Final answer:
The unrelated pair is e) Smooth endoplasmic reticulum: ribosomes, as the smooth endoplasmic reticulum does not have ribosomes on its surface, unlike the rough endoplasmic reticulum.
Step-by-step explanation:
The pair among the options that is unrelated is e) Smooth endoplasmic reticulum: ribosomes. This is because the smooth endoplasmic reticulum (SER) does not have ribosomes on its surface, which is a characteristic of the rough endoplasmic reticulum (RER).
The nucleus is responsible for storing hereditary material and is thus related to heredity. The endoplasmic reticulum, particularly the RER, is studded with ribosomes and is involved in macromolecule synthesis, including protein synthesis. The mitochondrion is the site of cellular respiration, where ATP is generated, and is often referred to as the power plant of the cell. Food vesicles are related to endocytosis as they are used to engulf and transport materials into the cell.
The SER, however, has functions distinct from the RER. It is involved in the synthesis of lipids, metabolism of carbohydrates, detoxification of drugs and poisons, and storage of calcium. Ribosomes, on the other hand, are cell structures responsible for protein synthesis and are found either floating freely in the cytoplasm or attached to the RER, but not associated with the SER.