The correct option is The Bhilangana.
Explanation
The Alaknanda and Bhagirathi are the two main headstreams of the River Ganga. The Alaknanda river originates from the Satopanth Glacier and is joined by several tributaries at specific confluences known as the 'Panch Prayag' in Uttarakhand.
Analysis of Options:
- The Pindar: This is a tributary of the Alaknanda. It originates from the Pindari Glacier and joins the Alaknanda at Karnaprayag.
- The Mandakini: This is a tributary of the Alaknanda. It originates from the Chorabari Glacier (near Kedarnath) and joins the Alaknanda at Rudraprayag.
- The Dhauli (Dhauli Ganga): This is a tributary of the Alaknanda. It joins the Alaknanda at Vishnuprayag.
- The Bhilangana: This is not a tributary of the Alaknanda. It is a major tributary of the Bhagirathi river. It rises from the Khatling Glacier and joins the Bhagirathi at Old Tehri (the site of the Tehri Dam).
Key Takeaway: The Bhilangana feeds into the Bhagirathi, whereas the Dhauli Ganga, Nandakini, Pindar, and Mandakini are tributaries of the Alaknanda. The Alaknanda and Bhagirathi eventually merge at Devprayag to form the Ganga.