Mathematics Induction and Binomial Theorem Online Test

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Question 1

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

Answer

None of these

Question 2

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

Answer

None of these

Question 3

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

Question 4

4. (x – 1/x)³ =

Answer

x³ + 3x + 3/x + 1/x³

Answer

x³ + x + 1/x + 1/x²

Answer

None of these

Answer

x³ – 3x + 3/x – 1/x³

Question 5

5. 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

Answer

None of these

Question 6

6. 99th term of the series 2 + 7 + 14 + 23 + 34 + ……… is

Answer

None of these

Question 7

7. The exponent in (a-b)¹⁷ is

Question 8

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

Question 9

9.

Question 10

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

Question 11

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

Question 12

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

Answer

None of these

Answer

N+2/3 th term

Answer

(n+1)th term

Question 13

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

Answer

81a⁴ + 36a²x

Answer

27a³ + 36a²x

Answer

27a³ – 36a²x

Answer

81a⁴ – 36a²x

Question 14

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

Answer

2(n – 1)

Question 15

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

Question 16

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

Question 17

17. 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

Answer

2/3 – 61x/48

Answer

3/2 – 48x/61

Answer

3/2 – 61x/48

Answer

1/2 – x/48

Question 18

18. (x – 1)³ =

Answer

x³ + 3x + 3x – 1

Answer

1 – 3x + 3x² – x³

Answer

x³ – 3x + 3x – 1

Answer

x³ – x² + x + 1

Question 19

19. (1 + x)ⁿ = 1 + nx + n(n – 1)/2! x² + n(n – 1)(n – 2)/3! x³ + …… is

Answer

Binomial theorem

Answer

None of these

Answer

Taylor series

Answer

Binomial series

Question 20

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

Answer

n/2(n–3)

Answer

n/3(n–2)

Question 21

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

Answer

- 27/1024x

Question 22

22. The middle term of (x + 1/x)¹⁰ is

Answer

None of these

Question 23

23. The number of terms in the binomial expansion is

Answer

One more than the exponent

Answer

One less than the exponent

Answer

Equal to the exponent

Answer

Two less than the exponent

Question 24

24.

Question 25

25.

Question 26

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

Question 27

27. The exponent in (a + b)⁷ is

Question 28

28. 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?

Question 29

29. (1 + 2x)⁴ =

Answer

1 + 8x + 24x² + 32x³ + 16x⁴

Answer

1 + 4x + 6x² + 4x³ + x⁴

Answer

1 – 8x + 24x² – 32x³ + 16x⁴

Answer

1 – 4x + 6x² – 4x³ + x⁴

Question 30

30. (1 + x)⁷ =

Answer

7+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

Answer

1-7x+21x²-35x³+35x⁴-21x⁵+7x⁶-x⁷

Answer

1+x+x²+x³+x⁴+x⁵+x⁶+x⁷

Answer

1+7x+21x²+35x³+35x⁴+21x⁵+7x⁶+x⁷

Question 31

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

Answer

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

Answer

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

Answer

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

Answer

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

Question 32

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

Question 33

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

Answer

None of these

Answer

(r – 1)th term

Answer

(r + 1)th term

Question 34

34. For (1+x)ⁿ the 2nd term is

Answer

n(n – 1)(n – 2)/2! x²

Answer

n(n – 1)(n – 2)/3! x³

Question 35

35. 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

Question 36

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

Question 37

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

Answer

-2≤x≤2

Answer

-1≤x≤1

Question 38

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

Answer

-2≤x≤2

Answer

-1≤x≤1

Question 39

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

Question 40

40.

Question 41

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

Question 42

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

Question 43

43.

Question 44

44. 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

Answer

(√a – √b/√2)²

Question 45

45. 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

Answer

None of these

Answer

P (12, 10)

Question 46

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

Question 47

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

Question 48

48.

Question 49

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

Answer

None of these

Answer

p = – ½, m = 6

Answer

p = 5/2, m =

Answer

p = 1/2, m = 6

Question 50

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

Answer

None of these

Question 51

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

Question 52

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

Answer

None of these

Question 53

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

Question 54

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

Answer

4th and 5th

Question 55

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

Answer

None of these

Question 56

56. The value of ¹⁵C₁₀ is equal to

Question 57

57.

Question 58

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

Answer

An even number

Answer

None of these

Answer

Not an odd number

Answer

Not a prime

Question 59

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

Question 60

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

Question 61

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

Question 62

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

Answer

None of these

Question 63

63. 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

Answer

Positive real numbers n

Answer

Positive integers n

Answer

Real numbers n

Answer

Integers n

Question 64

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

Answer 78

None of these

Answer 79

1 – ½ x

Answer 80

p–r/p–q

Answer 81

r–q/q–p

Answer 82

None of these

Answer 83

None of these

Answer 84

Seven term

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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Mathematics Induction and Binomial Theorem Online Test

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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:

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Maan Ali

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