I have passed JEE 2005, although with a pathetic rank-below 4000. I will share my thoughts about preparing for this. First thing is, stick to the basics. Know your definitions well. Most of us skip the basics, because we think they are too easy and will never come in JEE.
This is a mistake. The thing to do is, remember the ’derivation’ of every formula in physics, maths and physical chemistry. All these formulae are based on assumptions. IIT will twist these assumptions and ask the problem. So, u will have to derive the new formula, using the same algorithm.
Even in organic chemistry, be thorough with hydrocarbons and general organic chemistry. Most people mug some advanced hi-fi reagents and mechanisms, which dont come. For last few years there are always questions on ’conformers’ of alkanes, sn1 sn2 e1 e2 mechanisms and hydrocarbons.
For screening, practise mcq questions and be a little street smart. I mean you donot have to properly ’solve’ a problem. Most of the times, by looking at the options you can eliminate 2 options. Then you have a 50% chance of solving a problem. Also, attempt many questions.
Dont be overcautious in screening because of negative marking. Remember its +3 and -1. You cant say that I will attempt 40 questions of which I am sure of and score 120. That is rare. Even if u think ur right, in IIT you are mostly wrong. 6 mistakes like this and u go below 100, i.e. below the confort zone of passing screening.
In mains just write everything you know. You dont need to get perfectly every answer, if ur approach is right, u get marks and if you are good enough at analyzing, you are through.
About books and coaching classes, others have talked enough. But, definitely go for some correspndence test. FIITJEE has more no. of students competing, but papers are unnecessarily supertough. Brilliant papers are closer to actual JEE papers. Any class, u join u have to be among the top there. All the best.