$A$ value of $n$ such that $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1$ is

The work of $146 \, kJ$ is performed in order to compress one kilo mole of a gas adiabatically,and in this process,the temperature of the gas increases by $7 \, ^oC$. The gas is $(R = 8.3 \, J \, mol^{-1} \, K^{-1})$.

An elementary particle of mass $m$ and charge $+e$ is projected with velocity $v$ at a much more massive particle of charge $Ze$,where $Z > 0$. What is the closest possible approach of the incident particle?

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):

For a normal eye,the cornea of the eye provides a converging power of $40 \ D$ and the least converging power of the eye lens behind the cornea is $20 \ D$. Using this information,the distance between the retina and the cornea-eye lens can be estimated to be ......... $cm$.

$A$ ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$. The total distance covered before it comes to rest is