Step 1: Understanding the Concept:
The eukaryotic cell cycle partitions interphase into Gap 1 ($ ext{G}_1$), Synthesis (S), and Gap 2 ($ ext{G}_2$) phases prior to mitosis (M).
Key Formula or Approach:
\[ \text{Cell Cycle: } \text{G}_1 \longrightarrow \text{S (DNA Replication: } 2C \rightarrow 4C) \longrightarrow \text{G}_2 \longrightarrow \text{M (Mitosis)} \]
Step 2: Detailed Explanation:
During the eukaryotic cell cycle:
1. S Phase (Synthesis Phase): The entire nuclear genomic DNA is semi-conservatively replicated, doubling the nuclear DNA content from $2C$ to $4C$ while maintaining chromosome number ($2n$). Centrosome duplication also initiates in the cytoplasm during S phase.
2. G1 Phase: Biosynthesis of enzymes and RNA for cell growth.
3. G2 Phase: Synthesis of tubulin and proteins for mitotic spindle formation.
4. M Phase: Chromosome segregation and cytokinesis.
Step 3: Final Answer:
Hence, nuclear DNA replication occurs in S phase, corresponding to option (C).