Moon has no atmosphere because

An ideal gas filled in a cylinder occupies volume $V$. The gas is compressed isothermally to the volume $V/3$. Now,the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules should escape to bring the pressure in the cylinder back to its original value (in $\%$)?

$A$ rigid diatomic gas having molar mass $M$ is contained in an insulated container. The container is moving with velocity $V$. If it is stopped suddenly, the change in temperature is ($R$ - gas constant).

The number of air molecules per $cm^3$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is $.........$

Which of the following statements about the kinetic theory of gases is wrong?

Initially,a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature $250\, K$. Assuming that $25\%$ of the molecules get dissociated,causing a change in the number of moles. The pressure of the resulting gas at temperature $2000\, K$,when contained in a volume $2V_{1}$,is given by $P_{2}$. The ratio $\frac{P_{2}}{P_{1}}$ is: