How can I prepare for Mathematics Induction and Binomial Theorem Online Test?

You can prepare for Mathematics Induction and Binomial Theorem Online Test by attempting the free online quizzes at Gotest.com.pk. We provide instant results, performance reports, and detailed explanations for every question.

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.
Test Helpful For:	ECAT Entry Test Math Online Test Interview Questions about Math All Universities Entrance Test Recruitments Tests

Math Induction and Binomial Theorem Practice Test Online With Explanation

Please wait...

Page 1 of 4

Math

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

None of these

-1

2. 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

3. 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 !

4. The middle term of (x + 1/x)¹⁰ is

None of these

¹⁰C₃

¹⁰C₄

¹⁰C₅

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

p = 5/2, m =

p = 1/2, m = 6

None of these

p = – ½, m = 6

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

1771

3421

2891

1563

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

n > 5

n ≥ 5

n ≥ 3

n > 3

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

3rd term

Seven term

4th term

2nd term

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

2ⁿ⁻¹

2ⁿ

n²

2ⁿ⁻²

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

|x|<1/2

|x|<2/3

|x|<1

|x|<1/3

11. 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

164

112

None of these

12. 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

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

-1≤x≤1

-2≤x≤2

-1

14.

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

10 x 12

None of these

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

7/15

7/8

15/23

15/7

17. 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.

H.P.

None of these

18.

19.

20. 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

21.

22. (1 + x)⁷ =

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

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

None of these

n – 1

n + 1

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

9th term

6th term

7th term

8th term

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

-4/x²

-1024

- 27/1024x

Page 2 of 4

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

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

180

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

29. 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)

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

81a⁴ – 36a²x

81a⁴ + 36a²x

27a³ + 36a²x

27a³ – 36a²x

31. The exponent in (a + b)⁷ is

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

14th

15th

13th

16th

33. (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

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

35. 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

2a b/2+b

(√a – √b/√2)²

a+b/2

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

n < 2

n ≤

n ≥ 2

n > 2

37. 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, 10)

P (12, 2)

None of these

C (12, 2)

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

100000

1000

10000

100

39. (x – 1)³ =

x³ – 3x + 3x – 1

1 – 3x + 3x² – x³

x³ + 3x + 3x – 1

x³ – x² + x + 1

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

-4a

-2a²

12a

-8a

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

42. 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

43. 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

3/2 – 48x/61

2/3 – 61x/48

1/2 – x/48

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

Even

None of these

Odd

Prime

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

None of these

504/259

405/256

450/263

46. 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

47. 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

48.

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

-2

-1≤x≤1

-1

-2≤x≤2

50.

Page 3 of 4

51. 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

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

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

54. The value of ¹⁵C₁₀ is equal to

15/11

5/11

5/10

15/10

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

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

5th term

2nd term

4th term

3rd term

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

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

None of these

r th term

(r – 1)th term

(r + 1)th term

59. (1 + 2x)⁴ =

1 – 4x + 6x² – 4x³ + x⁴

1 + 8x + 24x² + 32x³ + 16x⁴

1 – 8x + 24x² – 32x³ + 16x⁴

1 + 4x + 6x² + 4x³ + x⁴

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

2ⁿ⁻¹

2(n – 1)

2ⁿ

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

n/n+1

n/n+2

n/2(n+1)

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

2n – 1

2²⁻ⁿ

2ⁿ

63. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

10000

None of these

9998

9999

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

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

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

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

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

65. The exponent in (a-b)¹⁷ is

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

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

1024

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

None of these

n th term

(n+1)th term

N+2/3 th term

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

70. (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

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

4th and 5th

5th

4th

6th

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

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

74. For (1+x)ⁿ the 2nd term is

n(n – 1)(n – 2)/2! x²

n(n – 1)(n – 2)/3! x³

75. 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

Page 4 of 4

76.

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

An even number

Not a prime

None of these

Not an odd number

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

11th

12th

13th

None of these

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

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

1594

924

2924

792

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

-28/243

-28/81

28/243

28/81

82. 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

2/3 and 9

2 and 9

3 and 2

3/2 and 6

83.

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

-2

-1

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.
Time Management: Attempt this online quiz multiple times to improve your speed.

More Related Resources

Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... Punjab Mathematics Online Test 11th... PPSC Syllabus for Mathematics Lectu...

Can't find what you're looking for? Search below:

Latest Updates

Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...
Punjab Mathematics Online Test 11th Class Model Paper Chapter No ...

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

Math

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

Key Preparation Tips:

More Related Resources

Latest Updates

Maan Ali

3 Comments

Leave a Reply Cancel reply