## **Core Concept**
The question tests knowledge of cranial nerve functions, specifically those controlling extraocular muscle movements. The deviation of the eyeball described as "down and out" is characteristic of a particular cranial nerve palsy. The cranial nerves responsible for eye movements are III (oculomotor), IV (trochlear), and VI (abducens).

## **Why the Correct Answer is Right**
The correct answer, **C. III (Oculomotor nerve)**, is right because the oculomotor nerve controls several extraocular muscles: the medial rectus, superior rectus, inferior rectus, and inferior oblique, as well as the levator palpebrae superioris. When the oculomotor nerve is paralyzed, the unopposed action of the lateral rectus (innervated by the abducens nerve) and the superior oblique (innervated by the trochlear nerve) muscles results in the eyeball deviating "down and out." This is because the lateral rectus muscle abducts the eye (pulls it outward), and without the opposing action of the medial rectus, the eye moves outward. The superior oblique muscle intorts and depresses the eye, contributing to the "down" component.

## **Why Each Wrong Option is Incorrect**
- **Option A: I (Olfactory nerve)**: This nerve is responsible for transmitting sensory information related to smell from the nose to the brain and has no role in controlling eye movements.
- **Option B: IV (Trochlear nerve)**: This nerve innervates the superior oblique muscle, which primarily intorts, depresses, and abducts the eyeball. Its paralysis leads to difficulty moving the eye downward when adducted but does not cause a "down and out" deviation.
- **Option D: VI (Abducens nerve)**: This nerve controls the lateral rectus muscle, which abducts the eyeball. Paralysis of the abducens nerve results in an inability to abduct the eye, leading to an "in" deviation, not "down and out."

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that a "down and out" position of the eyeball is indicative of a third cranial nerve (oculomotor) palsy. This condition can be due to various causes, including diabetes mellitus, hypertension, and aneurysms of the posterior communicating artery, which can compress the oculomotor nerve.

## **Correct Answer: C. III (Oculomotor nerve)**