Exercise 5.5: Choose the correct answer

CHAPTER : Binomial Theorem, Sequences And Series

1. The value of 2 + 4 + 6 +…….+ 2n is

(1) n(n-1)/2

(2) n(n+1)/2

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

(4) n(n + 1)

Solution

2. The coefficient of x⁶ in (2 + 2x)¹⁰ is

(1) ¹⁰C₆

(2) 2⁶

(3) ¹⁰C₆ 2⁶

(4) ¹⁰C₆ 2¹⁰.

Solution

3. The coefficient of x⁸y¹² in the expansion of (2x + 3y)²⁰ is

(1) 0

(2) 2⁸3¹²

(3) 2⁸3¹² + 2¹²3⁸

(4) ²⁰C₈ 2⁸3¹².

Solution

4. If ⁿC₁₀ > ⁿC_r for all possible r, then a value of n is

(1) 10

(2) 21

(3) 19

(4) 20.

Solution

5. If a is the arithmetic mean and g is the geometric mean of two numbers, then

(1) a ≤ g

(2) a ≥ g

(3) a = g

(4) a > g.

Solution

6. If (1 + x²)² (1 + x)ⁿ = a₀ + a₁x + a₂x² +……..+ xⁿ⁺⁴ and if a₀, a₁, a₂ are in AP, then n is

(1) 1

(2) 2

(3) 3

(4) 4.

Solution

7. If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

(1) 2

(2) 1

(3) 4

(4) 16.

Solution

8. The sequence  form an

(1) AP

(2) GP

(3) HP

(4) AGP.

Solution

9. The HM of two positive numbers whose AM and GM are 16, 8 respectively is

(1) 10

(2) 6

(3) 5

(4) 4.

Solution

10. If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n - 2S_n-1 + S_n-2 is

(1) 0

(2) 2d

(3) 4d

(4) d².

11. The remainder when 38¹⁵ is divided by 13 is

(1) 12

(2) 1

(3) 11

(4) 5.

Solution

12. The n^th term of the sequence 1, 2, 4, 7, 11,…….is

(1) n³ + 3n² + 2n

(2) n³ - 3n² + 3n

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

(4) n²-n+2 / 2 .

13. The sum up to n terms of the series  is

Ans: 4

Solution

14. The n^th term of the sequence 1/2 , 3/4 , 7/8 , 15/16 ,……….is

(1) 2ⁿ - n - 1

(2) 1 - 2^-n

(3) 2^-n + n - 1

(4) 2^n-1.

Solution

15. The sum up to n terms of the series √2 + √8 + √18 + √32 +……….is

(1) n(n+1) / 2

(2) 2n(n + 1)

(3) n(n+1) / 2

(4) 1.

Solution

16. The value of the series 1/2 + 7/4 + 13/8 + 19/16 +…………. is

(1) 14

(2) 7

(3) 4

(4) 6.

Solution

17. The sum of an infinite GP is 18. If the first term is 6, the common ratio is

(1) 1/3

(2) 2/3

(3) 1/6

(4) 3/4 .

Solution

18. The coefficient of x⁵ in the series e^-2x is

(1) 2/3

(2) 3/2

(3) -4/15

(4) 4/15 .

Solution

19. The value of 1/2! + 1/4! + 1/6! +……… is

(1) e²+1 / 2e

(2) (e+1)² / 2e

(3) (e-1)² / 2e

(4) e²+1 / 2e .

Solution

20. The value of  is

(1) log (5/3)

(2) 3/2 log(5/3)

(3) 5/3 log(5/3)

(4) 2/3 log(2/3)

Solution