Step 1: Understanding the Concept:
Identifying the authors of famous classical Sanskrit plays is an essential part of Sahitya studies. These plays represent the 'Nataka' and 'Prakarana' forms.
Step 3: Detailed Explanation:
1. Abhijnanashakuntalam: This is the masterpiece of Kalidasa.
It is considered the greatest play in Sanskrit literature, retelling the love story of King Dushyanta and Shakuntala.
Matching: A-IV.
2. Uttararamacharitam: This is authored by Bhavabhuti.
It is a tragic drama focused on the later life of Lord Rama after his separation from Sita. Bhavabhuti is the master of Karuna Rasa.
Matching: B-III.
3. Venisamharam: This play is written by Bhattanarayana.
It deals with an episode from the Mahabharata, specifically the braiding of Draupadi's hair after the death of Duhshasana. It is a Vira-Rasa dominated play.
Matching: C-I.
4. Mricchakatikam (The Little Clay Cart): This social play is written by Shudraka.
It is a 'Prakarana' involving the love between Charudatta and Vasantasena, noted for its realistic depiction of ancient city life.
Matching: D-II.
Resulting match: A-IV, B-III, C-I, D-II.
Step 4: Final Answer:
Matching the authors to their works: A-IV, B-III, C-I, D-II. Thus, Option (B) is correct.