The quantity having dimension $-1$ in the length is:

Let $[{\varepsilon _0}]$ denote the dimensional formula of the permittivity of free space and $[{\mu _0}]$ denote the dimensional formula of the permeability of free space. If $M = \text{mass}$,$L = \text{length}$,$T = \text{time}$,and $I = \text{electric current}$,then:

Which of the following quantities is dimensionless?

Dimensions of stress are

The dimensional formula for Boltzmann's constant is

If the equation for the velocity of a particle at time $t$ is $v = at + \frac{b}{t+c}$,then the dimensions of $a, b, c$ are respectively: