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Q.
The coefficient of $x^7$ in the expansion of $\left(\frac{x^{2}}{2}-\frac{2}{x}\right)^{9}$ is
Binomial Theorem
Solution:
$T_{r+1} = \,{}^{9}C_{r} \left(\frac{x^{2}}{2}\right)^{9-r} \left(-\frac{2}{x}\right)^{r}$
$= \,{}^{9}C_{r} \left(\frac{1}{2}\right)^{9-r} \left(-2\right)^{r}\,x^{18-3r}$
Now, for the coefficient of $x^{7}$, we put $18 - 3r = 7$
$\therefore r = 11/3$ (Not possible)
So, there is no term containing $x^{7}$.