$A$ $2 ~kg$ ball moving at $24 ~ms^{-1}$ undergoes an inelastic head-on collision with a $4 ~kg$ ball moving in the opposite direction at $48 ~ms^{-1}$. If the coefficient of restitution is $2/3$,what are their velocities in $ms^{-1}$ after the impact?

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after the collision with a velocity equal to $\frac{1}{10}$th of its original velocity. Then the mass of the second body is (in $kg$)

The work function of a certain metal is $3.31 \times 10^{-19} \, J$. The maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength $5000 \, \text{Å}$ is: (Given: $h = 6.62 \times 10^{-34} \, J \cdot s$, $c = 3 \times 10^8 \, m/s$, $e = 1.6 \times 10^{-19} \, C$) (in $\text{eV}$)

Which concentrations can be calculated if the mole fraction and density of an aqueous solution of $HCl$ are known?
$1.$ Molality $\ \ 2.$ Molarity $\ \ 3.$ $\%(w/w)$

Which of the following lubricates ligaments or tendons and is an important constituent of synovial fluid of bones?

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is