NDA 2019 Maths · Mathematics · Binomial Theorem · medium

All the binomial coefficients in the expansion of (1+x)^8 are even. 2. The expansion of (a+b)^9 has a single middle term.

Single correct option

Consider the following statements:
1. All the binomial coefficients in the expansion of

(1+x)^8

are even.
2. The expansion of

(a+b)^9

has a single middle term.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (D) Neither 1 nor 2

(1+x)^8

the first coefficient

\binom80=1

is odd, so statement 1 is false. The expansion of

(a+b)^9

has

10

terms, an even number, so there are two middle terms, the

5

th and the

6

th; statement 2 is false. Middle terms are single only when the exponent is even. Hence neither statement is correct.

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