If a gas contains only three molecules that move with velocities of $100, 200, 500 \ ms^{-1}$. What is the rms velocity of that gas in $ms^{-1}$?

At $T$ $(K)$,the $P$,$V$ and $u_{rms}$ of $1$ mole of an ideal gas were measured. The following graph is obtained. What is its slope $(m)$? ($x$-axis $= PV$; $y$-axis $= u_{rms}^2$,$M =$ Molar mass)

Two flasks $X$ and $Y$ have capacities of $1 \ L$ and $2 \ L$ respectively,and each contains $1 \ mol$ of gas. The temperature of the flasks is maintained such that the average speed of molecules in flask $X$ is twice that in flask $Y$. The pressure in flask $X$ is ...

Case $-1:$ An ideal gas of molecular weight $M$ at temperature $T$.
Case $-2:$ Another ideal gas of molecular weight $2M$ at temperature $T/2$.
Identify the correct statement in the context of the above two cases.

The volumes of ozone and chlorine gas diffusing in the same time are $35 \ mL$ and $29 \ mL$ respectively. If the molar mass of chlorine is $71$,calculate the molar mass of ozone. (in $.7$)

The ratio of most probable velocity $(u_{mp})$,average velocity $(u_{av})$,and root mean square velocity $(u_{rms})$ is: