The dimensions of ${\left({\mathrm{\mu }}_0{\mathrm{\epsilon }}_0\right)}^{-1/2}$ are:

1.  $\left[{\mathrm{L}}^{-1}\right]$ $\mathrm{T}$

2.  $\left[{\mathrm{LT}}^{-1}\right]$

3.  $\left[{\mathrm{L}}^{-1/2}\right]$ ${\mathrm{T}}^{1/2}$

4.  $\left[{\mathrm{L}}^{-1/2}\right]$ ${\mathrm{T}}^{-1/2}$

The dimensions of $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2$ where ${\epsilon }_0$ is the permittivity of free space and E is the electric field, are:

1. [ML²T^-2]

2. [ML^-1T^-2]

3.  [ML²T^-1]

4.  [MLT^-1]

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:

1. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}\right]$

2. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

3. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}{\mathrm{I}}^{-1}\right]$

4. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{I}}^{-2}\right]$

The velocity $v$ of a particle at time $t$ is given by $v=at+\dfrac{b}{t+c}$, where $a,$ $b$ and $c$ are constants. The dimensions of $a,$ $b$ and $c$ are respectively:
1. $\left[{LT}^{-2}\right],[{L}] \text { and }[{T}]$
2. ${\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]}$
3. ${\left[{LT}^2\right],[{LT}] \text { and }[{L}]}$
4. ${[{L}],[{LT}] \text { and }\left[{T}^2\right]}$

In an experiment, the percentage errors that occurred in the measurement of physical quantities $A,$ $B,$ $C,$ and $D$ are $1\%$, $2\%$, $3\%$, and $4\%$ respectively. Then, the maximum percentage of error in the measurement of $X,$ where $X=\frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3}$, will be:
1. $10\%$
2. $\frac{3}{13}\%$
3. $16\%$
4. $-10\%$