The correct answer is: B) Subsidiary Alliance system.
The Subsidiary Alliance system was a treaty system between the British East India Company and Indian princely states. Under the system, the princely states agreed to cede control of their foreign affairs and military to the British, in exchange for British protection. The Wodeyars of Mysore were one of the many Indian princely states that signed a Subsidiary Alliance with the British.
The Subsidiary Alliance system was a controversial system, with some historians arguing that it was a form of British imperialism, while others argue that it was a necessary evil to maintain stability in India. Regardless of the interpretation, the Subsidiary Alliance system had a profound impact on the history of India.
Option A is incorrect because the princely state of Mysore was not under direct British rule. The Wodeyars retained control of their internal affairs under the Subsidiary Alliance system.
Option C is incorrect because the princely state of Mysore was not independent. The Wodeyars were subject to British control under the Subsidiary Alliance system.
Option D is incorrect because the princely state of Mysore was not under French control. The Wodeyars were allied with the French against the British in the early 18th century, but they were never under French control.