Explanation

(d)
Since, $(3 + ax)^{9} = \ ^{9}C_{0}3^{9} + \ ^{9}C_{1}3^{8}(ax) + \ ^{9}C_{2}3^{7}(ax)^{2} + \ ^{9}C_{3}3^{6}(ax)^{3} + \ldots$
Since, coefficient of $x^{2} =$ coefficient of $x^{3}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ^{9}C_{2}3^{7}a^{2} = \ ^{9}C_{3}3^{6}a^{3}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{\ ^{9}C_{2}}{\ ^{9}C_{3}} \bullet 3 = a$
$\Longrightarrow \ \ \ \frac{\frac{9 \times 8}{2 \times 1}}{\frac{9 \times 8 \times 7}{3 \times 2}} \times 3 = a$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a = \frac{9}{7}$