I have got 97.037654 percentile and my obc NCL rank is 8201 which nit can I get And which one is better dtu or vnit(home state)?
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With a OBC NCL rank of 8201 and with your home state quota in VNIT, according to 2018 cutoffs, you can get Chemical engineering, Civil engineering, metallurgical and materials engineering, mining engineering at VNIT Nagpur. You have not mentioned your CRL, so it is difficult to predict whether you would get a DTU seat or not but I do think at this rank and due to outside Delhi region, you would get a seat at DTU as the closing CRL rank(not OBC rank) for OBC candidates was 34106 for Polymer Science and Chemical technology engineering.
You can also get Computer Science and engineering at NIT Patna, Electrical engineering at NIT Patna, ECE at NIT Patna.
At NIT Warangal, you can get Bio technology engineering. You can get many other NITs too at this rank.
I wish you all the best and for any queries, ask me in the comments.