Step 1: Identify the clinical entity. A teenage boy (classically 10-25 years, almost exclusively male) presenting with a reddish nasal/nasopharyngeal mass and recurrent, often profuse epistaxis is the textbook picture of a Juvenile Nasopharyngeal Angiofibroma (JNA). It is a benign but locally aggressive, highly vascular tumour arising near the sphenopalatine foramen.
Step 2: Why imaging is needed and what we want from it. JNA is intensely vascular, so blind biopsy is contraindicated because of the risk of torrential bleeding. Diagnosis is therefore made by imaging. The imaging must demonstrate (a) the highly vascular nature of the lesion (intense enhancement), (b) its exact extent into the pterygopalatine fossa, infratemporal fossa, orbit and skull base, and (c) the characteristic Holman-Miller sign (anterior bowing of the posterior wall of the maxillary antrum).
Step 3: Why option B is correct. Contrast-enhanced CT (CT with contrast) is the investigation of choice: a vascular tumour shows brisk, intense post-contrast enhancement, confirming the diagnosis, and CT best delineates bony erosion and extent for surgical planning. (Contrast-enhanced MRI is an excellent complement for soft-tissue/intracranial extent, but among the options given CECT is the answer.)
Step 4: Why the other options are wrong. (A) Plain CT shows the mass and bone changes but does NOT demonstrate the diagnostic intense vascular enhancement, so it is inferior to contrast CT. (C) X Ray Caldwell view (an occipitofrontal plain radiograph for frontal/ethmoid sinuses) gives no vascular information and cannot delineate skull-base extent. (D) X Ray with Pierre view is not a standard investigation for this lesion and provides no soft-tissue or vascular detail.
Final answer: B. CT with contrast.