Final answer:
The vestibulocochlear nerve is the one that does not contain both motor and sensory fibers among the options provided; it is exclusively a sensory nerve for balance and hearing.
Step-by-step explanation:
The human body has 12 cranial nerves, which are essential for transmitting information between the brain and various parts of the head and neck. Of the options given, nerves that carry both motor and sensory functions include the oculomotor, trigeminal, facial, and glossopharyngeal, but not the vestibulocochlear nerve, which is a sensory nerve. This nerve is involved in hearing and balance and does not carry motor fibers. The oculomotor nerve controls certain eye movements and eyelid opening, the trigeminal nerve conveys somatic sensation from the face, the facial nerve is responsible for facial expressions and taste, and the glossopharyngeal nerve is involved in taste and swallowing.