$\lim _{x \rightarrow 0} \frac{\tan x - \sin x}{x^3}$ is equal to

$A$ particle of mass $4 m$ explodes into three pieces of masses $m, m$ and $2 m$. The equal masses move along $X$-axis and $Y$-axis with velocities $4 ms^{-1}$ and $6 ms^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

$A$ satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth.

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively. Their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1 = 4$,then $r_2/r_1 = ?$

During electro-osmosis of $Fe(OH)_3$ sol,

The term independent of $x$ in the expansion of $\left(\sqrt{x}-\frac{2}{\sqrt{x}}\right)^{18}$ is