**Core Concept**
The parasympathetic nervous system is a branch of the autonomic nervous system that promotes rest and digestion. It is responsible for various involuntary functions, including heart rate, digestion, and pupillary constriction. In the cranial nerves, parasympathetic outflow is carried by specific nerves that have preganglionic neurons.

**Why the Correct Answer is Right**
The correct answer is the cranial nerve that does not have parasympathetic outflow. The parasympathetic nervous system is carried by the oculomotor nerve (III), the facial nerve (VII), the glossopharyngeal nerve (IX), and the vagus nerve (X). These nerves have preganglionic neurons that synapse in peripheral ganglia, allowing for parasympathetic functions.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the oculomotor nerve (III) carries parasympathetic outflow to the ciliary ganglion, which stimulates miosis and accommodation.
* **Option B:** This option is incorrect because the facial nerve (VII) carries parasympathetic outflow to the submandibular ganglion, which stimulates salivation and lacrimation.
* **Option C:** This option is incorrect because the glossopharyngeal nerve (IX) carries parasympathetic outflow to the otic ganglion, which stimulates salivation.
* **Option D:** This option is incorrect because the trigeminal nerve (V) does not carry parasympathetic outflow; it is a sensory nerve with some motor functions.

**Clinical Pearl / High-Yield Fact**
The cranial nerves that carry parasympathetic outflow are often remembered using the mnemonic "O-F-G-V": oculomotor (III), facial (VII), glossopharyngeal (IX), and vagus (X).

**Correct Answer:** D. Trigeminal nerve.