If $\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$, then the value of $a$ and $b$, are

Question

$a$ = 1 and $b$ = 2

$a$ = 1 and $b$ $ \in R$

$a$ $ \in R$ and $b$ = 2

$a$ $ \in R$ and $b$ $ \in R$

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