If in a $$\triangle A B C$$, with usual notations, $$\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$$ are in A.P. then $$\frac{\sin 3 B}{\sin B}=$$

The common region of the solutions of the inequations $$x+2 y \geq 4,2 x-y \leq 6$$ and $$x, y>0$$ is

If $$\int \frac{(\cos x-\sin x)}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c$$, then $$p=$$ (where $$\mathrm{c}$$ is a constant of integration)

Two identical particles each of mass '$$m$$' are separated by a distance '$$d$$'. The axis of rotation passes through the midpoint of '$$\mathrm{d}$$' and is perpendicular to the length $$\mathrm{d}$$. If '$$\mathrm{K}$$' is the average rotational kinetic energy of the system, then the angular frequency is