On which river is the Indira Sagar Hydroelectric Power Project located?

Concept — A river-valley project is defined by the river it impounds: the dam sits at a chosen gorge or narrow point on one river, and that river's drainage basin fixes the project's geography. So to name the river behind a project, locate the dam site, identify the valley it stands in, and match that valley to the river that drains it.

Application — The Indira Sagar Hydroelectric Power Project stands at Narmada Nagar (Punasa), in Khandwa district of Madhya Pradesh. That dam site lies inside the rift valley that runs east–west between the Vindhya range to the north and the Satpura range to the south — the valley drained by the Narmada. Impounding the Narmada there creates India's largest reservoir by storage volume (about 12.22 billion cubic metres) and drives an installed capacity of 1,000 MW (8 units of 125 MW). On the same river it lies upstream of the Omkareshwar and Sardar Sarovar projects, while Bargi (Rani Avanti Bai Sagar) lies further upstream of it.

Cross-check — The other rivers named here drain different valleys, so a dam in the Vindhya–Satpura rift cannot belong to any of them:

Hence the Indira Sagar Hydroelectric Power Project is located on the Narmada.