If $\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}=e^2\qquad(a,b\in N)$ then

Question

$\begin{array}{1 1}(a)\;a=4,b=2&(b)\;a=8,b=4\\(c)\;a=16,b=8&(d)\;None\;of\;these\end{array}$