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

3rd term

2nd term

Seven term

4th term

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

10 x 12

None of these

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

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

27a³ + 36a²x

81a⁴ + 36a²x

81a⁴ – 36a²x

27a³ – 36a²x

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

(r – 1)th term

None of these

r th term

(r + 1)th term

6. 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

99, 784

30, 240

None of these

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

|x|<1/2

|x|<1

|x|<2/3

|x|<1/3

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

28/243

28/81

-28/243

-28/81

11. The value of ¹⁵C₁₀ is equal to

15/11

15/10

5/11

5/10

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

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

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

9999

None of these

9998

10000

15. 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

112

140

None of these

16. (1 + 2x)⁴ =

1 – 8x + 24x² – 32x³ + 16x⁴

1 – 4x + 6x² – 4x³ + x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

17. 3 + 3 a + 3 a² + ………… ∞ is equal to 45/8, a > 0 then a is

15/7

7/8

7/15

15/23

18. The exponent in (a-b)¹⁷ is

19. 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

20.

21. 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

2a b/2+b

a–b/a

(√a – √b/√2)²

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

8th term

9th term

7th term

6th term

23. 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

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

n – 1

None of these

n + 1

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

Page 2 of 4

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

-1024

- 27/1024x

-4/x²

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

(n+1)th term

n th term

None of these

N+2/3 th term

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

29.

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

2²⁻ⁿ

2ⁿ

2n – 1

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

-2a²

-4a

-8a

12a

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

None of these

504/259

405/256

450/263

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

n ≥ 2

n > 2

n < 2

n ≤

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

-1

-2

35. 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 = – ½, m = 6

p = 1/2, m = 6

36.

37. (1 + x)⁷ =

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

38. 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

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

40. 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

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

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

1 – ½ x

1 + ½ x

1 – x

1 + x

43. 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

44. 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)

None of these

C (12, 2)

P (12, 10)

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

n/2(n+1)

n/3(n–2)

n/2(n–3)

n(n+3)

46. 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

Real numbers n

Integers n

Positive integers n

47. The middle term of (x + 1/x)¹⁰ is

¹⁰C₅

¹⁰C₄

None of these

¹⁰C₃

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

Not an odd number

Not a prime

An even number

None of these

49.

50. (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

Page 3 of 4

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

n/n+2

n/n+1

n/2(n+1)

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

4th and 5th

5th

4th

6th

53. The exponent in (a + b)⁷ is

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

1563

3421

1771

2891

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

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

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

58. 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

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

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

61.

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

2924

924

792

1594

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

2(n – 1)

2ⁿ

2ⁿ⁻¹

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

100000

1000

10000

100

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

G.P.

A.P.

None of these

H.P.

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

4th term

5th term

3rd term

2nd term

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

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

n > 3

n > 5

n ≥ 3

n ≥ 5

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

180

70. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/3! x³

n(n – 1)(n – 2)/2! x²

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

2ⁿ⁻²

2ⁿ⁻¹

n²

2ⁿ

72. 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

1/2 – x/48

3/2 – 48x/61

3/2 – 61x/48

2/3 – 61x/48

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

Prime

None of these

Even

Odd

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

14th

15th

13th

16th

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

None of these

-1

Page 4 of 4

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

-1≤x≤1

-1

-2≤x≤2

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

1024

78.

79. (x – 1)³ =

x³ + 3x + 3x – 1

1 – 3x + 3x² – x³

x³ – x² + x + 1

x³ – 3x + 3x – 1

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?

4 ! 3 !

5 (3 !)

5 ! 3 !

5 !

81. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Binomial theorem

Taylor series

None of these

Binomial series

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

-1

-2

-2≤x≤2

-1≤x≤1

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

11th

None of these

13th

12th

84. 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

p–r/p–q

None of these

p+q/r+q

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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