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

1.  $[$ $L^{-1}T$ $]$

2.  $[$ $L{T}^{-1}$ $]$

3.  $[$ $L^{1/2}{T}^{1/2}$ $]$

4. $[$ $L^{1/2}{T}^{-1/2}$ $]$

Taking into account the significant figures, what is the value of \((9.99~\text{m}-0.0099~\text{m})\text{?}\)
1. \(9.98~\text{m}\)
2. \(9.980~\text{m}\)
3. \(9.9~\text{m}\)
4. \(9.9801~\text{m}\)

If the error in measurement of the radius of a sphere is \(0.1\%,\) then the error in its volume will be:
1. \(0.3\%\)
2. \(0.4\%\)
3. \(0.5\%\)
4. \(0.6\%\)

The relative error in \(Z,\) if \(Z=\dfrac{A^{4}B^{1/3}}{CD^{3/2}}\) is:

1. \(\dfrac{\Delta A}{A}+\dfrac{\Delta B}{B}+\dfrac{\Delta C}{C}+\dfrac{\Delta D}{D}\)

2. \(4\dfrac{\Delta A}{A}+\dfrac{1}{3}\dfrac{\Delta B}{B}-\dfrac{\Delta C}{C}- \dfrac{3}{2}\dfrac{\Delta D}{D}\)

3. \(4\dfrac{\Delta A}{A}+\dfrac{1}{3}\dfrac{\Delta B}{B}+\dfrac{\Delta C}{C}+\dfrac{2}{3}\dfrac{\Delta D}{D}\)

4. \(4\dfrac{\Delta A}{A}+\dfrac{1}{3}\dfrac{\Delta B}{B}+\dfrac{\Delta C}{C}+\dfrac{3}{2}\dfrac{\Delta D}{D}\)

\(5.74\) g of a substance occupies \(1.2~\text{cm}^3\). Its density by keeping the significant figures in view is:
1. \(4.7333~\text{g/cm}^3\)
2. \(3.8~\text{g/cm}^3\)
3. \(4.8~\text{g/cm}^3\)
4. \(3.7833~\text{g/cm}^3\)

If speed \(V,\) area \(A,\) and force \(F\) are chosen as fundamental units, then the dimension of Young's modulus will be:
1. \(\left [ FA^{-1}V^0 \right ]\)
2. \(\left [ FA^{2}V^{-1} \right ]\)
3. \(\left [ FA^{2}V^{-3} \right ]\)
4. \(\left [ FA^{2}V^{-2} \right ]\)

Which of the following measurement is most precise?
1. \(5.00~\text{mm}\) 
2. \(5.00~\text{cm}\) 
3. \(5.00~\text{m}\) 
4. \(5.00~\text{km}\) 

How many significant figures are in \(0.0006032~\text{m}^2?\)
1. \(8\)
2. \(4\)
3. \(9\)
4. none of these

Which of the following pairs represent units of the same physical quantity?

1.  kelvin and joule

2.  kelvin and calorie

3.  newton and calorie

4.  joule and calorie.