In a eukaryotic cell glycolysis takes place within the mitochondria, whereas in a prokaryotic cell in the cytoplasm

Answer

**Step-by-Step Solution:**

1. **Understanding the Statement**: The statement claims that glycolysis occurs in the mitochondria of eukaryotic cells and in the cytoplasm of prokaryotic cells.

2. **Identifying the Location of Glycolysis**: Glycolysis is a metabolic pathway that breaks down glucose to produce energy. It is important to note that glycolysis occurs in the cytoplasm of both eukaryotic and prokaryotic cells.

3. **Analyzing Eukaryotic Cells**: In eukaryotic cells, while glycolysis occurs in the cytoplasm, the subsequent processes of aerobic respiration, such as the Krebs cycle and oxidative phosphorylation, occur in the mitochondria.

4. **Analyzing Prokaryotic Cells**: Prokaryotic cells do not have membrane-bound organelles, including mitochondria. Therefore, all metabolic processes, including glycolysis, occur in the cytoplasm.

5. **Conclusion**: Since glycolysis occurs in the cytoplasm for both eukaryotic and prokaryotic cells, the original statement is false.

6. **Final Statement**: The statement "In a eukaryotic cell glycolysis takes place within the mitochondria, whereas in a prokaryotic cell in the cytoplasm" is false.

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