If $\lim \limits_{x \to \infty}$ \bigg( 1+ \large\frac{a}{x}-\frac{4]{x^2} \bigg)^{2x} =e^3$, then 'a' is equal to :

Question

$\begin{array}{1 1} (1) 2 \\ (2) \large\frac{3}{2} \\ (3) \large\frac{2}{3} \\ (4) \large\frac{1}{2} \end{array}$