In an electromagnetic system,the quantity representing the ratio of electric flux and magnetic flux has dimensions of $M^{P} L^{Q} T^{R} A^{S}$. The values of $Q$ and $R$ are:

The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$,where $P$ is the pressure difference and $v$ is the velocity. Then,the relation between $x$ and $y$ is

Given that $v$ is the speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

$A$ beaker contains a fluid of density $\rho \, kg/m^3$,specific heat $S \, J/kg \, ^\circ C$,and viscosity $\eta$. The beaker is filled up to height $h$. To estimate the rate of heat transfer per unit area $(Q/A)$ by convection when the beaker is placed on a hot plate,a student proposes that it should depend on $\eta$,$\left( \frac{S\Delta \theta}{h} \right)$,and $\left( \frac{1}{\rho g} \right)$,where $\Delta \theta$ (in $^\circ C$) is the temperature difference between the bottom and top of the fluid. In that situation,the correct option for $(Q/A)$ is:

$A$ physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon_0}$ is $[c$ is velocity of light,$G$ is the universal gravitational constant and $e$ is charge$]$.

The foundations of dimensional analysis were laid down by