If the equation $7 x^2-14 x y+p y^2-12 x+q y-4=0$ represents a pair of parallel lines then the value of $\sqrt{p^2+q^2-p q}$ is

If $\mathrm{P}(x, y)$ denotes $\mathrm{z}=x+\mathrm{i} y x, y \in \mathbb{R}$ and $\mathrm{i}=\sqrt{-1}$ in Argand's plane and $\left|\frac{z-1}{z+2 i}\right|=1$, then the locus of P is

The general solution of $2 \sqrt{3} \cos ^2 \theta=\sin \theta$ is

If $(2+\sin x) \frac{\mathrm{d} y}{\mathrm{~d} x}+(y+1) \cos x=0$ and $y(0)=1$ then $y\left(\frac{\pi}{2}\right)$ is equal to