The equation $\frac{{dV}}{{dt}} = At - BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are

The $SI$ unit of energy is $J=k g\, m^{2} \,s^{-2} ;$ that of speed $v$ is $m s^{-1}$ and of acceleration $a$ is $m s ^{-2} .$ Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ( $m$ stands for the mass of the body ):

$(a)$ $K=m^{2} v^{3}$

$(b)$ $K=(1 / 2) m v^{2}$

$(c)$ $K=m a$

$(d)$ $K=(3 / 16) m v^{2}$

$(e)$ $K=(1 / 2) m v^{2}+m a$

The dimension of the ratio of magnetic flux and the resistance is equal to that of :

The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as

Which of the following is dimensionally correct

If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: