Who among the following Peshwas signed the Treaty of Bassein with the British East India Company?

Correct option is A

The correct answer is (a) Baji Rao II.
Baji Rao II, the last Peshwa of the Maratha Empire, signed the Treaty of Bassein with the British East India Company in December 1802. This treaty was a significant turning point in Indian history as it marked the effective end of the Maratha Empire's independence and led to the establishment of British supremacy in India.
Background of the Treaty of Bassein:
 After suffering a defeat at the Battle of Poona against the Holkar ruler, Baji Rao II sought the support of the British to regain his position and authority. The Treaty of Bassein was the result, under which Baji Rao II accepted the protection of the British East India Company and agreed to certain terms that substantially reduced the sovereignty of the Maratha state.
 The treaty stipulated that Baji Rao II would have a British force permanently stationed in his territory and he would pay for its maintenance. It also required that he cede territories for the maintenance of this force and agree to conduct his foreign affairs in consultation with the British.
The signing of the Treaty of Bassein essentially made Baji Rao II a subsidiary ally of the British, and it precipitated the Second Anglo-Maratha War (1803-1805), as other Maratha leaders such as the Scindias, the Bhonsles, and the Holkars opposed the agreement and the resultant shift in power towards British dominance.