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

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. \(\left [ FA^{2}V^{-2} \right ]\)

If \(y=a\sin(bt-cx),\) where \(y\) and \(x\) represent length; \(t\) represents time, then which of the following has the same dimensions as that of \(\dfrac{ab^2}{c}?\)
1. \(\text{(Speed)}^2\)
2. Momentum
3. Angle
4. Acceleration