The binding energy per nucleon versus mass number curve for nuclei is shown in the figure. $W, X, Y$ and $Z$ are four nuclei indicated on the curve. The process that would release energy is:

The terminal velocity of a liquid drop of radius $r$ falling through air is $v$. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air).

$A$ plot of the kinetic energy $\left(\frac{1}{2} m v^2\right)$ of ejected electrons as a function of the frequency $(\nu)$ of incident radiation for four alkali metals $(M_1, M_2, M_3, M_4)$ is shown below.
The alkali metals $M_1, M_2, M_3$ and $M_4$ are,respectively:

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \, years$ and $810 \, years$. The time (in years) after which one-fourth of the material remains is

If the gravitational acceleration at the surface of the Earth is $g$,then the increase in potential energy in lifting an object of mass $m$ to a height equal to half of the radius of the Earth from the surface will be

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to