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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2010 · Mathematics · Binomial Theorem

What is the coefficient of x^4 in the expansion of ((1-x)/(1+x))^2 ?

What is the coefficient of x4x^4 in the expansion of (1−x1+x)2\left(\frac{1-x}{1+x}\right)^2 ?

Options

  1. A-16
  2. B16
  3. C8
  4. D-8

Correct answer

B. 16

Step-by-step solution

 Coefficient of  x4 in (1−2x+x2)(1+x)−2⇒ Coefficient of x4 in (1−2x+x2)(1−2x+3x2−4x3+5x4−…)⇒5+8+3⇒16\begin{aligned} & \text{ Coefficient\text{ 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}
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