The rulers of Sandur state were patrons of:

Music and dance
Ayurvedic medicine
Temple architecture
Military innovation

The correct answer is: a) Music and dance.

The rulers of Sandur state were patrons of music and dance. They built many temples and palaces, and they also supported the arts. The Sandur rulers were known for their love of music and dance, and they often held festivals and competitions to showcase the talents of their subjects.

Option b) is incorrect because Ayurvedic medicine is a system of traditional medicine that originated in India. It is based on the belief that health is a state of balance between the mind, body, and spirit. Ayurvedic medicine uses a variety of treatments, including herbs, massage, and diet, to restore balance and promote health.

Option c) is incorrect because temple architecture is the design and construction of temples. Temples are religious buildings that are dedicated to a particular deity or deities. They are often very ornate and decorated, and they can be found in many different cultures around the world.

Option d) is incorrect because military innovation is the development of new technologies and tactics for use in warfare. Military innovation has played a major role in the history of warfare, and it has led to the development of new weapons, armor, and strategies.