For those who are interested in scientific research as career, Indian Institute of Science (IISc) is on the top of the list of institutes in India. KVPY (http://kvpy.iisc.ernet.in/main/eligibility.htm) and JEE are two of the common ways to get admission to the institute.
The following link usually has the cutoffs from previous years. Here are some quotes to give you an idea:
2017 JEE Main: The cut off marks for shortlisted candidates in different categories in the JEE (Main) stream are: 310(General); 250(OBC-NCL); 250(SC); 130(ST), 250(KM) and 250(PH).
2017 JEE Advanced: The All India Rank cut off for shortlisted candidates in different categories in the JEE Advanced and NEET-UG are: 100(General); 1000(OBC-NCL); 1000(SC); 10000(ST), 1000(KM) and 1000(PH) (Please note that the above are not category ranks).
KVPY: Offers were made to general category applicants selected with ranks of up to 215, 1 and 215 for the KVPY-SA, SB and SX streams respectively.
Offers were made to all OBC(NCL) category applicants selected in KVPY SA and SX streams.
Offers were made to SC category applicants selected with ranks of up to 60 for both KVPY-SA-E and KVPY-SX-E streams.
Offers were made to all ST category applicants selected in KVPY-SA-E and KVPY-SX-E streams.
Offers were also made to PwD category applicants selected with ranks of up to 1 and 6 for the KVPY-SA-E and KVPY-SX-E streams respectively.
When all seats are not filled up, they open up to further ranks for the spot admissions.