Match column - I with column - II $$ \begin{array}{|l|l|} \hline \multicolumn{1}{|c|} {\text { Column - I }} & \multicolumn{1}{|c|} {\text { Column - II }} \\ \hline \text { (1) capacitance } & \text { (a) } \mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1} \\ \hline \text { (2) Electricfield } & \text { (b) } \mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \\ \hline \text { (3) planck's constant } & \text { (c) } \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2} \\ \hline \text { (4) Angular momentum } & \text { (d) } \mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \\ \hline \end{array} $$ (a) \(a, c, b, d\) (b) \(c, a, d, b\) (c) \(c, a, b, d\) (d) \(a, b, d, c\)

We need to recall the dimensional formulas for each quantity: (1) Capacitance (C): \(\mathrm{[C] = \displaystyle\frac{Q}{V}}\) (2) Electric field (E): \(\mathrm{[E] = \displaystyle\frac{F}{q}}\) (3) Planck's constant (h): \(\mathrm{[h] = E \cdot T}\) (4) Angular momentum (L): \(\mathrm{[L] = I \cdot \omega}\)

First, we need to find the dimension of each quantity in terms of mass (M), length (L), time (T), and current (A) using the above formulas. (1) Capacitance (C): Using the formula, \(\displaystyle\frac{Q}{V} \rightarrow \frac{\mathrm{[ML^2T^{-3}A^{-1}]}{\mathrm{[LT^{-1}A^{-1}]}}\), we get \(\mathrm{[C] = M^{-1}L^{-2}T^{4}A^{2}}\) (2) Electric field (E): Using the formula, \(\displaystyle\frac{F}{q} \rightarrow \frac{\mathrm{[MLT^{-2}]}{\mathrm{[IT]}}\), we get \(\mathrm{[E] = M^{1}L^{1}T^{-3}A^{-1}}\) (3) Planck's constant (h): Using the formula, \(ET \rightarrow \mathrm{[ML^2T^{-2}]}\cdot\mathrm{[T]}\), we get \(\mathrm{[h] = M^{1}L^{2}T^{-1}}\) (4) Angular momentum (L): Using the formula, \(I\omega \rightarrow \mathrm{[ML^2]}\cdot\mathrm{[T^{-1}]}\), we get \(\mathrm{[L] = M^{1}L^{2}T^{-1}}\)

Now, we need to match the dimension of each quantity `(1, 2, 3, 4)` with its respective dimensional formula `(a, b, c, d)` as follows: (1) Capacitance (C): \(\mathrm{[C] = M^{-1}L^{-2}T^{4}A^{2}}\) (c) (2) Electric field (E): \(\mathrm{[E] = M^{1}L^{1}T^{-3}A^{-1}}\) (a) (3) Planck's constant (h): \(\mathrm{[h] = M^{1}L^{2}T^{-1}}\) (d) (4) Angular momentum (L): \(\mathrm{[L] = M^{1}L^{2}T^{-1}}\) (b) So the correct matching is: (1) Capacitance → (c), (2) Electric field → (a), (3) Planck's constant → (d), and (4) Angular momentum → (b). Therefore, the correct answer is the option (b) \(c, a, d, b\).