The correct answer to the question is option 1, Baji Rao II. The Treaty of Bassein was signed on December 31, 1802, by Baji Rao II, who was a Maratha statesman.

Option 2, Vithuji Holkar, is incorrect. Vithuji Holkar was a prominent ruler of the Holkar dynasty in the Maratha Empire, but he did not sign the Treaty of Bassein.

Option 3, Daulat Rao Sindhia, is also incorrect. Daulat Rao Sindhia was another powerful Maratha statesman during that time, but he was not the one who signed the Treaty of Bassein.

Option 4, Madhava Rao Narayan, is also incorrect. Madhava Rao Narayan was a minister in the Peshwa administration, but he did not sign the Treaty of Bassein.

Therefore, the correct answer is option 1, Baji Rao II, who signed the Treaty of Bassein on December 31, 1802.