NDA 2019 Maths · Mathematics · Binomial Theorem · hard

If the coefficients of the 5th, 6th and 7th terms in the expansion of (1+x)^n are in AP, the sum of all possible values of n is

Single correct option

If the coefficients of the

5

th,

6

th and

7

th terms in the expansion of

(1+x)^n

are in AP, the sum of all possible values of

n

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Answer: (B) $21$

The coefficients are

\binom n4,\binom n5,\binom n6

. The AP condition

2\binom n5=\binom n4+\binom n6

simplifies to

n^2-21n+98=0

, i.e.

(n-7)(n-14)=0

. So

n=7

n=14

, and the sum is

21

. Answering

14

takes only the larger root, while

n=7

must be accepted since

\binom76

is defined.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake