Two black spheres $\mathrm{P} \& \mathrm{Q}$ have radii in the ratio $4: 3$. The wavelength of maximum intensity of radiation are in the ratio $4: 5$ respectively. The ratio of radiated power by P to Q is

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^{\circ} \mathrm{C}$ at constant pressure is (Molecular weight of nitrogen $=28, R=$ gas constant, $\mathrm{C}_{\mathrm{p}}=\frac{7}{2} \mathrm{R}$ for diatomic gas)

The difference in length between two rods A and B is 60 cm at all temperatures. If $\alpha_{\mathrm{A}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $\alpha_{\mathrm{B}}=27 \times 10^{-6} /{ }^{\circ} \mathrm{C}$, then the length of $\operatorname{rod} \mathrm{A}$ and $\operatorname{rod} \mathrm{B}$ at $0^{\circ} \mathrm{C}$ is respectively