Dear candidate, the cutoff ranks in last round for BIT Mesra, Ranchi were:

• Bio-Technology                                                    71267
• Chemical Engineering                                         52796
• Chemical Engineering (Plastic and Polymer)   64887
• Civil Engineering                                                   51711
• Computer Science and Engineering                  11409
• Electrical and Electronics Engineering              30640
• Electronics and Communication Engineering  21605
• Information Technology                                      13231
• Mechanical Engineering                                       38523
• Production Engineering                                        59346

Check how much marks you need to get your desired branch by checking percentile vs marks vs rank list in JEE Main here:

https://engineering.careers360.com/articles/jee-main-marks-vs-percentile

Hope, it helps!