$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-

- A
$log (A -B)$

- B
$sin (A + Bx)$

- C
$e^{(AB)}$

- D
$\tan \left[ {\frac{A}{B}\left( {\frac{B}{A}n} \right)} \right]$

The potential energy $u$ of a particle varies with distance $x$ from a fixed origin as $u=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constants. The dimensions of $A$ and $B$ are respectively

In the following list, the only pair which have different dimensions, is

Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is

Dimensional formula for thermal conductivity is (here $K$ denotes the temperature)

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

- [KVPY 2011]