Final answer:
The optic nerve (CN II) is the purely sensory cranial nerve listed, responsible for vision. The facial nerve (CN VII) is involved in taste and facial expressions, while the oculomotor nerve (CN III) controls eye movements and pupil constriction.
Step-by-step explanation:
The cranial nerve that is purely sensory among the ones listed is the optic nerve (CN II). Cranial nerves like the trigeminal (CN V), accessory (CN XI), and hypoglossal (CN XII) are either mixed or primarily motor in their function. The vagus nerve (CN X) is also not purely sensory as it also contains motor and parasympathetic fibers.
Regarding the specific functions of other cranial nerves, the facial nerve (CN VII) carries taste from the anterior two-thirds of the tongue and also controls muscles used in facial expressions. The glossopharyngeal nerve (CN IX) carries taste from the posterior one-third of the tongue and helps in swallowing. The oculomotor nerve (CN III) contains preganglionic parasympathetic fibers that innervate muscles controlling pupil constriction and lens shape.