Question

Find the middle term of (1 −3x + 3x2 – x3)2n
1. nC3n (x)3n
2. nC3n (x)2n
3. nC3n (−x)3n
4. nC3n (−x)2n

Answer 1

Correct Answer - Option 3 : nC3n (−x)3n

Calculation:

⇒ (1 − 3x + 3x2 – x3)2n = [(1 − x)3]2n = (1 − x)6n

⇒ Middle Term = [(6n/2) + 1] term = 6nC3n (−x)³ⁿ

⇒ If n is even then (n/2 + 1) Term is the middle Term.

⇒ If n is odd then [(n+1)/2]th and [(n+3)/2)th terms are the middle terms.