Epsom salt is a hydrate of which of the following?

If $x=\log _{0.1} 0.001$ and $y=\log _9 81$,then $\sqrt{x-2 \sqrt{y}}$ is equal to

If $\frac{1}{2} \leq x \leq 1$,then $\cos ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^2}\right)$ is equal to

An electron is travelling along the $x$-direction. It encounters a magnetic field in the $y$-direction. Its subsequent motion will be

Consider the following two statements,$A$ and $B$ and identify the correct answer given below:
$A$. Nuclear density is same for all nuclei.
$B$. Radius of the nucleus $R$ and its mass number $A$ are related as $\sqrt{A} \propto R^{1 / 6}$.

Two bodies of $6 \ kg$ and $4 \ kg$ masses have their velocities $5 \hat{i}-2 \hat{j}+10 \hat{k}$ and $10 \hat{i}-2 \hat{j}+5 \hat{k}$ respectively. Then the velocity of their centre of mass is