Kinetic Theory of Gases

Match Column - I and Column - II and choose the correct match from the given choices.

At what temperature will the rms speed of oxygen molecules becomes just sufficient for escaping from the Earth's atmosphere? (Given Mass of oxygen molecules $m=2.76\times {10}^{-26}\mathrm{ kg}$, Boltzmann's constant $k_B=1.38\times {10}^{-23}\mathrm{ J }{\mathrm{K}}^{-1}$)

The molecules of a given mass of gas have RMS velocity of $200$ $\mathrm{m }{\mathrm{s}}^{-1}$ at ${27}^{\mathrm{o}}\mathrm{C}$ and $1.0\times {10}^5\mathrm{ }\mathrm{N }{\mathrm{m}}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, ${127}^{\mathrm{o}}\mathrm{C}$ and $0.05\times {10}^5\mathrm{ }\mathrm{N }{\mathrm{m}}^{-2}$, the r.m.s. velocity of its molecules in $\mathrm{m }{\mathrm{s}}^{-1}$ is:

Two vessels separately contain two ideal gases $\mathrm{A}$ and $\mathrm{B}$ at the same temperature, the pressure of $\mathrm{A}$ being twice that of $\mathrm{B}$. Under such conditions, the density of $\mathrm{A}$ is found to be $\text{1.5}$ times the density of $\mathrm{B}$. The ratio of molecular weights of $\mathrm{A}$ and $\mathrm{B}$ is