$\tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A = $

The mass defect in a particular nuclear reaction is $0.3\, g$. The amount of energy liberated in kilowatt-hours $(kWh)$ is (Velocity of light = $3 \times 10^8\, m/s$)

An integrating factor of the differential equation $(1-x^2) \frac{dy}{dx} + xy = \frac{x^4}{(1+x^5)} (\sqrt{1-x^2})^3$ is

An oxide of an element is a gas and dissolves in water to give an acidic solution. The element belongs to

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):

$\operatorname{sech}^{-1}(\sin \theta)$ is equal to