question_answer

If \[f(x)=\left\{ \begin{align}   & \sin x,x\ne n\pi ,n\in Z \\  & \,\,\,\,\,\,0,\,\,\text{otherwise} \\ \end{align} \right.\] and \[g(x)=\left\{ \begin{align}   & {{x}^{2}}+1,x\ne 0,\,2 \\  & \,\,\,\,\,\,\,\,4,x=0 \\  & \,\,\,\,\,\,\,\,\,5,x=2 \\ \end{align} \right.\] then \[\underset{x\to 0}{\mathop{\lim }}\,g\{f(x)\}=\] [Karnataka CET 2000]

A)                 1

B)                 0

C)                 \[\frac{1}{2}\]

D)                 \[\frac{1}{4}\]