By what ratio does the average velocity of a gas molecule change when the temperature is raised from $50^{\circ}C$ to $200^{\circ}C$ (in $: 1$)?

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 $16$)

If the most probable speed of methane $(CH_4)$ at a certain temperature is $400 \ ms^{-1}$,what is the kinetic energy of one mole of methane at the same temperature in $J$?

At $27 \ ^oC$,the ratio of $rms$ velocities of ozone to oxygen is

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 $ms^{-1}$?

The $r.m.s.$ velocity of a certain gas is $v$ at $300 \ K$. The temperature,at which the $r.m.s.$ velocity becomes double,is ............... $K$.