$3.65 \ g$ of $HCl$ is dissolved in $16.2 \ g$ of water. The mole fraction of $HCl$ in the resulting solution is

When a metallic surface is illuminated with radiation of wavelength $\lambda$,the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2\lambda$,the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is:

A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is . . . . . . . . . . .
($g =$ gravitational acceleration)

On a temperature scale $Y$,water freezes at $-160^{\circ} Y$ and boils at $-50^{\circ} Y$. On this $Y$ scale,a temperature of $340 \ K$ is (in $^{\circ} Y$)

If $I_n = \int \sin^n x \, dx$,then $n I_n - (n-1) I_{n-2}$ equals

$A$ proton, a deuteron (nucleus of ${ }_1 H^2$) and an $\alpha$-particle with the same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is: