If (1–x+x 2 ) n =a 0 +a 1 x+a 2 x 2 + …. + a 2n x 2n then a…

Maths Binomial Theorem & Mathematical Induction Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If (1–x+x 2 ) n =a 0 +a 1 x+a 2 x 2 + …. + a 2n x 2n then a 0 + a 2 + a 4 + …. +a 2n equals

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The correct answer is:

Put x = 1 ⇒ ⇒ 1 = a 0 + a 1 + a 2 + L  + a 2n .

Put x = − − 1 ⇒ ⇒ 3 n = a 0 − − a 1 + a 2 − − a 3 + L  + a 2n .

Adding, 3 n + 1 = 2 (a 0 + a 2 + a 4 + L  + a 2n )

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