Option 1: Bhakra-Nangal - This is incorrect. Bhakra-Nangal is a multi-purpose project located in the state of Himachal Pradesh and Punjab. It is one of the largest dams in India but it was not the first multi-purpose project of independent India.

Option 2: Damodar - This is the correct answer. The Damodar Valley Corporation (DVC) was the first multi-purpose project of independent India. It was established in 1948 for the development of the Damodar River Basin which spans across the states of West Bengal and Jharkhand. The project aims to control floods, generate hydroelectric power, and facilitate irrigation and navigation in the region.

Option 3: Hirakud - This is incorrect. Hirakud Dam is a major multipurpose project located on the Mahanadi River in Odisha. It was completed in 1953, after the establishment of the Damodar Valley Corporation.

Option 4: Nagarjunasagar - This is incorrect. Nagarjunasagar is a dam located on the Krishna River in Telangana and Andhra Pradesh. It was completed in 1969, long after the establishment of the Damodar Valley Corporation.

In conclusion, the correct