The rms velocity of a gas molecule of mass $m$ at a given temperature is proportional to

The r.m.s. speed of a group of $7$ gas molecules having speeds $(6, 4, 2, 0, -2, -4, -6) \, m/s$ is ...... $m/s$.

The temperature of a gas is $-50^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed is increased by $3$ times?

At what temperature is the $rms$ speed of hydrogen molecules equal to the $rms$ speed of oxygen molecules at $47^{\circ}C$ (in $K$)?

If the $rms$ speeds of helium and oxygen are equal,then the ratio of the temperatures of helium and oxygen is

The $rms$ velocity of molecules of a given mass of gas at $27^{\circ}C$ and $1.0 \times 10^5 \, Nm^{-2}$ pressure is $200 \, m \, s^{-1}$. What will be the $rms$ velocity if the temperature and pressure are $127^{\circ}C$ and $0.5 \times 10^5 \, Nm^{-2}$ respectively?