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

None of these

450/263

504/259

405/256

2. 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 (3 !)

4 ! 3 !

5 ! 3 !

5 !

3. 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)

C (12, 2)

None of these

P (12, 10)

4. 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

Real numbers n

Positive real numbers n

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

n²

2ⁿ⁻²

2ⁿ

2ⁿ⁻¹

6. 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

3/2 – 48x/61

1/2 – x/48

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

1771

3421

1563

2891

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

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

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

Odd

None of these

Even

Prime

11. The number of terms in the binomial expansion is

One less than the exponent

Equal to the exponent

One more than the exponent

Two less than the exponent

12. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

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

10 x 12

None of these

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

None of these

-1

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

16. 3 + 3 a + 3 a² + ………… ∞ is equal to 45/8, a > 0 then a is

15/7

7/8

7/15

15/23

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

-28/243

28/243

-28/81

28/81

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

-1≤x≤1

-1

-2≤x≤2

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

2²⁻ⁿ

2ⁿ

2n – 1

20.

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

H.P.

None of these

A.P.

G.P.

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

4th term

5th term

2nd term

3rd term

23.

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

25. 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

Page 2 of 4

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

6th

4th

5th

4th and 5th

27. 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

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

16th

15th

13th

14th

29. 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

30. The exponent in (a + b)⁷ is

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

Seven term

2nd term

4th term

3rd term

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

33. 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

2/3 and 9

2 and 9

3/2 and 6

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

13th

None of these

12th

11th

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

2ⁿ

2ⁿ⁻¹

2(n – 1)

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

-8a

-2a²

-4a

12a

37. (x – 1/x)³ =

x³ – 3x + 3/x – 1/x³

x³ + x + 1/x + 1/x²

None of these

x³ + 3x + 3/x + 1/x³

38. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

9998

10000

None of these

9999

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

40. 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

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

1024

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

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

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

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

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

43.

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

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

|x|<1/2

|x|<2/3

|x|<1

|x|<1/3

46. The exponent in (a-b)¹⁷ is

47. The middle term of (x + 1/x)¹⁰ is

¹⁰C₄

None of these

¹⁰C₃

¹⁰C₅

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

49.

50. (x – 1)³ =

x³ + 3x + 3x – 1

x³ – 3x + 3x – 1

x³ – x² + x + 1

1 – 3x + 3x² – x³

Page 3 of 4

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

52.

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

-1024

- 27/1024x

-4/x²

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

100000

10000

100

1000

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

Not an odd number

Not a prime

None of these

An even number

56. 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

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

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

n ≥ 3

n > 5

n ≥ 5

n > 3

59. The value of ¹⁵C₁₀ is equal to

15/10

5/11

15/11

5/10

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

61. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Taylor series

None of these

Binomial series

Binomial theorem

62.

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

-2

-2≤x≤2

-1

-1≤x≤1

64. 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

65. (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

66. 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

164

112

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

p = – ½, m = 6

p = 1/2, m = 6

None of these

p = 5/2, m =

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

180

69. 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

69, 760

None of these

99, 784

30, 240

70.

71. (1 + 2x)⁴ =

1 – 8x + 24x² – 32x³ + 16x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 – 4x + 6x² – 4x³ + x⁴

1 + 4x + 6x² + 4x³ + x⁴

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

n²+1/2

n²–1/2

n–1/2

n–2/2

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

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

9th term

6th term

8th term

7th term

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

None of these

n – 1

n + 1

Page 4 of 4

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

1 + ½ x

1 – x

1 + x

1 – ½ x

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

-1

-2

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

n ≥ 2

n ≤

n < 2

n > 2

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

r th term

(r – 1)th term

None of these

(r + 1)th term

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

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

27a³ – 36a²x

81a⁴ – 36a²x

27a³ + 36a²x

81a⁴ + 36a²x

82.

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

N+2/3 th term

n th term

(n+1)th term

None of these

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

n/2(n+1)

n(n+3)

n/3(n–2)

n/2(n–3)

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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