To match List-I with List-II correctly, we need to understand what happens in each phase of the cell cycle:

1. G$_1$ Phase: This is the first phase in interphase. During this phase, cells are metabolically active and proliferate. It fits for "Cells are metabolically active and proliferate".

2. S Phase: This is the phase where DNA replication takes place. It fits for "DNA replication takes place".

3. G$_2$ Phase: During this phase, the cell continues to grow and proteins are synthesized in preparation for mitosis. It fits for "Proteins are synthesized".

4. G$_0$ Phase: This is a resting or quiescent stage where cells remain metabolically active but do not proliferate. It fits for "Quiescent stage with metabolically active cells".

Now, let's match the items:

(A) Cells are metabolically active and proliferate - matches with G$_1$ phase (II)

(B) DNA replication takes place - matches with S phase (IV)

(C) Proteins are synthesized - matches with G$_2$ phase (I)

(D) Quiescent stage with metabolically active cells - matches with G$_0$ phase (III)

Therefore, the correct matching is:

(A) - (II)

(B) - (IV)

(C) - (I)

(D) - (III)

The correct answer is:

Option D

A-II, B-IV, C-I, D-III