If $z^2+z+1=0$ then $\left(z^3+\frac{1}{z^3}\right)^2+\left(z^4+\frac{1}{z^4}\right)^2=$ where $z=w=$ complex cube root of unity

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

A gas expands in such a way that its pressure and volume satisfy the condition $\mathrm{PV}^2=$ constant. Then the temperature of the gas

A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed ' $N$ ' r.p.s. about its axis perpendicular to the plane. If ' $B$ ' is the magnetic field at the centre, the charge on the ring is ( $\mu_0=$ permeability of free space)