The correct relation between $$\gamma = {{{c_p}} \over {{c_v}}}$$ and temperature T is :

If a source of electromagnetic radiation having power $$15 \mathrm{~kW}$$ produces $$10^{16}$$ photons per second, the radiation belongs to a part of spectrum is.

(Take Planck constant $$h=6 \times 10^{-34} \mathrm{Js}$$ )

A lift of mass $$\mathrm{M}=500 \mathrm{~kg}$$ is descending with speed of $$2 \mathrm{~ms}^{-1}$$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $$2 \mathrm{~ms}^{-2}$$. The kinetic energy of the lift at the end of fall through to a distance of $$6 \mathrm{~m}$$ will be _____________ $$\mathrm{kJ}$$.

For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $$\lambda_{1}$$ and $$\lambda_{2}$$ is $$\frac{x}{32}$$. The value of $$x$$ is __________.