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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

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

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

81a⁴ + 36a²x

81a⁴ – 36a²x

27a³ + 36a²x

27a³ – 36a²x

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

450/263

None of these

504/259

405/256

5. 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 !

5 ! 3 !

6. 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

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

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

15/7

7/8

15/23

7/15

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

None of these

-1

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

9th term

6th term

8th term

7th term

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

2ⁿ

2ⁿ⁻²

n²

2ⁿ⁻¹

13.

14. The number of terms in the binomial expansion is

Two less than the exponent

One less than the exponent

Equal to the exponent

One more than the exponent

15. 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)

None of these

P (12, 10)

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

-8a

12a

-2a²

-4a

17.

18. 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

19. 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

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

21. 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)

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

2nd term

3rd term

Seven term

4th term

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

-1≤x≤1

-2

-1

-2≤x≤2

24.

25. 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

2/3 – 61x/48

3/2 – 61x/48

3/2 – 48x/61

Page 2 of 4

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

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

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

29. (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

30. The exponent in (a-b)¹⁷ is

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

180

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

n/3(n–2)

n/2(n–3)

n/2(n+1)

n(n+3)

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

2ⁿ

2(n – 1)

2ⁿ⁻¹

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

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

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

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

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

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

None of these

(n+1)th term

N+2/3 th term

n th term

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

n + 1

None of these

n – 1

37. 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

38. (x – 1)³ =

1 – 3x + 3x² – x³

x³ – 3x + 3x – 1

x³ + 3x + 3x – 1

x³ – x² + x + 1

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

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

1563

1771

2891

3421

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

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

16th

15th

14th

13th

43. The exponent in (a + b)⁷ is

44. (1 + x)⁷ =

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

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

46. The middle term of (x + 1/x)¹⁰ is

¹⁰C₃

¹⁰C₅

None of these

¹⁰C₄

47.

48. 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

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

1024

50.

Page 3 of 4

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

11th

13th

None of these

12th

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

-1≤x≤1

-1

-2≤x≤2

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

|x|<2/3

|x|<1/3

|x|<1/2

|x|<1

54. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Taylor series

Binomial theorem

None of these

Binomial series

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

Even

Odd

Prime

None of these

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

n < 2

n > 2

n ≤

n ≥ 2

57.

58. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

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

(r + 1)th term

r th term

(r – 1)th term

None of these

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

-4/x²

-1024

- 27/1024x

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

4th

6th

5th

4th and 5th

62. 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

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

10 x 12

None of these

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

Not a prime

An even number

None of these

Not an odd number

65. 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

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

3rd term

4th term

5th term

2nd term

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

-1

-2

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

2²⁻ⁿ

2n – 1

2ⁿ

69. 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

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

-28/243

-28/81

28/81

28/243

71. 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

3/2 and 6

2/3 and 9

2 and 9

72. If the pth, qth and rth terms of an A.P. are in G.P:., then the common ratio of the G.P. is

p+q/r+q

None of these

p–r/p–q

r–q/q–p

73.

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

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

Page 4 of 4

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

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

G.P.

H.P.

None of these

A.P.

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

n > 5

n ≥ 5

n ≥ 3

n > 3

79. 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/√2)²

a–b/a

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

10000

100

100000

1000

81. 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

None of these

140

112

82. The value of ¹⁵C₁₀ is equal to

15/10

5/11

5/10

15/11

83. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

9999

10000

None of these

9998

84. (1 + 2x)⁴ =

1 – 8x + 24x² – 32x³ + 16x⁴

1 + 4x + 6x² + 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 – 4x + 6x² – 4x³ + x⁴

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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