Step 1: Build the clinical picture. An 18-year-old male presents with hepatosplenomegaly, lymphadenopathy (LN+), anaemia (Hb 7 g/dL), a markedly raised white cell count (WBC 50,000/\(\mu\)L), and thrombocytopenia (platelets 30,000/\(\mu\)L) manifesting as petechiae and purpura, along with fatigue. The combination of leucocytosis with anaemia and thrombocytopenia (i.e. marrow failure of the other two lineages) plus organomegaly and lymph node enlargement in a young patient is classic for Acute Lymphoblastic Leukaemia (ALL), the commonest acute leukaemia in this age group, with prominent lymphadenopathy and hepatosplenomegaly.
Step 2: Choose the management. The backbone of ALL induction therapy is a corticosteroid (Prednisolone) plus Vincristine/Vinblastine, with additional agents such as L-asparaginase and an anthracycline. Among the options given, Prednisolone + Vinblastine (option C) represents this chemotherapy induction approach and is the most appropriate management of the underlying leukaemia.
Step 3: Why the other options are wrong. Cytarabine + ... (option A) is the backbone for Acute Myeloid Leukaemia (the "7+3" cytarabine-anthracycline regimen), which does not fit this picture of lymphadenopathy in a young patient. IVIG x 2 days (option B) treats immune (idiopathic) thrombocytopenic purpura - but ITP causes isolated thrombocytopenia, NOT pancytopenia with high WBC, organomegaly, and lymphadenopathy, so it does not address this disease. Radiotherapy to lymph nodes (option D) is a localised treatment used in lymphomas; it cannot treat a systemic leukaemia with marrow involvement and circulating blasts.
Final answer: Option C - Prednisolone + Vinblastine.