When pressure remains constant,at what temperature will the $r.m.s.$ speed of gas molecules increase by $10 \%$ of the $r.m.s.$ speed at $STP$?

The speed distribution for a sample of $N$ gas particles is shown below. $P(v) = 0$ for $v > 2 v_0$. How many particles have speeds between $1.2 v_0$ and $1.8 v_0$ (in $N$)?

$A$ vessel is partitioned into two equal halves by a fixed diathermic separator. Two different ideal gases are filled in the left $(L)$ and right $(R)$ halves. The $rms$ speed of the molecules in the $L$ part is equal to the mean speed of the molecules in the $R$ part. Then the ratio of the mass of a molecule in the $L$ part to that of a molecule in the $R$ part is

The temperature at which the root mean square velocity of a molecule will be doubled than its value at $100^{\circ}C$ is:

The $rms$ speed of a molecule of a diatomic gas is $v$. When the temperature is doubled,the molecule dissociates into two atoms. The new $rms$ speed of the atom is:

Six molecules of a gas in a container have speeds $2 \,m/s, 5 \,m/s, 3 \,m/s, 6 \,m/s, 3 \,m/s$ and $5 \,m/s$. The root mean square (r.m.s.) speed is: (in $\,m/s$)