NDA 2023 Maths · Mathematics · Binomial Theorem · medium

The value of dbinom121+dbinom123+dbinom125+…+dbinom1211 is

Single correct option

The value of

\dbinom{12}{1}+\dbinom{12}{3}+\dbinom{12}{5}+\dots+\dbinom{12}{11}

Show answer and solution

Answer: (C) $2048$

The sums of binomial coefficients over even and over odd indices are equal, each being half of

2^{12}=4096

. So the odd-index sum is

2^{11}=2048

. The value

2047

results from wrongly subtracting the term

\binom{12}{0}

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