Explanation

(a)
Given that, $(1 + ax)^{n} = 1 + 8x + 24x^{2} + ...$
$\Rightarrow 1 + \frac{n}{1}ax + \frac{n(n - 1)}{1.2}a^{2}x^{2} + ... = 1 + 8x + 24x^{2} + ...$
On comparing the coefficients of $x,\ x^{2}$, we get
$na = 8,\ \frac{n(n - 1)}{1.2}a^{2} = 24$
$\Rightarrow \ na(n - 1)a = 48$
$\Rightarrow \ 8(8 - a) = 48$
$\Rightarrow \ 8 - a = 6$
$\Rightarrow \ a = 2\ \Rightarrow \ n = 4$