You have good chances...try for it in JOSAA councelling. If not possible also check CSAB.

With a Rank of 68k, you may have chances of securing a Good Branch in BIT Mesra only in the CSAB Spot Rounds, assuming youre a General Category Aspirant. Incase youre a Jharkhand Home State General Aspirant, by Last Round of JoSAA you may have chances in securing one of Chemical, Chemical (Polymer), Civil, Production or Biotechnology at BIT Mesra (57-67k Range). Of course incase youre from Reserved Category youll definitely have strong chances of securing a seat at BIT Mesra.

For more information and College Prediction do follow the link below

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

For more information and BIT Mesra Cutoff do follow the link below

https://www.careers360.com/university/birla-institute-of-technology-mesra/cut-off