Option 1: Ibn-Batuta - Ibn-Batuta was a Moroccan scholar and explorer. However, there is no evidence or historical record to suggest that he translated the Mahabharatha into Persian.

Option 2: Abul Fazal - Abul Fazal was a courtier and historian in the court of Akbar. While he was involved in the translation and compilation of various texts, there is no evidence to suggest that he translated the Mahabharatha into Persian.

Option 3: Babar - Babar was the first Mughal emperor of India and the founder of the Mughal dynasty. While he was a great patron of art and literature, there is no historical record to suggest that he translated the Mahabharatha into Persian.

Option 4: Badauni - Badauni, also known as Abdul Qadir Badauni, was a prominent historian in the Mughal court during the reigns of Akbar and Jahangir. He is credited with translating the Mahabharatha into Persian, making it accessible to a wider audience. This option is the correct answer.

In conclusion, Badauni is the one who translated the Mahabharatha into Persian.