Step 1: Recall the basic make-up of a pharyngeal (branchial) arch. Each arch is a core of mesoderm covered externally by ectoderm and lined internally by endoderm. Within this core, muscular and skeletal elements, aortic arch vessels and nerve networks develop.
Step 2: Neural crest cells are bilateral strips of cells that arise from the ectoderm at the margins of the neural tube. They migrate widely and form the peripheral nervous system, including the sensory, sympathetic and parasympathetic ganglia and the neural tissue that populates the pharyngeal arches.
Step 3: The nerve elements and much of the connective tissue of the arches come from cranial neural crest cells that migrate dorsolaterally into the arches as ectomesenchyme. Hence the nerves of the branchial arch are of neural crest origin, making option c correct.
Step 4: Why the distractors are wrong: mesoderm gives the muscular and some skeletal/vascular components, not the nerves; endoderm forms the epithelial lining and pouch derivatives; "neuroectoderm" forms the central neural tube itself, but the arch nerves specifically derive from the neural crest population, not the neural tube proper.