If the dimensions of $A$ and $B$ are different,which of the following operations is physically meaningful?

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

What is dimensional analysis? Write the limitations of dimensional analysis.

If $A, B$ and $C$ are three different physical quantities with different dimensional formulae, then the combination which can never give a proper physical quantity is

The refractive index of the medium is $\mu = A + \frac{B}{\lambda^{2}}$,where $A$ and $B$ are constants and $\lambda$ is the wavelength of light. The dimensions of $B$ are the same as that of

If energy $(E)$,velocity $(V)$,and time $(T)$ are chosen as the fundamental quantities,the dimensional formula of surface tension will be