The physical quantities not having same dimensions are :

A particles with initial velocity $\mathrm{u}$ is moving with uniform acceleration $\mathrm{a}.$ The distance moved by the particle in the ${\mathrm{t}}^{\mathrm{th}}$ second is given by $\mathrm{s}=\mathrm{u}+\frac{1}{2} \mathrm{a}\left(2\mathrm{t}-1\right).$ The dimension of $\mathrm{s}$ must be :

The time dependent of a physical quantity $\mathrm{P}$ is given by $\mathrm{P}={\mathrm{P}}_0{\mathrm{e}}^{-\mathrm{\alpha }{t}^2},$ where $\mathrm{\alpha }$ is a constant and $\mathrm{t}$ is time. The constant $\mathrm{\alpha }$

The ground-state energy of electron in hydrogen atom is given by $\mathrm{E}=-\mathrm{R} \mathrm{h} \mathrm{c},$ where $\mathrm{R}$ is Rydberg constant. The dimension of $\mathrm{R} \mathrm{are}$ :

If force $=\frac{\mathrm{\alpha }}{{\mathrm{\beta }}^3+\mathrm{density}},$ then the dimensions of $\mathrm{\alpha }$ and $\mathrm{\beta }$ will be:

The notations $\mathrm{E}, \mathrm{m}, \mathrm{J} \mathrm{and} \mathrm{G}$ repersent energy, mass, angular momentum and gravitational constant respectively. $\mathrm{E} {\mathrm{J}}^2/ {\mathrm{m}}^5 {\mathrm{G}}^2$ has the dimensions of :

If force $\left(\mathrm{F}\right),$ velocity $\left(\mathrm{V}\right)$ and time $\left(\mathrm{T}\right)$ are taken as fundamental units, the dimensions of mass are :

The variation of pressure $\mathrm{P}$ with distance $\mathrm{z}$ is given by

                                                                   $\mathrm{P}=\frac{\mathrm{\alpha }}{\mathrm{\beta }}\mathrm{e}-\mathrm{\alpha z}/\mathrm{k\theta },$

where $\mathrm{\alpha },\mathrm{\beta }$ are constants, $\mathrm{k}$ is Boltzmann constant and $\mathrm{\theta }$ is temperature. The dimensional formula of $\mathrm{\beta }$ will be:

Choose the correct statement (s) :