Q195 / 270 · NDA 2021 (Phase 1) · Mathematics

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

  • Correct answer
    A
    $8064$
  • B
    $4032$
  • C
    $2016$
  • D
    $1008$

Solution

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

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

Relevant Questions