The princely state of Mysore was ruled by the:

Wodeyar dynasty
Hoysala dynasty
Chalukya dynasty
Rashtrakuta dynasty

The correct answer is A) Wodeyar dynasty.

The Wodeyar dynasty was a Hindu dynasty that ruled the princely state of Mysore in southern India from the 14th century to 1947. The dynasty was founded by Yaduraya Wodeyar, who was a feudatory of the Hoysala dynasty. The Wodeyars reached the height of their power under the rule of Tipu Sultan, who was a military genius and a patron of the arts. Tipu Sultan was defeated by the British in 1799, and the Wodeyars were restored to power. The dynasty continued to rule Mysore until it was merged with the Indian Union in 1947.

The Hoysala dynasty was a Hindu dynasty that ruled the Deccan Plateau in southern India from the 11th to the 14th centuries. The dynasty was founded by Vishnuvardhana, who was a feudatory of the Chalukya dynasty. The Hoysalas reached the height of their power under the rule of Ballala III, who was a great military leader and a patron of the arts. The Hoysalas were defeated by the Delhi Sultanate in the 13th century, and the dynasty declined thereafter.

The Chalukya dynasty was a Hindu dynasty that ruled the Deccan Plateau in southern India from the 6th to the 12th centuries. The dynasty was founded by Pulakesin I, who was a feudatory of the Kadamba dynasty. The Chalukyas reached the height of their power under the rule of Vikramaditya II, who was a great military leader and a patron of the arts. The Chalukyas were defeated by the Chola dynasty in the 12th century, and the dynasty declined thereafter.

The Rashtrakuta dynasty was a Hindu dynasty that ruled the Deccan Plateau in southern India from the 8th to the 10th centuries. The dynasty was founded by Dantidurga, who was a feudatory of the Chalukya dynasty. The Rashtrakutas reached the height of their power under the rule of Krishna I, who was a great military leader and a patron of the arts. The Rashtrakutas were defeated by the Chalukyas in the 10th century, and the dynasty declined thereafter.