The Nagarjuna Sagar Dam, located in the state of Telangana, is one of the largest dams in India. It is built across the Godavari River, making option 'A' the correct answer.

Background:
- The Godavari River is one of the longest rivers in India, originating in the Western Ghats of Maharashtra and flowing through several states before emptying into the Bay of Bengal.
- The river has immense significance and is considered sacred by many people. It plays a crucial role in irrigation, agriculture, and hydroelectric power generation in the region.

The Nagarjuna Sagar Dam:
- The Nagarjuna Sagar Dam is a masonry dam constructed across the Godavari River in the Nalgonda district of Telangana.
- It is named after the nearby town of Nagarjuna Sagar, which is renowned for its ancient Buddhist civilizations.
- The dam was built between 1955 and 1967 as a multipurpose project aimed at providing irrigation, hydroelectric power, and drinking water supply to the region.
- It stands at a height of 124 meters and has a length of approximately 1,550 meters, making it one of the largest masonry dams in the world.

Key Features:
- Irrigation: The primary purpose of the Nagarjuna Sagar Dam is to provide water for irrigation to the surrounding agricultural lands. The dam's reservoir has a storage capacity of 11,472 million cubic meters, which helps in irrigating vast agricultural areas, mainly in the districts of Nalgonda, Khammam, and Krishna.

- Hydroelectric Power Generation: The dam also serves as a source of hydroelectric power generation. It has a powerhouse with 26 turbines, each with a capacity of 40 MW. The total installed capacity of the hydroelectric power plants at Nagarjuna Sagar is 960 MW.

- Drinking Water Supply: The dam supplies drinking water to several towns and cities in the region, including Hyderabad, the capital city of Telangana. The water from the reservoir is treated and supplied to meet the drinking water requirements of the population.

- Tourism: The Nagarjuna Sagar Dam has also become a popular tourist attraction due to its scenic beauty and the Nagarjuna Sagar Wildlife Sanctuary located nearby. The reservoir formed by the dam provides a picturesque environment for boating and other recreational activities.

Conclusion:
The Nagarjuna Sagar Dam is a significant infrastructure project built across the Godavari River in Telangana. It serves multiple purposes, including irrigation, hydroelectric power generation, and drinking water supply to the region.