If you are a Bihar domicile candidate, you need not to worry as you should easily walk through. If you  are not a Bihar domicile candidate you should keep other options open as chances look bleak. All the best!

Hi dear,

With the rank of 4000 in ST category in JEE mains Paper 1 you can very easily get seat in BITS Mesra,Patna in Mechanical Engineering only in Home state quota. You may also get admission in Bachelors of Architecture in BITS Mesra with this rank only in Home state quota.

If you are Outside Bihar , getting seat in BITS Mesra will be quite difficult for you.