The correct answer is option 4: Kavery River. The Krishna Raja Sagara Dam, also known as the KRS Dam, is developed on the Kavery River. The Kavery River, also spelled as Cauvery, is a major river in the southern part of India. It flows through the states of Karnataka and Tamil Nadu, and is considered to be one of the most important rivers in the region.

The Krishna Raja Sagara Dam is located near the town of Mysuru in the state of Karnataka. It was constructed across the Kavery River in the 1920s, primarily for the purpose of irrigation and hydroelectric power generation. The dam is a popular tourist destination and also serves as a major source of water for both agricultural and domestic use in the surrounding areas.

In conclusion, the Krishna Raja Sagara Dam is developed on the Kavery River, making option 4 the correct answer.