$A$ ball of mass $1.2 \ kg$ moving with a velocity of $12 \ ms^{-1}$ makes a one-dimensional collision with another stationary ball of mass $1.2 \ kg$. If the coefficient of restitution is $\frac{1}{\sqrt{2}}$,then the ratio of the total kinetic energy of the balls after collision to the initial kinetic energy is:

$A$ body of mass $M \ kg$ is at the top point of a smooth hemisphere of radius $5 \ m$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \ m/s$. At this instant,the angle made by the radius vector of the body with the vertical is: (Acceleration due to gravity $g = 10 \ m/s^2$) (in $^{\circ}$)

The Earth $E$ moves in an elliptical orbit with the Sun $S$ at one of the foci as shown in the figure. Its speed of motion will be maximum at the point:

$A$ vessel contains $1 \, mole$ of $O_2$ gas (molar mass $32$) at a temperature $T$. The pressure of the gas is $P$. An identical vessel containing one mole of $He$ gas (molar mass $4$) at a temperature $2T$ has a pressure of:

What is the equivalent capacitance of the system of capacitors between $A$ and $B$?

Which of the following metals becomes passive towards concentrated $HNO_3$?