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Hi Anusha,
Refer the below website to know more about KVPY exam:
www.kvpy.iisc.ernet.in/
My friend attempted the KVPY SX stream with the subjects Physics, Chemistry, and Biology. The books she referred were, luckily, extremely helpful.
For physics, do not ignore Concepts of Physics by Dr H C Verma. Two questions in the first part of the 2014 question paper were modified questions from this book. Also, Principles of Physics by Resnick and Halliday helps a lot.
For Chemistry, do not refer any book other than the NCERT books. Chemistry is the simplest section in KVPY. However, do refer A new pattern textbook of Inorganic Chemistry for JEE by Dr O P Tandon for the chapter Coordination Compounds. Especially for Crystal Field Splitting Energy.
For Biology, the good part is that many large, time-consuming lessons can be skipped. Analyse the previous years' question papers to get an idea. Then study the NCERT books, NCERT exemplar problems. Now you're 50% ready. After you've finished the syllabus this way, read Biological Science by Taylor, Green, and Stout, Cambridge University Press publication.
She followed these steps and managed to get a relatively high score ( &get; 75 ) in the aptitude test.
I hope you find this answer helpful.

There are various colleges which provide LLB through correspondence which are approved by Bar Council of India:
- Dogra Law College, University of Jammu
- Basavarshree College of Law, Karnataka State Law University
- Lloyd Law College, Greater Noida
- Institute of Law and Research, Faridabad
- Amity Law School, Gwalior
- ITM Law School, Gurgaon
- Harlal School of Law, Greater Noida
- Ajaymeru Law College, Ajmer
Well yes you can practice law after completing LLB but I don't know if you will get the right exposure through a distance course in law.
If you really want to practice law then you should do it regular because you will get a lot of exposure in real court as an internship during your LLB Program.