Hello aspirant,
As your JEE Mains percentile is 81.19 which means you have not qualified JEE Mains. And as per your percentile your rank would be around 2 lakhs which is much larger thank the closing rank for Mechanical engineering in bhagalpur engineering Colleges and mujaffarnagar Institute of Technology.
Sorry, you are not eligible to get admission in these colleges for these streams but you can apply for another streams like IT, Chemical Engineering, ECE etc.
Good Luck.

Hello student there's fair chances you can get admission in these two colleges but I request you to plz help me with your category so that I can provide you exact information.

Mit muzaffarpur and bhagalpur engineering college are one of the best engineering colleges in bihar.

As onward this year bcece is not going to held admission is totally on based on JEE Marks.

Also it's very easy to predict college on by clicking on the link mentioned below its very user friendly and very helpful.

https://engineering.careers360.com/jee-main-college-predictor

Feel free to comment if you have any doubt
Good luck

MIT Muzaffarpur

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