Solution:North Koel is a river flowing from Jharkhand, a tributary of the Son River, it joins the right bank of the Son River. The Son River is the second longest (first Yamuna) tributary of the Ganges River from the southern part of the Ganges near Patna.The southern Koel river flows into Jharkhand and Odisha. The southern Koel river flows in association with the Northern Karo River as the Koel River, which joins the Sankh River near Rourkela in Odisha as the Brahmani River.
The Barakar River is the main tributary of the Damodar River, which originates from the Koderma Plateau in Jharkhand and Joins Damodar via Hazaribagh. Damodar joins the Hooghly River in the lower Ganges basin.
The Damodar River Basin is a sub-basin of the Ganges River Basin. Thus, Barakar and North Koel are sub-rivers of the Ganges river valley. Hence the correct answer to this question is option (e).