B.Sc

Yes, you can apply for KVPY has a specific cutoff that varies every year depending on the paper. However if you score 55-60 in the paper. You are sure to qualify in SA stream. Try to get an intern every summer (maybe a couple of winters). Mail a good professor in your area of interest and state you are a KVPY scholar. You will get a response. Going through those internships will help you expand your horizons immensely (and I cannot stress this enough). Just meeting and talking to professors, research group will help you very much identify your interests and future endeavors. Not to forget the good experience of knowing more people and making friends and contacts. KVPY is a very good opportunity for a select few people.