Does RMS velocity depend on number of gas molecules in a gas sample? The expression of RMS velocity clearly has square root of number of gas molecules in the denominator and square root of squares of velocities of the gas molecules in the numerator. Then why RMS velocity does not depend on number of gas molecules? By looking at the expression, it seems as if it does depend on number of gas molecules.
No, it does not depend directly on the number of molecules. The expression is
$$c_{rms}=\sqrt{\frac{3RT}{M}}$$
where $T$ is the temperature in K, $M$ is the molar mass in kg/mol and $R$ is of course the gas constant in J mol-1 K-1.
However, it is possible to have a situation where the number of molecule affects the temperature of the gas, which would change the r.m.s. velocity. For example, in Joule-Thompson effect, increasing the pressure causes the gas to heat up. It might be possible to do this by pumping in more gas into an insulated constant volume vessel. (although it sounds a bit contrived to be honest!)