To solve this problem, we need to match the stages of the cell cycle in List I with their corresponding descriptions in List II. Let's analyze each stage:$\newline \bullet\$A. M phase:$\newline$The M phase, or mitotic phase, involves the process of cell division where one cell divides into two daughter cells.$\newline$This is known as equational division because the chromosome number remains the same in the daughter cells as in the parent cell.$\newline$Therefore, M phase matches with IV. Equational division.$\newline \bullet\$B. G$_2$ Phase:$\newline$The G$_2$ phase is the second gap phase, following DNA synthesis (S phase) and preceding mitosis.$\newline$During this phase, the cell synthesizes proteins and continues to grow, preparing for mitosis.$\newline$Therefore, G$_2$ phase matches with I. Proteins are synthesized.$\newline \bullet\$C. Quiescent stage (G$_0$ phase):$\newline$The quiescent stage is a resting phase where the cell is not actively preparing to divide.$\newline$Cells in this phase are in an inactive state in terms of cell division.$\newline$Therefore, the quiescent stage matches with II. Inactive phase.$\newline \bullet\$D. G$_1$ Phase:$\newline$The G$_1$ phase is the first gap phase, occurring after mitosis and before the S phase.$\newline$It is the interval between mitosis and the initiation of DNA replication.$\newline$Therefore, G$_1$ phase matches with III. Interval between mitosis and initiation of DNA replication.$\newline\newline$Now, let's match the items from List I with List II:$\newline A \rightarrow IV, B \rightarrow I, C \rightarrow II, D \rightarrow III \newline\textbf{This corresponds to Option 3}.$