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. \(5.00~\text{km}\) 

Which of the following ratios, express pressure?

Choose the correct option:

The following is/are not a unit of time:

Choose the correct option:

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes \(8~\text{min}\) and \(20~\text{s}\) to cover this distance?
1. \(125\)
2. \(250\)
3. \(350\)
4. \(500\)

A calorie is a unit of heat (energy in transit) and it equals about \(4.2~\text J\) where \(1~\text J = 1~\mathrm{kgm^{2}s^{–2}}.\) Suppose we employ a system of units in which the unit of mass equals \(\alpha~\text{kg},\) the unit of length equals \(\beta~\text{m}\), the unit of time is \(\gamma~\text{s}.\) What is the magnitude of a calorie in terms of the new units?
1. \(4.2\alpha^{–1}\beta^{–1}\gamma^2\)
2. \(4.2\alpha^{–2}\beta^{–2}\gamma^2\)
3. \(4.2\alpha^{–1}\beta^{–2}\gamma^2\)
4. \(4.2\alpha^{–1}\beta^{–2}\gamma^1\)

38. A physical quantity X is related to four measurable quantities a, b, c, and d as follows $\mathrm{X}={\mathrm{a}}^2{\mathrm{b}}^3{\mathrm{c}}^{5/2}{\mathrm{d}}^{-2}$. The percentage error in measuring a, b, c, and d is 1%, 2%, 3%, and 4%, respectively. What is the percentage error in quantity X?

(1) 22.1 %

(2) 13.2 %

(3) 34.6 %

(4) 23.5 %

This objective question is based on NCERT Exemplar subjective Question.

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. $[$ $L^{1/2}{T}^{-1/2}$ $]$

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]