In SI units, the dimensions of \(\sqrt{\frac{\varepsilon_0}{\mu_0}} \) is:
1. \( A T^{-3} M L^{3 / 2} \)
2. \( A^{-1} T M L^3 \)
3. \( A T^2 M^{-1} L^{-1} \)
4. \( A^2 T^3 M^{-1} L^{-2}\)

If surface tension (\(S\)), Moment of Inertia (\(I\)) and Plank's constant (\(h\)), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:
1. \( S^{3 / 2} I^{1 / 2} h^0 \)
2. \( S^{1 / 2} I^{1 / 2} h^{-1} \)
3. \( S^{1 / 2} I^{3 / 2} h^{-1} \)
4. \( S^{1 / 2} I^{1 / 2} h^0\)

In the formula \(X=5YZ^2\), \(X\) and \(Z\) have dimensions of capacitance and magnetic field, respectively. What are the dimensions of \(Y\) in SI units?
1. \(\left[M^{-3} L^{-2} T^8 A^4\right]\)
2. \(\left[M^{-2} L^{-2} T^6 A^3\right]\)
3. \(\left[M^{-1} L^{-2} T^4 A^2\right]\)
4. \(\left[M^{-2} L^0 T^{-4} A^{-2}\right]\)

Which of the following combinations has the dimension of electrical resistance (\(\varepsilon_0\) is the permittivity of the vacuum and \(\mu_0\) is the permeability of vacuum)?
1. \(\sqrt{\frac{\varepsilon_0}{\mu_0}}\)
2. \(\frac{\varepsilon_0}{\mu_0}\)
3. \(\frac{\mu_0}{\varepsilon_0}\)
4. \(\sqrt{\frac{\mu_0}{\varepsilon_0}}\)

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. \(\left[FA^2 v^{-2}\right] \)