Explanation

(d)
$The\ 14th\ term\ in\ the\ expansion\ of\ \left( \frac{3\sqrt{x}}{7} - \frac{5}{2x\sqrt{x}} \right)^{13n}\ is$
$T_{14} = \ ^{13n}C_{13}\left( \frac{3}{7}x^{1/2} \right)^{13n - 13}{( - 1)}^{13}\left( \frac{5}{2}x^{- 3/2} \right)^{13}$
$= \ ^{13n}C_{13}\left( \frac{3}{7} \right)^{13n - 13}( - 1)^{13}\left( \frac{5}{2} \right)^{13}x^{\frac{13n - 13}{2}\ - \ \frac{39}{2}}$
For this term to be independent of $x$, we put
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 13n - 52 = 0$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 4$