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Q1.

The value of $\lim_{x \to 0}\left(\dfrac{x^2\sin^2 x}{x^2 - \sin^2 x}\right)$ is:

(A)

$2$

(B)

$3$

(C)

$4$

(D)

$6$

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Q2.

Let $f(x) = \lim_{y \to 0} \dfrac{(1 - \cos(xy)) \tan(xy)}{y^3}$. Then the number of solutions of the equation $f(x) = \sin x$, $x \in \mathbf{R}$ is :

(A)

$0$

(B)

$2$

(C)

$3$

(D)

$1$

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