$E, m, l$ and $G$ denote energy,mass,angular momentum,and gravitational constant respectively. Then the dimensions of $\frac{El^2}{m^5G^2}$ are:

The $SI$ unit of energy is $J = kg \, m^{2} \, s^{-2}$; 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):
$(a)$ $K = m^{2} v^{3}$
$(b)$ $K = (1/2) m v^{2}$
$(c)$ $K = m a$
$(d)$ $K = (3/16) m v^{2}$
$(e)$ $K = (1/2) m v^{2} + m a$

What could be a correct expression for the speed of ocean waves in terms of its wavelength $\lambda$,the depth $h$ of the ocean,the density $\rho$ of sea water,and the acceleration of free fall $g$?

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$: Time period of oscillation of a liquid drop depends on surface tension $(S)$,if density of the liquid is $\rho$ and radius of the drop is $r$,then $T = k \sqrt{\rho r^{3} / S}$ is dimensionally correct,where $k$ is dimensionless.
Reason $(R)$: Using dimensional analysis,we find that the $R.H.S.$ has different dimensions than that of the time period.

In a particular system of units,a physical quantity can be expressed in terms of the electric charge $e$,electron mass $m_e$,Planck's constant $h$,and Coulomb's constant $k = \frac{1}{4 \pi \epsilon_0}$,where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants,the dimension of the magnetic field is $[B] = [e]^\alpha [m_e]^\beta [h]^\gamma [k]^\delta$. The value of $\alpha + \beta + \gamma + \delta$ is . . . . .

The conversion of $1 \;MW$ power in a new system having basic units of mass,length,and time as $10 \;kg$,$1 \;dm$,and $1 \;minute$ respectively is: