IIT JEE 1983 Maths - MCQ Question 15

$\begin{aligned} \left(\frac x2-\frac 3{x^2}\right)^{10} & = \frac {x^{10}}{2^{10}} {\color{#3D99F6}\left(1-\frac 6{x^3}\right)^{10}} \\ & = \frac {x^{10}}{2^{10}} {\color{#3D99F6} \sum_{n=0}^{10} (-1)^n {10 \choose n} \left(\frac 6{x^3}\right)^n} & \small \color{#3D99F6} \text{We get }x^4 \text{ when }n=2 \\ & = \cdots + \frac {x^{10}}{2^{10}} (-1)^{\color{#3D99F6}2} {10 \choose {\color{#3D99F6}2}} \left(\frac 6{x^3}\right)^{\color{#3D99F6}2} + \cdots \\ & = \cdots + \frac 1{2^{10}} \cdot 1 \cdot \frac {10\cdot 9}{1 \cdot 2} \cdot 36 x^4 + \cdots \\ & = \cdots + \boxed{\dfrac {405}{256}} x^4 + \cdots \end{aligned}$