The princely states within the Madras Presidency were under the indirect control of the:

Mughal Empire
British East India Company
French East India Company
Maratha Empire

The correct answer is: b) British East India Company.

The Madras Presidency was a British colonial administrative division in southern India. It was established in 1639 by the British East India Company, and it existed until 1947, when India gained independence. The Madras Presidency included the present-day states of Tamil Nadu, Andhra Pradesh, Karnataka, and Kerala.

The princely states within the Madras Presidency were under the indirect control of the British East India Company. This meant that the Company had control over the foreign affairs and defense of the states, but the internal affairs of the states were left to the rulers. The Company appointed Residents to the princely states to oversee the Company’s interests.

The Mughal Empire was a Muslim empire that ruled over most of India from the 16th to the 18th centuries. The French East India Company was a trading company that was founded in 1664 by Louis XIV of France. The Maratha Empire was a Hindu empire that ruled over much of central and western India from the 17th to the 19th centuries.