The $rms$ velocity of hydrogen is $\sqrt{7}$ times the $rms$ velocity of nitrogen. If the temperature of the gas is $T$,then which of the following is true?

If the kinetic energy and $RMS$ speed of a gas at a certain temperature are $4.0 \ kJ \ mol^{-1}$ and $5.0 \times 10^4 \ cm \ s^{-1}$,respectively,the molecular weight of the gas is:

$\alpha, v$ and $u$ represent the most probable velocity, average velocity, and root mean square velocity, respectively, of a gas at a particular temperature. The correct order among the following is:

$A$ gas bulb of $1 \ L$ capacity contains $2.0 \times 10^{21}$ molecules of nitrogen gas at a pressure of $7.57 \times 10^3 \ N \ m^{-2}$. Calculate the root mean square speed in $cm \ sec^{-1}$. (in $.5$)

The density of a gas at $100 \, kPa$ pressure is $0.1 \, g \, dm^{-3}$. The root mean square speed of the gas in $ms^{-1}$ 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 $16$)