JEE Math Practice Question

Let y = y(x) satisfies the equation $${{dy} \over {dx}} - |A| = 0$$, for all x > 0, where $$A = \left[ {\begin{matrix} y & {\sin x} & 1 \\ 0 & { - 1} & 1 \\ 2 & 0 & {{1 \over x}} \\ \end{matrix} } \right]$$. If $$y(\pi ) = \pi + 2$$, then the value of $$y\left( {{\pi \over 2}} \right)$$ is :

1. A.$${\pi \over 2} + {4 \over \pi }$$
2. B.$${\pi \over 2} - {1 \over \pi }$$
3. C.$${{3\pi } \over 2} - {1 \over \pi }$$
4. D.$${\pi \over 2} - {4 \over \pi }$$