Diagnosis-driven approach. Before choosing a drug, name the disease. The blood counts tell a clear story: high WBC (50,000) with simultaneous anaemia (Hb 7) and thrombocytopenia (platelets 30,000, hence the petechiae and purpura). When one lineage is grossly elevated while the other two are suppressed in a young person, the marrow is being crowded out by a proliferating clone - acute leukaemia. The added findings of lymphadenopathy and hepatosplenomegaly in an 18-year-old point specifically to Acute Lymphoblastic Leukaemia, where lymph node and visceral infiltration are typical.
Management then follows directly from the diagnosis. ALL induction is built on a steroid plus a vinca alkaloid (with asparaginase and an anthracycline). Of the four choices, only Prednisolone + Vinblastine matches this lymphoid-leukaemia induction backbone.
Ruling out the distractors quickly:
• Cytarabine-based therapy belongs to AML, not ALL.
• IVIG is reserved for immune thrombocytopenic purpura, which shows isolated low platelets - not a high WBC with organomegaly.
• Nodal radiotherapy is a focal treatment for lymphoma and is useless against marrow-based, blood-borne leukaemia.
So the most appropriate management is Prednisolone + Vinblastine (Option C).