If $A$ and $B$ are two physical quantities having different dimensions,then which of the following cannot denote a physical quantity?

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

If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as $[\eta^x \rho^y r^z]$,where $\eta, \rho,$ and $r$ are the coefficient of viscosity of the liquid,density of the liquid,and radius of the tube respectively,then the values of $x, y,$ and $z$ are given by:

Applying the principle of homogeneity of dimensions,determine which one is correct. Where $T$ is time period,$G$ is gravitational constant,$M$ is mass,and $r$ is the radius of the orbit.

The expressions below give current $I$ through an electronic component as a function of applied potential $V$. $I_0$ and $V_0$ are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect?
$(A)$ $I=I_0\left(e^{\frac{2 V}{V_0}}+1\right)$
$(B)$ $I=I_0\left(e^{\frac{V}{2 V_0}}-1\right)$
$(C)$ $I=I_0 V_0\left(e^{\frac{V}{V_0}}-1\right)$
$(D)$ $I=I_0\left(\frac{V}{V_0}\right)\left(e^{\frac{V}{V_0}}-1\right)$

If energy $E = G^p h^q c^r$,where $G$ is the universal gravitational constant,$h$ is Planck's constant,and $c$ is the speed of light,find the values of $p, q$,and $r$ respectively.