$A$ ball moving with velocity $2 \, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$,then their velocities (in $m/s$) after collision will be

The primary winding of a transformer has $100$ turns and its secondary winding has $200$ turns. The primary is connected to an $AC$ supply of $120$ $V$ and the current flowing in it is $10$ $A$. The voltage and the current in the secondary are:

If $\int e^x \left( \frac{1-\sin x}{1-\cos x} \right) dx = f(x) + \text{constant}$,then $f(x)$ is equal to

What is the other name for the structure shown in the given figure?

If $\int \frac{dx}{(1+\sqrt{x}) \sqrt{x-x^2}} = \frac{A \sqrt{x}}{\sqrt{1-x}} + \frac{B}{\sqrt{1-x}} + C$,where $C$ is a real constant,then $A+B$ equals to

$A$ liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.
$a$. What is the initial effect of the change on vapour pressure?
$b$. How do rates of evaporation and condensation change initially?
$c$. What happens when equilibrium is restored finally and what will be the final vapour pressure?