Let $\left[{\epsilon }_0\right]$ denote the dimensional formula of the permittivity of the vacuum and $\left[{\mu }_0\right]$ that of the permeability of the vacuum. If $M=$mass,$L=$length, $T=$time and $I=$electric current, then:

 

If the dimension of physical quantity are given by  $M^{\mathit{a}}{L}^{\mathit{b}}{T}^{\mathit{c}}$ then physical quantity will be

A drop of liquid of radius $\mathrm{r}$, density $\rho$ and surface tension $\sigma$ oscillates in gravity free space as shown in figure. If the time period of oscillation of this drop is $2$ sec, if the time period of oscillation of a drop of radius $2\mathrm{r}$ is $\sqrt{x} \mathrm{s}$. What is the value of $x$?

The second drop is made of same liquid as first.

In the figure shown $S_1$ and $S_2$ are two identical coherent sources of sound, separated by d. A receiver moves along line $XY$ which is parallel to $S_1{ S}_2$ to detect intensity of sound at various points on the line. Distance of line $XY$ from $S_1{ S}_2$ is $D\left(>>d\right).$ Distance of first intensity maxima on line $XY$ measured from $O$ is $\mathrm{y}.$ Find percentage change in value of $y$ if the temperature of air increases by $1\%.$ If your answer is $X\%$ fill value of $6X.$