Match List-I with List-II regarding the equivalent induced emf...

The induced emf across an equivalent inductance $L_{eq}$ is given by $E = L_{eq} \dfrac{dI}{dt}$.

(A) For two inductors in series, $L_{eq} = L + L = 2L$.
Induced emf = $2L \dfrac{dI}{dt}$. (Matches with II)

(B) For two inductors in parallel, $L_{eq} = \dfrac{L \times L}{L + L} = \dfrac{L}{2}$.
Induced emf = $\dfrac{1}{2}L \dfrac{dI}{dt}$. (Matches with I)

(C) For three inductors in parallel, $\dfrac{1}{L_{eq}} = \dfrac{1}{L} + \dfrac{1}{L} + \dfrac{1}{L} = \dfrac{3}{L} \Rightarrow L_{eq} = \dfrac{L}{3}$.
Induced emf = $\dfrac{1}{3}L \dfrac{dI}{dt}$. (Matches with IV)

(D) For two inductors in parallel connected in series with a third, $L_{eq} = \dfrac{L}{2} + L = \dfrac{3L}{2}$.
Induced emf = $\dfrac{3}{2}L \dfrac{dI}{dt}$. (Matches with III)

Therefore, the correct matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).

Answer: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)