Not a branch of external carotid artery:

Ans: D (Ophthalmic) Ref: Gray's Anatomy, 40th edition, pg. 399 Explanation:Common carotid artery lies within the carotid sheath of deep cervical fascia, together with the internal jugular vein and vagus nerve.At the level of the upper border of the thyroid cartilage (C4), the common carotid artery bifurcates into external and internal carotid arteries.The external carotid artery gives off:Superior thyroidLingualPosterior auricular arteryFacialOccipitalAscending pharyngeal--only medial branchTerminal branches, maxillary and superficial temporal arteries.Mneumonic-Sister Louis Powdered Face Often Attract Medical Students (SLPFOAMS).* External carotid artery branches anastomose with branches of the internal carotid arteries on the scalp, forehead, and face, and in the orbit, nasopharynx and nasal cavity, and with branches of the subclavian artery in the pharynx, larynx and thyroid glands.