Step 1: Define the gag reflex. The gag (pharyngeal) reflex is a protective reflex in which touching the posterior pharyngeal wall, soft palate or base of tongue triggers elevation and constriction of the pharynx to prevent aspiration.
Step 2: Identify the afferent (sensory) limb. The sensory information from the posterior pharyngeal wall and posterior third of the tongue travels through the glossopharyngeal nerve (cranial nerve IX).
Step 3: Identify the efferent (motor) limb. The motor response - contraction of the pharyngeal constrictors and elevation of the palate - is carried mainly by the vagus nerve (cranial nerve X) via the pharyngeal plexus.
Step 4: Combine to answer. Because the reflex arc is IX (afferent) and X (efferent), an injury to cranial nerves 9 and 10 abolishes the gag reflex. Hence option B is correct.
Step 5: Exclude the distractors.
- 5 and 10: CN V (trigeminal) carries general sensation from the anterior tongue/face, not the gag arc.
- 10 and 12: CN XII (hypoglossal) is pure tongue motor, not part of the gag reflex.
- 7 and 9: CN VII (facial) supplies facial muscles and anterior-two-thirds taste, not the pharyngeal reflex.
Final answer: B. 9 and 10.