Q249 / 270 · NDA 2010 (Phase 2) · Mathematics

What is the coefficient of $x^4$ in the expansion of $\left(\frac{1-x}{1+x}\right)^2$ ?

  • A
    -16
  • Correct answer
    B
    16
  • C
    8
  • D
    -8

Solution

$\begin{aligned} & \text { Coefficient of } x^4 \text { in }\left(1-2 x+x^2\right)(1+x)^{-2} \\ & \Rightarrow \text { Coefficient of } x^4 \text { in }\left(1-2 x+x^2\right)(1-2 x+ \\ & \left.\qquad 3 x^2-4 x^3+5 x^4-\ldots\right) \\ & \Rightarrow 5+8+3 \\ & \Rightarrow 16\end{aligned}$

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

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