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NDA 2023 Maths · Mathematics · Binomial Theorem · medium

If binom n0+binom n2+binom n4+…=128, then n equals

Single correct option

If (n0)+(n2)+(n4)+⋯=128\binom n0+\binom n2+\binom n4+\cdots=128, then nn equals
  1. A. 77
  2. B. 99
  3. C. 1616
  4. D. 88
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Answer: (D) 88

The sum of the even-indexed binomial coefficients is 2n−12^{n-1}. Setting 2n−1=128=272^{n-1}=128=2^7 gives n=8n=8. Using the full sum 2n=1282^n=128 would give n=7n=7, which is the trap in the second option.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake