Start from the histology buzzword. A granuloma whose center has soft, structureless caseous necrosis, ringed by epithelioid cells and Langhans giant cells, is the signature of tuberculosis. Add the clinical frame, an $11$-year-old with weeks of cough and cervical node enlargement (scrofula), and TB becomes the obvious read.
Run the differentials by their granuloma type. Sarcoidosis makes tidy non-caseating granulomas with no necrosis, so the presence of caseation excludes it. Leprosy granulomas track along nerves and carry acid-fast bacilli, while tertiary syphilis forms plasma-cell-laden gummas with obliterative endarteritis. None of these show the central caseation seen here.
Hence the diagnosis is $TB$, option (c).