A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300K. Find the ratio of average rotational kinetic energies per $O_2$ molecules to per $N_2$  molecules.

Both gases will have same number of rotational degree of freedom (equal to 2). Since both are diatomic and are at the same temperature. Average rotational kinetic energy per molecular for both the gases $=2\left(\frac{1}{2}KT\right).$   Required ratio $=1$