Final answer:
The trigeminal nerve is responsible for the sensation of pain and heat from hot peppers, which stimulates its free nerve endings. The correct option is C.
Step-by-step explanation:
Hot pepper stimulates the free nerve endings of the trigeminal nerve (option c), not the taste buds of the tongue. The trigeminal nerve is responsible for somatosensation in the face, including sensations such as pain and temperature, which are what's triggered when eating hot peppers.
The facial nerve (option a) is involved in taste in the anterior two-thirds of the tongue, the glossopharyngeal nerve (option b) in the posterior third, and the vagus nerve in the extreme posterior, but it's the trigeminal nerve that carries the sensation of the spicy heat from capsaicin found in hot peppers.