JEE Math Practice Question

The value of $$p$$ and $$q$$ for which the function $$f\left( x \right) = \left\{ {\begin{matrix} {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \\ q & {,x = 0} \\ {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{3/2}}}}} & {,x > 0} \\ \end{matrix} } \right.$$ is continuous for all $$x$$ in R, are

1. A.$$p =$$ $${5 \over 2}$$, $$q = $$ $${1 \over 2}$$
2. B.$$p =$$ $$-{3 \over 2}$$, $$q = $$ $${1 \over 2}$$
3. C.$$p =$$ $${1 \over 2}$$, $$q = $$ $${3 \over 2}$$
4. D.$$p =$$ $${1 \over 2}$$, $$q = $$ $$-{3 \over 2}$$