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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2021 · Mathematics · Binomial Theorem

What is the coefficient of the middle term in the expansion of (1+4...

What is the coefficient of the middle term in the expansion of (1+4x+4x2)5\left(1+4 x+4 x^2\right)^5 ?

Options

  1. A80648064
  2. B40324032
  3. C20162016
  4. D10081008

Correct answer

A. 80648064

Step-by-step solution

(1+4x+4x2)5=(1+2x)2×5=(1+2x)10∴ Middle term =10C5(2x)5=10!5!5!⋅25⋅x5\begin{aligned} & \left(1+4 x+4 x^2\right)^5=(1+2 x)^{2 \times 5}=(1+2 x)^{10} \\ & \therefore \text{ Middle term }={ }^{10} C_5(2 x)^5=\frac{10!}{5!5!} \cdot 2^5 \cdot x^5\end{aligned} Co-efficient of middle term =8064=8064.
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