Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful?

The velocity of water waves $v$ may depend upon their wavelength $\lambda$,the density of water $\rho$,and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as:

In a measurement,it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of $[M^a L^b T^c]$. If $b = 3$,the value of $c$ is . . . . . . .

Given a charge $q$,current $I$ and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum?

If velocity $(V)$,force $(F)$ and time $(T)$ are chosen as fundamental quantities,then the dimensions of energy are:

Write the dimensions of $a/b$ in the relation $P = \frac{a - t^2}{bx}$,where $P$ is pressure,$x$ is distance,and $t$ is time.