Hi,

You haven't mentioned your CRL or EWS rank. Due to this I have to predict your rank. At 87.93 percentile, your CRL rank would be around 120000+ . The Last rank for a Female who got a seat in NIT Patna was 9245 EWS Rank. Your EWS rank would be greater than 10000+ . So It is difficult to get NIT Patna. However , 10000+ is a predicted EWS rank. If you provide your EWS rank, I would be able to answer more accurately.

In order to predict colleges , you could use this tool: JEE Mains 2021 College Predictor

Thanks!!!