The entry in bit mesra, ranchi is on the basis of two examinations , i.e. jee main and Jharkhand Engineering Entrance Competitive Examination (JEECE) . The students can appear in any of these to get into the college . In jee main you need to qualify secure a good rank in jee mains. If you are applying through jee main then the cut off ranks  fort last year was:

Biotechnology27639- 33942

Chemical Engineering13217-  26205

Civil engineering 20979 -   26743

Computer Science and Engineering 2593-  9207

Electronics and Communication Engineering 9419   -14854

Electrical Engineering11705  -  16775

MechanicalEngineering12402  - 20326

Production Engineering25940   - 31467

Information Technology9361  -  10556

Architecture1206 -  2076

And if you apply through Jharkhand Engineering Entrance Competitive Examination (JEECE) then you need to be among the top rankers , within 100 or so , if you want a branch of your choice. In other case you can also see for bit sindri, which is another Birla institute in Jharkhand.