28/81

28/243

-28/243

28/81

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

-2

-1

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

35. 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

36. The value of ¹⁵C₁₀ is equal to

5/11

15/11

15/10

5/10

37. 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

38. 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

Positive integers n

Integers n

Real numbers n

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

2nd term

5th term

4th term

3rd term

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

11th

13th

None of these

12th

41. 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

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

4th

4th and 5th

5th

6th

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

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

None of these

An even number

Not an odd number

Not a prime

45. The exponent in (a-b)¹⁷ is

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

2ⁿ

2(n – 1)

2ⁿ⁻¹

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

n/3(n–2)

n(n+3)

n/2(n–3)

n/2(n+1)

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

2nd term

4th term

Seven term

3rd term

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

50. (1 + x)⁷ =

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

Page 3 of 4

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

None of these

450/263

504/259

405/256

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

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

-1≤x≤1

-2≤x≤2

-1

54. (x – 1)³ =

x³ – x² + x + 1

x³ + 3x + 3x – 1

x³ – 3x + 3x – 1

1 – 3x + 3x² – x³

55. 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 th term

(n+1)th term

56. (1 + 2x)⁴ =

1 – 4x + 6x² – 4x³ + x⁴

1 – 8x + 24x² – 32x³ + 16x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 + 4x + 6x² + 4x³ + x⁴

57.

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

180

59. 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 = – ½, m = 6

p = 5/2, m =

None of these

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

2ⁿ

2n – 1

2²⁻ⁿ

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

16th

14th

13th

15th

62. The middle term of (x + 1/x)¹⁰ is

¹⁰C₃

¹⁰C₄

None of these

¹⁰C₅

63.

64.

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

10 x 12

None of these

66. (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

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

1771

1563

3421

2891

68. 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)

C (12, 2)

None of these

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

-4a

-2a²

-8a

12a

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

n + 1

None of these

n – 1

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

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

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

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

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

72. 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.

G.P.

None of these

73.

74. 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

75. 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

2/3 – 61x/48

1/2 – x/48

Page 4 of 4

76.

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

|x|<2/3

|x|<1

|x|<1/2

|x|<1/3

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

1000

10000

100000

100

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

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

2ⁿ⁻²

2ⁿ

n²

2ⁿ⁻¹

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

82.

83.

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

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

Mastering scientific subjects requires conceptual clarity.

Key Preparation Tips:

Concepts First: Ensure you understand the underlying theories before attempting the MCQs.
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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%

Mathematics Induction and Binomial Theorem Online Test

Important Math Induction and Binomial Theorem Question and Answer

Math Induction and Binomial Theorem Practice Test Online With Explanation

Math

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