For top 10000 ranks, students get preferred IIT.

But for rnaks between 10000-50000, students go for following colleges :

IISER Thiruvanthapuram, Pune, Kolkata, Bhopal and Mohali Campus
IiPE Vishakhapatnam
IIST Thiruvanthapuram
IISc Bangalore.

https://engineering.careers360.com/articles/jee-advanced-cutoff
All abive colleges accept Jee advanced apart from top IITs. The cutoff close diwn within 50000 ranks.

Again i will say it is also category dependent!

If you belongs to general categoey than best option would be IIT Indore / IIT Guwahati.
If you are obc than ISM Dhanbaad (iit dhanbaad)
If ST/SC you can get iit kanpur!

But yeah you will not get your favourite branch.

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