Nasopharyngeal carcinoma: This is the correct answer. Nasopharyngeal carcinoma (NPC) is a malignancy that commonly presents with painless cervical lymphadenopathy, which is often unilateral. The patient's conductive hearing loss (associated with a dull tympanic membrane) and decreased mobility of the soft palate are indicative of eustachian tube dysfunction or involvement of the nasopharynx by the tumor. NPC is common in older males, especially in certain geographic regions, and can also lead to symptoms like ear fullness or otalgia.
Adenoid cystic cancer: While adenoid cystic carcinoma can affect the head and neck region, it is less likely to present with symptoms like conductive hearing loss or soft palate dysfunction. This type of cancer usually causes symptoms related to salivary glands or nasal cavity rather than the specific findings described in this case.
Juvenile nasopharyngeal angiofibroma: This condition typically affects adolescent males and presents with epistaxis, nasal obstruction, and potentially nasal deformity. It is less likely to cause the lymphadenopathy and ear-related symptoms described here.
Quinsy: Quinsy, or peritonsillar abscess, presents with severe throat pain, fever, and difficulty swallowing, but it would not typically cause conductive hearing loss or soft palate dysfunction.
Thus, the correct answer is Nasopharyngeal carcinoma (1), as it fits the clinical findings of lymphadenopathy, hearing loss, and soft palate involvement.