Hey
I would tell you to prepare for both of the exams. BITS Pilani is a very prestigious college that produces lot of meritorious Engineers every year to the Nation. It stands on par with many top IIT’s and NIT’s. So you should also aim at trying to attempt the exam to get into BITS Pilani too while attempting the JEE Mains.
The preparation procedure for both of the exams is completely same with a slight variation. So you should plan your strategy for attempting the exams when you are giving them. The syllabus and the question standard is the same in both of the exams, so there won’t be any harm in preparing for both of them. You would generally be having a 2 month gap between the both exams ( excluding this special case of global pandemic ) so that gap would help you to prepare for your logical reasoning and English part while revising the regular PCM ( Physics – Chemistry – Maths ) stuff without fail.