Which one of the following rivers thrice forks into two streams and reunites a few miles farther on, thus forming the islands of Srirangappattanam, Sivasamudram and Srirangam ?

The river described is the Cauvery (Kaveri). The Kaveri is known for splitting into multiple channels and forming riverine islands as it enters the plains and approaches Tiruchirappalli and the delta region; the text notes the river “fans out” forming a quadrant-delta in Thanjavur district and flowing around islands below gorges near the plateau course [1]. Historical/landscape accounts specifically record the Cauvery flowing around Srirangapatna (Srirangappattanam) and creating prominent island settlements, matching the option list. Travel and regional studies of the Kaveri also document its numerous channels and distributaries through the plains that form islands such as Sivasamudram and Srirangam. Hence, option 1 (Cauvery) is correct.

Sources

1. [1] Geography of India ,Majid Husain, (McGrawHill 9th ed.) > Chapter 3: The Drainage System of India > The Kaveri > p. 21