MCQ
Let $y=y(x)$ satisfies the equation $\frac{d y}{d x}-|A|=0$, for all $x>0$, where $A=\left[\begin{array}{ccc}y & \sin x & 1 \\ 0 & -1 & 1 \\ 2 & 0 & \frac{1}{x}\end{array}\right] .$
If $y(\pi)=\pi+2$, then the value of $y\left(\frac{\pi}{2}\right)$ is:
- A$\frac{\pi}{2}-\frac{4}{\pi}$
- B$\frac{\pi}{2}-\frac{4}{\pi}$
- C$\frac{\pi}{2}-\frac{1}{\pi}$
- D$\frac{\pi}{2}+\frac{4}{\pi}$