The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$,its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,

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

In the equation $S = a + bt + ct^2$,where $S$ is measured in metres and $t$ is measured in seconds,the unit of $c$ is:

If mass is written as $m=kc^{p} G^{-1 / 2} \,h^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $k$ a dimensionless constant)

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 time period of revolution of a satellite $(T)$ around the earth depends on the radius of the circular orbit $(R)$,mass of the earth $(M)$,and universal gravitational constant $(G)$. The expression for $T$,using dimensional analysis is ($K$ is a constant of proportionality):