Yes, you are eligible to apply for KVPY SB stream after you clear class 12 and take admission in programme in Basic Sciences namely Physics/Chemistry/Mathematics & Biology leading to B.Sc./B.S./B.Stat./B.Math./Int. M.Sc./Int. M.S. and have secured a minimum of 60% (50% for SC/ST/PWD) marks in aggregate in MATHEMATICS and SCIENCE subjects (Physics/Chemistry/Biology)  in the XII Standard Board Examination. But do remember, this is the last time you can apply for the KVPY fellowship so give it your best!

• Yes a 12th passout can appear for KVPY.
• The eligibility criteria is that the person must have scored minimun 60% aggregate in Science subjects in 12th Standard.
• Also since the candidate has already passed out 12th standard ; he/she must take BSc courses ( pure science ) in Mathematics , Physics , Chemistry or Biology.
• Based on the performance in the aptitude test conducted all over India , the shortlisted students are called for an interview which is the final step of selection procedure.
• For receiving a fellowship , both interview and aptitude marks are considered.
• If you still have any queries feel free to ask in the comment section down below.

Yes 12th pass students can apply for SB stream in KVPY exam. 

Even 12th appearing student can apply provided they qualify with minimum marks required . 

Detailed eligibility criteria below. 

http://kvpy.iisc.ernet.in/main/eligibility.htm