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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2017 · Mathematics · Binomial Theorem

In the expansion of (1+x)^ 50 , the sum of the coefficients of odd...

In the expansion of (1+x)50(1+x)^{50}, the sum of the coefficients of odd powers of xx is

Options

  1. A2262^{26}
  2. B2492^{49}
  3. C2502^{50}
  4. D2512^{51}

Correct answer

B. 2492^{49}

Step-by-step solution

Sum of odd terms of expansion (a+b)n(\mathrm{a}+\mathrm{b})^{\mathrm{n}} is 12⋅2n\frac{1}{2} \cdot 2^{\mathrm{n}}. ∴\therefore Sum of odd terms of expansion (1+x)50(1+x)^{50} is 12⋅250\frac{1}{2} \cdot 2^{50}. =2−1⋅250=249=2^{-1} \cdot 2^{50}=2^{49}.
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