The correct answer is A) Chalukyas of Badami.
The Chalukyas of Badami were a dynasty that ruled parts of Telangana in the early medieval period. They were known for their patronage of art and architecture. The Chalukyas built many temples and other monuments in Telangana, including the Virupaksha Temple in Pattadakal and the Badami Caves.
The Rashtrakutas were another dynasty that ruled parts of Telangana in the early medieval period. They were not as well-known for their patronage of art and architecture as the Chalukyas. However, they did build some important temples in Telangana, including the Kailasa Temple in Ellora.
The Pallavas and Cholas were dynasties that ruled parts of southern India in the early medieval period. They did not rule any part of Telangana. However, they were both known for their patronage of art and architecture. The Pallavas built many temples in Tamil Nadu, including the Shore Temple in Mahabalipuram. The Cholas built many temples in Tamil Nadu and Sri Lanka, including the Brihadeeswarar Temple in Thanjavur.
In conclusion, the Chalukyas of Badami were the dynasty that ruled parts of Telangana in the early medieval period and were known for their patronage of art and architecture.