# The coefficient of $x^7$ in the expansion of $(\large\frac{x^2}{2}-\frac{2}{x})^9$ is

$\begin{array}{1 1}(A)\;-56\\(B)\;14\\(C)\;-14\\(D)\;\text{None of these}\end{array}$

Toolbox:
• $T_{r+1}=nC_ra^{n-r} b^r$
$T_{r+1}=9C_r(\large\frac{x^2}{2})^{9-r}(-\large\frac{2}{x})^r$
$\Rightarrow 9C_r(\large\frac{1}{2})^r$$(-2)^r x^{18-3r}$
$18-3r=7$
$-3r=7-18$
$r=\large\frac{11}{3}$
Since the value of r is non-negative integral,there is no term containing $x^7$
Hence (D) is the correct answer.