Board eligibility criteria is 45 % for bit mesra

Hello Aspirant.

No, As per NTA norms you cannot be allotted a college through JEE main examination untill and unless you fulfill it's eligibility criteria which is that the candidate must score atleast 75%(general) aggregate, 65%(sc/st/pwd) in class 12th.

If you're unable to clear it. You won't get any of the above mentioned college.

Or else you need to be in the top 20 percentile of your board to get college through JEE main

Best of luck