Q168 / 270 · NDA 2017 (Phase 2) · Mathematics

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

  • A
    $2^{26}$
  • Correct answer
    B
    $2^{49}$
  • C
    $2^{50}$
  • D
    $2^{51}$

Solution

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

Hence, the correct answer is option: 'B'.

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