Question

What is the even value of n, if the middle term of (a + b)^2n – 3 is 11?

(a) 12

(b) 10

(c) 20

(d) 22

I had been asked this question in examination.

The origin of the question is Binomial Theorem topic in division Binomial Theorem of Mathematics – Class 11

Answer 1

Correct option is (a) 12

The best explanation: If 2n – 3 is even, then the middle term is the \((\frac{2n-3}{2}+1)^{th}\) term.

Else if 2n – 3 is odd, there are two middle terms which are the \((\frac{2n-3+1}{2})^{th}\) term and the \((\frac{2n-3+3}{2})^{th}\) term.

Case 1: \(\frac{2n-3}{2}\) + 1= 11 ; n = 11.5

Case 2: \(\frac{2n-2}{2}\) = 11 ; n = 12

Case 3: \(\frac{2n}{2}\) = 11 ; n = 11