NDA 2020 Maths · Mathematics · Binomial Theorem · easy

The expansion of (x+a)^10 has two middle terms. 2. The expansion of (x+a)^11 has two middle terms.

Single correct option

Consider the following statements:
1. The expansion of

(x+a)^{10}

has two middle terms.
2. The expansion of

(x+a)^{11}

has two middle terms.
Which of the statements is/are correct?

Show answer and solution

Answer: (B) 2 only

(x+a)^n

has

n+1

terms. For

n=10

there are 11 terms, so there is exactly one middle term (the 6th). For

n=11

there are 12 terms, so the 6th and 7th are the two middle terms. Only statement 2 is correct.

Original question written in the NDA 2020 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