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.                 \[\frac{1}{4}\]