Each side of a cube is measured to be \(7.203\) \(\mathrm{m}.\) What are the total surface area and the volume respectively of the cube to appropriate significant figures?

1.	\(373.7~\mathrm{m^2}\) and \(311.3~\mathrm{m^3}\)
2.	\(311.3~\mathrm{m^2}\) and \(373.7~\mathrm{m^3}\)
3.	\(311.2992~\mathrm{m^2}\) and \(373.7147~\mathrm{m^3}\)
4.	\(373.7147~\mathrm{m^2}\) and \(311.2992~\mathrm{m^3}\)

 

The angle of \(1^\circ\) (degree) will be equal to:
(Use \(360^\circ=2\pi\) rad)
1. \(1.034\times10^{-3}\) rad
2. \(1.745\times10^{-2}\) rad
3. \(1.524\times10^{-2}\) rad
4. \(1.745\times10^{3}\) rad

A physical quantity is measured and the result is expressed as \(nu\) where \(u\) is the unit used and \(n\) is the numerical value. If the result is expressed in various units then: 
1. \(n\propto \mathrm{size~of}~u\) 
2. \(n\propto u^2\) 
3. \(n\propto \sqrt u\) 
4. \(n\propto \frac{1}{u}\)

A dimensionless quantity,

\(\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]\)
The value of \(\mathrm{n}\) is:
1. \(0\)
2. \(-1\)
3. \(1\)
4. none of these

The dimensions of \(\left [ML^{-1} T^{-2} \right ]\) may correspond to:

Choose the correct option:

The radius of a circle is stated as \(2.12\) cm. Its area should be written as:
1. \(14\mathrm{~cm^2}\) 
2. \(14.1\mathrm{~cm^2}\) 
3. \(14.11\mathrm{~cm^2}\)
4. \(14.1124\mathrm{~cm^2}\) 

The angle of \(1'\) (minute of an arc) in radian is nearly equal to:
1. \(2.91 \times 10^{-4} ~\mathrm{rad} \)
2. \(4.85 \times 10^{-4} ~\mathrm{rad} \)
3. \(4.80 \times 10^{-6} ~\mathrm{rad} \)
4. \(1.75 \times 10^{-2} ~\mathrm{rad}\)

Which of the following equations is dimensionally correct?
\((I)~~ v=\sqrt{\frac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\frac{mgl}{I}}~~~~~~(III)~~v=\frac{Pr^2}{2\eta l}\)
(where  \(v=\) speed, \(P=\) pressure; \(r,\) \(l\) are lengths; \(\rho=\)  density, \(m=\) mass, \(g=\) acceleration due to gravity, \(I=\) moment of inertia, and \(\eta=\) coefficient of viscosity)

The acceleration due to gravity on the surface of the earth is \(g=10\) m/s². The value in km/(minute)² is:
1. \(36\)
2. \(0.6\)
3. \(\frac{10}{6}\)
4. \(3.6\)