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

If $\cos x = \tan y$,$\cot y = \tan z$ and $\cot z = \tan x$,then $\sin x$ equals to

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction,when the angle of inclination of the plane is $60^{\circ}$,is

Benzene and toluene form an ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at $T \ K$ are $50 \ mm \ Hg$ and $40 \ mm \ Hg$ respectively. What is the mole fraction of toluene in vapour phase when $117 \ g$ of benzene is mixed with $46 \ g$ of toluene? (molar mass of benzene and toluene are $78 \ g \ mol^{-1}$ and $92 \ g \ mol^{-1}$ respectively)

The relation between pressure $p$ and volume $V$ is given by $p V^{1/4} = \text{constant}$. If the percentage decrease in volume is $\frac{1}{2} \%$,then the percentage increase in pressure is:

Which tissue is mainly composed of fat-storing cells?