JEE Main

Here is alink for the last years cutoff please check the opening and closing ranks acording tou your state.
http://www.eduarena.com/bit-patna-opening-and-closing-rank-bit-patna-cutoffs-bit-patna-branchwise-cutoffs/
This should give you a good idea as to would it be possible to get in. I would also request you to keep a college in your mind if the things dont work out with BIT Patna . just as a caution.
Enjoy

I would requst you to kindly jot down a list of the colleges that u or Your family jave in mind . acording to the vicinity where u live or the place you wanna go . at a rank of 48k you can get into any decent private university. Also mention your marks in class 12th.
Enjoy

Not to demotivate you but going into any college with less JEE marks is difficult. But your board numbers are good. You can try for other state pannel colleges like Upsc or ip. If that is not the case then u can try for private colleges like amity noida,gurgaon or any other branch though its orivate but is one of the best colleges to study and recive the right exposure.
Enjoy

Dear don't go for coachings they will kill Your real self

yes, you should. you have fair chance in your home state NIT.

ya u can get nits of north east states

you can try for galgotia, abes, kiet, akgec

what is your rank?

I think you should not go for LPU