Step 1: Aim.
Name the playwright whose play has Duryodhana as its central character.
Step 2: Core fact.
'Urubhangam' by Bhasa is based on the last day of the Kurukshetra war. The dying Duryodhana is shown as brave, proud and sad. This tragic view of Duryodhana is unusual and makes the play famous.
Step 3: Test each author.
Kalidasa: romantic plays on Shakuntala and Malavika, so no.
Bhasa: Urubhangam, so yes.
Sudraka: a social drama of love and politics, so no.
Bhavabhuti: plays on Rama's story and love, so no.
Step 4: Answer.
Bhasa is the only match among the four names.
Always read the options slowly and match each name with a clear fact you know about it. Names that sound close can belong to very different traditions, so do not guess from the sound of a name alone. Writing the key fact next to each name, as done above, makes the elimination quick and safe. This habit also helps in similar questions on theatre personalities, plays and groups.
Final Answer:
Bhasa is correct, so the answer is option 2.
\[ \boxed{\text{Option 2}} \]