$A$ point charge $+q$ is placed at the centre of a cube of side $L$. The electric flux emerging from the cube is

If $f_n(x) = \log \log \log \ldots \log x$ (where $\log$ is repeated $n$ times),then $\int (x f_1(x) f_2(x) \ldots f_n(x))^{-1} dx$ is equal to

An aluminium ring $B$ faces an electromagnet $A$. The current $I$ through $A$ can be altered. Which of the following statements is correct?

Assertion: One molal aqueous solution of glucose contains $180 \text{ g}$ of glucose in $1 \text{ kg}$ of water.
Reason: $A$ solution containing one mole of solute in $1000 \text{ g}$ of solvent is called a one molal solution.

In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth,the work done is

If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to