At what temperature is the $R$.$M$.$S$. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $K$)? (Molecular weight of hydrogen $= 2$,molecular weight of oxygen $= 32$)

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

$A$ mixture of $2\, moles$ of helium gas (atomic mass $= 4\, u$) and $1\, mole$ of argon gas (atomic mass $= 40\, u$) is kept at $300\, K$ in a container. The ratio of their rms speeds $\left[ \frac{V_{rms}(\text{helium})}{V_{rms}(\text{argon})} \right]$ is close to:

Nitrogen gas is at $300^{\circ} C$ temperature. The temperature (in $K$) at which the $rms$ speed of a $H_{2}$ molecule would be equal to the $rms$ speed of a nitrogen molecule is........ (Molar mass of $N_{2}$ gas = $28 \ g/mol$,Molar mass of $H_{2}$ gas = $2 \ g/mol$)

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the r.m.s. velocity of its molecules at $100 \ K$,then at $400 \ K$,the r.m.s. velocity becomes:

If the temperature of a gas is increased from $127^{\circ} C$ to $527^{\circ} C$, then the rms speed of the gas molecules