Hello Eeshan Mattey, If you got 96 percentile in JEE Main then your rank after JEE Main April will be around 40 thousand, this is only JEE Main rank.
Admission in BITS Pilani,BITS Hyderabad, BITS Goa and BITS Dubai is on the basis of BITSAT. Birla Institute of Technology and Science Admission Test (BITSAT) is a different exam as compared to JEE Main, its question paper is quite easy as compared to JEE Main.
BITSAT also ask questions from English and Logical Reasoning but in JEE Main English and Logical Reasoning are not present. Also the level of questions are very different from JEE Main. There are 150 questions in BITSAT and more over if someone attempted all 150 questions then he/she can get 12 extra questions and cutoff of BITSAT are also high as compared to JEE Main as paper is quite easy.
So No body can exactly predict how much rank you will get by seeing you Main result. it only depends upon on you how you deals with BITSAT,and how is your practice of English and Logical Reasonings.

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