The refractive index of prism is $$\mu=\sqrt{3}$$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _________$$^\circ$$.

A wire of resistance $$R$$ and radius $$r$$ is stretched till its radius became $$r / 2$$. If new resistance of the stretched wire is $$x ~R$$, then value of $$x$$ is ________.

When a $$d c$$ voltage of $$100 \mathrm{~V}$$ is applied to an inductor, a $$d c$$ current of $$5 \mathrm{~A}$$ flows through it. When an ac voltage of $$200 \mathrm{~V}$$ peak value is connected to inductor, its inductive reactance is found to be $$20 \sqrt{3} \Omega$$. The power dissipated in the circuit is _________ W.

A circular coil having 200 turns, $$2.5 \times 10^{-4} \mathrm{~m}^2$$ area and carrying $$100 \mu \mathrm{A}$$ current is placed in a uniform magnetic field of $$1 \mathrm{~T}$$. Initially the magnetic dipole moment $$(\vec{M})$$ was directed along $$\vec{B}$$. Amount of work, required to rotate the coil through $$90^{\circ}$$ from its initial orientation such that $$\vec{M}$$ becomes perpendicular to $$\vec{B}$$, is ________ $$\mu$$J.