Best books for JEE Mains, Advanced and Olympiad

BEST BOOKS FOR JEE MAINS AND ADVANCED 

PHYSICS-
Must have books-
1. HC Verma - God book of JEE Physics. Must do for all. Read theory and solve questions. As many as possible. If you are buying one book, this is it.
2. NCERT - Another must have. Reading NCERT will help you answer the theoretical problems asked in the paper, and will help you with JEE(Main). It will give you a heads up for boards too.
3.Previous Year Questions- Must solve each and everyone of them.
For more practice(and must have for those who don't go for any 
Arihant Physics Series- Its an awesome resource for quality problems and must have for self-study students who are serious. It will help you clear all the concepts which are taught in coaching. Coaching guys can use it as extra practice. This is must solve for self-study guys if you wanna crack JEE(Advanced). It has really nice problems and theory.
2. Cengage Series- This is an equally good series. You can use it as an alternative to Arihant(avoid using both, it will confuse you), if you r teachers/ friends discuss it, or you like it. As you wish.
Books for problem practice-

You can do Coaching sheet+must have books+ Problem books as a complete package(I did this too). Include the books above(in point 2) if you don't go to coaching.
1. DC Pandey-Awesome numericals.
2. D. Mukherji- Awesome book for theoretical questions. Simple, and very conceptual book.
Books for a high rank/Olympiads-

1. I.E Irodov- Must solve this if you are aiming for top 100/Olympiads(shown above).
2. Resnik, Haliday- Mainly for Olympiads, but it has great theory and problems. A notch above HCV.
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MATHEMATICS
The must-have book for coaching student is just NCERT and past papers. To be honest, NCERT isn't needed much in Mathematics, but you can read it for JEE(Main) specific topics or boards. Just solve your coaching stuff really well(or follow the next point if you are not satisfied, or aspire for more).
So, you can choose between Arihant Skills in Mathematics or Cengage Series by G. Tewani. Both have good questions.
For Extra practice, you can go for A. Das Gupta (specially for class 11 students).
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CHEMISTRY-

Again, like mathematics, Chemistry is best taught by Coaching classes. It would be best if you try to get your hands on them. Still, for self-study guys, I would suggest you to go for popular books on the subject, like the ones given below, for theory. There is no good book of Physical Chemistry for theory known to me, but you can go for N. Awasthi for problems. ( You can again follow Cengage or Arihant series if you are studying on your own. But students with access to good coaching material should avoid books for theory.
Also, NCERT is very important for chemistry section.
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There are countless books available out there. But not all books are good. Don't get confused by buying many boooks..
Good Luck.