The Narmada is the odd one out, because it flows west into the Arabian Sea while the other three drain east into the Bay of Bengal — option 2.

Why most peninsular rivers flow east. The Deccan plateau is tilted, with the Western Ghats forming a high edge close to the Arabian Sea and the land sloping gently down towards the east. The great rivers — Godavari, Krishna, Kaveri, Mahanadi — therefore rise in the Ghats and run right across the peninsula to the Bay of Bengal, building large deltas as they go.

Why the Narmada is different. It does not follow the general slope at all. It flows through a rift valley, a trough between the Vindhya range to the north and the Satpura range to the south, formed by faulting rather than by erosion. Because it runs in a steep-sided trough and reaches the sea through an estuary, it carries its sediment straight out and builds no delta. The Tapi is the other major river of the same kind, running in a parallel trough to the south.

A second way to see the grouping. Two of the others are tributaries and one is an independent river, so tributary status does not separate them cleanly; direction of flow does, and it isolates exactly one river.

A few Narmada facts. It rises at Amarkantak in Madhya Pradesh, runs about 1,312 km, forms the Dhuandhar falls at Bhedaghat near Jabalpur where it cuts through the marble rocks, and is dammed by the Sardar Sarovar project in Gujarat.

Hence, the answer is Narmada.