NDA 2024 Maths · Mathematics · Binomial Theorem · hard

What is the sum of the coefficients of the even powers of x in the expansion of (1+x)^10?

Single correct option

What is the sum of the coefficients of the even powers of

x

in the expansion of

(1+x)^{10}

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Answer: (C) $512$

Put

x=1

and

x=-1

: the total is

2^{10}=1024

and the alternating sum is

0

, so the even-power coefficients and odd-power coefficients each sum to

\frac{1024}2=512

. Trap: quoting the total 1024.

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