The $rms$ speed of hydrogen is $\sqrt{7}$ times the $rms$ speed of nitrogen. If the temperature of the gases is $T$,then:

The average speed $(U_{avg})$ of $O_2$ at $\pi \times 10 \ bar$ pressure in an $8 \ L$ container containing $2 \ moles$ is:

At a temperature of $27\,^{\circ}C$,$0.5 \, mol$ of $O_2$ gas is filled in a $50 \, L$ container at a pressure of $2 \, atm$. If half of the $O_2$ molecules are removed from the container,the $rms$ speed of the $O_2$ molecules will........

At $400 \ K$,the root mean square $(rms)$ speed of a gas $X$ (molecular weight $= 40$) is equal to the most probable speed of gas $Y$ at $60 \ K$. The molecular weight of the gas $Y$ is:

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

Choose the correct arrangement of molecular speeds,where the symbols have their usual meanings.