The correct answer is (b). The Treaty of Bassein was signed between the British East India Company and the Maratha Empire in 1802. The treaty was signed by the British representative, General Gerard Lake, and the Maratha representative, Nana Fadnavis. The treaty marked the end of the Second Anglo-Maratha War and the beginning of the British dominance in India.
The treaty granted the British control over a number of Maratha territories, including Bassein, Surat, and Ahmedabad. The Maratha Empire was also forced to pay a large indemnity to the British. The treaty was a major setback for the Maratha Empire and led to its decline.
The other options are incorrect. Option (a) is incorrect because the Treaty of Bassein was signed in 1802, while Bajirao I died in 1740. Option (c) is incorrect because the French were not involved in the Second Anglo-Maratha War. Option (d) is incorrect because the Dutch were not a major power in India at the time of the treaty.