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

-2

-1

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

2²⁻ⁿ

2n – 1

2ⁿ

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

4. 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 !)

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

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

1024

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

Odd

None of these

Prime

Even

8. The sum of odd co-efficient in the expansion (1+x)⁴ 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. If ‘n’ is even them the middle term in the expansion of (a+b)ⁿ will be

n th term

N+2/3 th term

(n+1)th term

None of these

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

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

14th

16th

13th

15th

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

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

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

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

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

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

|x|<1

|x|<1/3

|x|<2/3

|x|<1/2

15.

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

2ⁿ⁻¹

2ⁿ

2(n – 1)

17. The middle term of (x + 1/x)¹⁰ is

¹⁰C₄

¹⁰C₅

¹⁰C₃

None of these

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

8th term

6th term

9th term

7th term

19. 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

1594

924

792

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

7/15

7/8

15/23

15/7

21. 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

22. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

23. The exponent in (a-b)¹⁷ is

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

Not an odd number

An even number

None of these

Not a prime

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

(r – 1)th term

None of these

r th term

(r + 1)th term

Page 2 of 4

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

27. The exponent in (a + b)⁷ is

28. 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

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

n ≥ 3

n > 5

n > 3

n ≥ 5

30. 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

31. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

None of these

Taylor series

Binomial series

Binomial theorem

32.

33.

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

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

n/2(n+1)

n/n+2

n/n+1

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

-1

-1≤x≤1

-2≤x≤2

37.

38. 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

1/2 – x/48

2/3 – 61x/48

3/2 – 48x/61

39. (x – 1/x)³ =

x³ – 3x + 3/x – 1/x³

None of these

x³ + x + 1/x + 1/x²

x³ + 3x + 3/x + 1/x³

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

4th and 5th

5th

4th

6th

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

42. 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

Real numbers n

Positive real numbers n

Positive integers n

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

-1≤x≤1

-2≤x≤2

-2

-1

44. The value of ¹⁵C₁₀ is equal to

5/10

5/11

15/11

15/10

45. 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

200

100

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

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

2nd term

4th term

5th term

3rd term

48. (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

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

405/256

None of these

450/263

504/259

50. 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

Page 3 of 4

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

n – 1

None of these

n + 1

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

2ⁿ⁻¹

n²

2ⁿ

2ⁿ⁻²

53.

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

180

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

n < 2

n ≤

n ≥ 2

n > 2

56. 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

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

2nd term

4th term

Seven term

3rd term

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

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

60. 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 = 1/2, m = 6

p = 5/2, m =

p = – ½, m = 6

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

62.

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

n(n+3)

n/3(n–2)

n/2(n–3)

n/2(n+1)

64. 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

2a b/2+b

(√a – √b/√2)²

a+b/2

a–b/a

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

81a⁴ + 36a²x

27a³ + 36a²x

27a³ – 36a²x

81a⁴ – 36a²x

66. (x – 1)³ =

x³ – x² + x + 1

x³ – 3x + 3x – 1

1 – 3x + 3x² – x³

x³ + 3x + 3x – 1

67. 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, 10)

P (12, 2)

None of these

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

69. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

10000

9998

9999

None of these

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

-1

None of these

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

3421

1771

2891

1563

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

73. (1 + 2x)⁴ =

1 – 4x + 6x² – 4x³ + x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 – 8x + 24x² – 32x³ + 16x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

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

-4/x²

- 27/1024x

-1024

75. 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

p–r/p–q

p+q/r+q

r–q/q–p

Page 4 of 4

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

G.P.

None of these

H.P.

A.P.

77.

78.

79. 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

80. 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

30, 240

99, 784

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

10 x 12

None of these

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

11th

13th

12th

None of these

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

-8a

-4a

-2a²

12a

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

100

100000

1000

10000

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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