Question

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

• A. $-56$
• B. $14$
• C. $-14$
• D. None of these

Answer 1

Answer: (D)

$T_{r+1}={}^9{C}_r{\left(\frac{x^2}{2}\right)}^{9-r}{\left(-\frac{2}{x}\right)}^r$
$={}^9{C}_r{\left(\frac{1}{2}\right)}^{9-r}{\left(-2\right)}^r{x}^{18-3r}$
Now, for the coefficient of $x^7$, we put $18-3r=7$
$\therefore r=11/3$ (Not possible)
So, there is no term containing $x^7$.