Chapter 5: Binomial theorem, Sequences and Series

The value of 2 + 4 + 6 + …………… + 2n is

(4) n(n + 1)

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

(4) 10C₆2¹⁰

The coefficient of x⁸ y¹² in the expansion of (2x + 3y)²⁰ is

(4) 20C₈ 2⁸ 3¹²

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

(4) 20

If a is the Arithmetic mean and g is the Geometric mean of two numbers then

(2) a ≥ g

If (1 + x²)² (1 + x)ⁿ = a₀ + a₁x + a₂x² + ………… + x^{n + 4} and if a₀, a₁, a₂ are in A. P then n is

(3) 2

If a, 8, b are in A .P , a, 4 , b are in G. P and if a, x ,b are in H . P then x is

(1) 2

(3) H.P

The H.M of two positive numbers whose A.M and G.M are 16,8 respectively is

(4) 4

If S denote the sum of n terms of an A. P whose common difference is d, the value of S_n – 2S_{n- 1} + S_{n – 2} is

(1) d

The remainder when 38¹⁵ is divided by 13 is

(1) 12

The nth term of the sequence 1, 2, 4, 7, 11, ………….. is

(4) n2−n+2/2

The sum up to n terms of the series

(4) √2n+1−1 /2

The n^th term of the sequence

(2) 1 – 2^-n

The sum up to n terms of the series

(3) n(n+1)/√2

The value of the series

(1) 14

The sum of an infinite G.P is 18. If the first term is 6 the common ratio is

(2) 2/3

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

(3) −4/15

The value of

(3) (e−1)²/2e

The value of

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