The number $(101)^{100}-1$ is divisible by

If $\frac{1+\sqrt{3}i}{2}$ is a root of the equation $x^4-x^2+x-1=0$,then its real roots are: 

$A$ wire in the form of a square of side $a$ carries a current $i$. Then,the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)

$A$ particle carrying a charge equal to $100$ times the charge on an electron is rotating per second in a circular path of radius $0.8 \ m$. The value of the magnetic field produced at the centre will be (where ${\mu _0}$ is the permeability of vacuum).

In the following compounds,the order of acidity is:
$(I)$ Phenol
$(II)$ $p$-Cresol ($4$-methylphenol)
$(III)$ $m$-Nitrophenol
$(IV)$ $p$-Nitrophenol

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6 \ cm \ s^{-1}$. If they coalesce to form one big drop,what will be the terminal speed of the bigger drop? (Neglect the buoyancy of the air) ....... $cm \ s^{-1}$