Indian National Physics Olympiad: The most competitive Physics exam in India, with only ~40 people qualifying from all over the country. The preparation for INPhO doesn't require any special skills as such. A deep understanding of the +2 level concepts is more than enough. However, to be able to clear INPhO, one definitely needs an aptitude to solve subjective problems, which isn't that easy to develop.
Seeing a simple harmonic motion in the context of thermodynamics (INPhO 2013) is sure to force you to think beyond the JEE syllabus and so one should really have an in-depth understanding of the subject to ace this exam.
Here are the required books for INPhO
- The usual God book - IE Irodov
- Arihant INPhO, old edition
- Arihant INPhO, new edition
Indian National Chemistry Olympiad: Well, this is also a really tough exam. I scored 56/97 and I was among the top 40 in India to qualify for this exam. With my score, you can easily estimate the difficulty level of this exam.
A deep knowledge of organic chemistry is needed, much beyond JEE syllabus and its worth investing some time here to learn more new concepts (basics of NMR spectroscopy, biochemistry, etc)
Here are some good books to assist you:
- Organic Chemistry by LG Wade
- Physical chemistry by OP Tondon
- Inorganic chemistry by OP Tondon
- Arihant INChO
INMO: since I never appeared for RMO, I have least idea here, but I heard some people using this book: