If feasible region is as shown in the figure, then related inequalities are

The general solution of the equation $$3 \sec ^2 \theta=2 \operatorname{cosec} \theta$$ is

A right circular cone has height $$9 \mathrm{~cm}$$ and radius of base $$5 \mathrm{~cm}$$. It is inverted and water is poured into it. If at any instant, the water level rises at the rate $$\frac{\pi}{\mathrm{A}} \mathrm{cm} / \mathrm{sec}$$. where $$\mathrm{A}$$ is area of the water surface at that instant, then cone is completely filled in

If $$\theta$$ is angle between the vectors $$\bar{a}$$ and $$\bar{b}$$ where $$|\bar{a}|=4,|\bar{b}|=3$$ and $$\theta \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$$, then $$|(\bar{a}-\bar{b}) \times(\bar{a}+\bar{b})|^2+4(\bar{a} \cdot \bar{b})^2$$ has the value