$A$ and $B$ possess unequal dimensional formulas. Then,which of the following operations is not possible in any case?

The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

$A$ flywheel can rotate in order to store kinetic energy. The flywheel is a uniform disk made of a material with a density $\rho$ and tensile strength $\sigma$ (measured in Pascals),a radius $r$,and a thickness $h$. The flywheel is rotating at the maximum possible angular velocity so that it does not break. Which of the following expressions correctly gives the maximum kinetic energy per kilogram that can be stored in the flywheel? Assume that $\alpha$ is a dimensionless constant.

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ are:

If time $(t)$,velocity $(u)$,and angular momentum $(I)$ are taken as the fundamental units,then the dimension of mass $(m)$ in terms of $(t)$,$(u)$,and $(I)$ is:

If the charge of electron $e$,mass of electron $m$,speed of light in vacuum $c$,and Planck's constant $h$ are taken as fundamental quantities,then the permeability of vacuum $\mu_0$ can be expressed as