Step 1: Project Recall.
The Nagarjunasagar dam, a globally significant masonry structure, was constructed for irrigation, hydroelectric power, and water supply.
Step 2: River Identification.
Located in Andhra Pradesh and Telangana, the project is situated on the Krishna River, serving a vast command area and representing a key Indian multipurpose river valley initiative.
Step 3: Exclusion of Other Rivers.
- The Godavari River hosts projects like Polavaram and Jayakwadi. - The Pennar River features smaller irrigation schemes. - The Mahanadi River is the location of the Hirakud Dam.
Step 4: Determination.
Consequently, the Nagarjunasagar project is established on the Krishna River.
Final Answer: \[\boxed{\text{Nagarjunasagar project is on the Krishna River.}}\]