Explanation

(d)
General term
$T_{r + 1} = {( - 1)}^{r}\ ^{11}C_{r}\left( \frac{2\sqrt{x}}{5} \right)^{11 - r}\left( \frac{1}{{2x}^{3/2}}\ \right)^{r}$
$= \frac{2^{11 - 2r}}{5^{11 - r}}( - 1)^{r}\ ^{11}C_{r}x^{\frac{11 - r}{2}\ - \ \frac{3r}{2}}$
$For\ term\ independent\ of\ x,\ put\frac{11 - r}{2} - \frac{3r}{2} = 0$
$\Longrightarrow \frac{11 - 4r}{2} = 0 \Longrightarrow r = \frac{11}{4} \notin N$
$\therefore$ There is no term which is independent of $x$.