CBSE 12th

PUC is the most preferred step after 10th grade in Karnataka. It's a two-year course which ends with one board exam at the end of the second year.
It is offered in three different streams: Science, Commerce and Arts/Humanities. You will have to study 4 core subjects which will depend on which stream you are in along with 1st language (English) and a 2nd language (more than 10 different languages are available). It is the most accepted qualification for graduation. There are many colleges which offer classes in the evening too which makes it very easy for those who wish to earn while they are studying. A little about each stream:
Commerce: Commerce has been the preferred stream in our country and opens up a wide arena of options for you to choose from as a career choice. Science: This course gives you the scientific perspective of things and readies you to pursue pure Science careers such as Medicine, Pharmacy, Research, etc. Science enthusiasts and even math enthusiasts would love this course.
Arts/Humanities: From advertising to acting to doing social work to making that funny video you watched on YouTube scope for arts is everywhere. Demand for psychologists and content creating personnel and many creative services are increasing and making the arts stream a very lucrative option. Diploma courses are heavily job oriented. They train you to do a specific job or profession in short span of time as opposed to studying an entire stream and choosing a career path later. Many students opt for Diploma courses but it's not the most popular. It is also heavily skilled based and hence requires precision and concentration. They are usually range from 6 months to 3 years. There are roughly two kinds of Diploma Courses: Technical Diploma Courses and Non technical Diploma Courses.
Technical Diploma: Technical Diploma courses usually deal with courses on engineering and technology. The careers are not usually very high paying but it is a boon for what is arguably India's the biggest strength: its manpower. Diplomas help increase the number of skilled workers in the country.
Non-Technical Diploma: Non-Technical Diploma deals with skills which require precision and training but not necessarily technical. Non-technical Diplomas too produce a huge amount of skilled workers who can be easily employed.

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.