The physical quantity that has no dimensions

Given that $\int {{e^{ax}}\left. {dx} \right|}  = {a^m}{e^{ax}} + C$, then which statement is incorrect (Dimension of $x =  L^1$) ?

The physical quantity which has dimensional formula as that of $\frac{{{\rm{Energy}}}}{{{\rm{Mass}} \times {\rm{Length}}}}$ is

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in $SI$ units.

($1$) The relation between $[E]$ and $[B]$ is

$(A)$ $[ E ]=[ B ][ L ][ T ]$  $(B)$ $[ E ]=[ B ][ L ]^{-1}[ T ]$  $(C)$ $[ E ]=[ B ][ L ][ T ]^{-1}$  $(D)$ $[ E ]=[ B ][ L ]^{-1}[ T ]^{-1}$

($2$) The relation between $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ is

$(A)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^2[ T ]^{-2}$  $(B)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^{-2}[ T ]^2$   $(C)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^2[ T ]^{-2}$  $(D)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^{-2}[ T ]^2$

Give the answer or quetion ($1$) and ($2$)

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $c$, electron mass $m_c$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_0}$, where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is $[B]=[c]^\alpha\left[m_c\right]^\beta[h]^\gamma[k]^\delta$. The value of $\alpha+\beta+\gamma+\delta$ is. . . . .

The velocity of a freely falling body changes as ${g^p}{h^q}$ where g is acceleration due to gravity and $h$ is the height. The values of $p$ and $q$ are