The correct answer is option 'A' - Cauvery.

Krishna Raja Sagara Dam, also known as KRS Dam, is located in the state of Karnataka, India. It is built on the river Cauvery. Let's explore some details about the dam and the river it is constructed on.

The Krishna Raja Sagara Dam:
The Krishna Raja Sagara Dam is a masonry dam built on the river Cauvery. It is located in the Mandya district of Karnataka. The dam was constructed in the early 20th century and is one of the major irrigation and hydroelectric projects in the state.

Key Points about the Krishna Raja Sagara Dam:
1. Construction: The construction of the Krishna Raja Sagara Dam started in 1911 and was completed in 1931. It was named after the then ruler of Mysore, Krishnaraja Wodeyar IV.
2. Purpose: The primary purpose of the dam is to provide irrigation water to the surrounding agricultural lands and to generate hydroelectric power.
3. Dam Design: The Krishna Raja Sagara Dam is a gravity dam made of stone and concrete. It is around 49 meters high and 1,525 meters long.
4. Reservoir: The dam forms a large reservoir called the Krishna Raja Sagara Lake. The reservoir has a storage capacity of about 49,000 million cubic feet and is one of the largest in Karnataka.
5. Irrigation: The dam provides water for irrigation to a vast command area of about 1.2 million acres, benefiting farmers in the region.
6. Hydroelectric Power Generation: The dam has a power station with a capacity of 42 megawatts. It generates electricity using the water released from the reservoir.
7. Tourism and Recreation: Krishna Raja Sagara Dam and its surroundings have become popular tourist destinations. The serene lake, lush greenery, and picturesque landscapes attract visitors from near and far.

In conclusion, the Krishna Raja Sagara Dam is built on the river Cauvery in Karnataka, serving the purpose of irrigation and hydroelectric power generation. It has played a significant role in the agricultural development of the region and has become a prominent tourist spot.