The area of a square is \(5.29~\text{cm}^2. \) The area of \(7\) such squares taking into account the significant figures is:
1. \(37.03~\text{cm}^2\)
2. \(37.0~\text{cm}^2\)
3. \(37~\text{cm}^2\)
4. \(37.030~\text{cm}^2\)

The least count of the main scale of a vernier callipers is \(1~\mathrm{mm}\). Its vernier scale is divided into \(10\) divisions and coincide with \(9\) divisions of the main scale. When jaws are touching each other, the \(7^{th}\) division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between \(3.1~\mathrm{cm}\) and \(3.2~\mathrm{cm}\) and \(4^{th}\) VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)
1. \(3.21~\text{cm}\)
2. \(2.99 ~\text{cm}\) 
3. \(3.2~\text{cm}\)
4. \(3.07~\text{cm}\)

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 momentum \((P), \) area \((A) ,\) and time \((T)\) are taken as the fundamental physical quantities, then the dimensional formula of energy in terms of \(P,\) \(A,\) and \(T\) is:

Using a screw gauge with pitch \(0.1 ~\text{cm}\) and \(50\) divisions on its circular scale, the thickness of an object is measured. It should be accurately recorded as:
1. \(2.124~\text{cm}\)
2. \(2.121~\text{cm}\)
3. \(2.125~\text{cm}\)
4. \(2.123~\text{cm}\)

The amount of solar energy received on the earth’s surface per unit area per unit time is defined as a solar constant. Dimension of solar constant is:
1. \(\left[ M L^2 T^{-2}\right]\)
2. \(\left[M^2 L^0 T^{-1}\right] \)
3. \( \left[ML T^{-2}\right] \)
4. \( \left[M L^0 T^{-3}\right]\)

A physical quantity \(z\) depends on four observables \(a,b,c\) and \(d\), as \(z=\frac{a^2 b^{\frac{2}{3}}}{\sqrt{c }d^3}\) The percentage of error in the measurement of  \(a,b,c\) and \(d\) is  \(2\%\), \(1.5\%\), \(4\%\) and \(2.5\%\) respectively. The percentage of error in \(z\) is:
1. \(12.25\%\)
2. \(14.5\%\)
3. \(16.5\%\)
4. \(13.5\%\)

The quantities \(x=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}, y=\frac{E}{B} \) and \(z=\frac{L}{C R}\) are defined where \(C\)-capacitance, \(R\)-Resistance, \(L\)-length, \(E\)-Electric field, \(B\)-magnetic field and \(\varepsilon_0, \mu_0\) free space permittivity and permeability respectively. Then:

The dimensional formula for thermal conductivity is: (here \(K\) denotes the temperature)
1. \( \left[M L T^{-2} K\right] \)
2. \( \left[M L T^{-3} K\right] \)
3. \( \left[M L T^{-3} K^{-1}\right] \)
4. \( \left[M L T^{-2} K^{-2}\right]\)

A quantity \(x\) is given by \(\left(\frac{IFv^2}{WL^4}\right) \) in terms of moment of inertia \(I\), force \(F\), velocity \(v\), work \(W\), and Length \(L\). The dimensional formula for \(x\) is the same as that of: