The classification of organisms into prokaryotes and eukaryotes is based on which characteristic?

If $\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)$ is finite,then the values of $a, b$ are respectively :

$\sinh^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)$ is equal to

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0 = \text{permeability of free space}$ and $H = \text{magnetic field intensity}$) is:

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

$A$ body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is acceleration due to gravity).