Which of the following does NOT occur in the mitochondria of a cell?

The pentose phosphate pathway, also known as the pentose phosphate shunt, primarily occurs in the cytoplasm of the cell rather than in the mitochondria. This pathway is crucial for generating NADPH and ribose-5-phosphate, which are vital for anabolic reactions and nucleotide synthesis respectively.

In contrast, beta oxidation of fatty acids occurs in the mitochondria, where fatty acids are broken down to generate acetyl-CoA, which then enters the citric acid cycle. The electron transport chain is also located in the mitochondrial inner membrane, where it plays a key role in cellular respiration by producing ATP through oxidative phosphorylation. Additionally, the citric acid cycle (Krebs cycle) takes place in the mitochondrial matrix, contributing to the production of energy carriers like NADH and FADH2.

Therefore, since the pentose phosphate pathway does not take place within the mitochondria, it is the correct answer to indicate what does not occur in that organelle.