JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Binomial Theorem

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of

(1 + x)^{N + 5}

are in the ratio

5 : 10 : 14

, then the largest coefficient in the expansion is:

Answer: (D)

Solution

Let the three consecutive coefficients be

(R - 1 N + 5)

(R N + 5)

(R + 1 N + 5)

in the ratio

5 : 10 : 14

. The first ratio gives

2 (R - 1 N + 5) = (R N + 5)

, so

3 R = N + 6

, and the second gives

7 (R N + 5) = 5 (R + 1 N + 5)

, so

12 R = 5 N + 18

. Solving together yields

N = 6

and

R = 4

, so the expansion is

(1 + x)^{11}

, whose largest coefficient is

(5 11) = (6 11) = 462

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Single correct option