Which of the following rivers is not the tributary of the Yamuna river?

A tributary is a river that flows into and merges with a larger "main" river, contributing to its discharge without keeping a separate name downstream of the confluence. The Yamuna, itself the largest tributary of the Ganga, has its own network of tributaries that join it as it flows through Uttarakhand, Himachal Pradesh, Delhi, Haryana, and Uttar Pradesh before it finally merges into the Ganga at Prayagraj.

Applying this to the four rivers listed: Chambal, Betwa, and Ken all rise in the Malwa Plateau / Vindhya-Kaimur hill region of Madhya Pradesh and flow north-eastward to join the Yamuna directly, each on its right bank in Uttar Pradesh. The Gandak, in contrast, rises in the Nepal Himalayas and flows south-eastward through Bihar to merge with the Ganga itself at Hajipur, near Patna — it never touches the Yamuna at all.

• Chambal joins the Yamuna near Etawah/Bhareh (Uttar Pradesh).

• Betwa joins the Yamuna near Hamirpur (Uttar Pradesh).

• Ken joins the Yamuna near Chilla, Banda district (Uttar Pradesh).

• Gandak joins the Ganga at Hajipur (Bihar), not the Yamuna.

Since Chambal, Betwa, and Ken are confirmed right-bank tributaries of the Yamuna while the Gandak instead drains into the Ganga, Gandak is the river that is NOT a tributary of the Yamuna — confirming Gandak as the correct answer.