1. Books followed include Pradeeps for Phy and Chem; R.D. Sharma (for class XI or XII) for Maths. These are not the right books when it comes to preparation for the competitions. There might be a 'competitions section' in each of these books containing good problems related to engineering entrance exams, but they do not have a good explanation of concepts which is critical in solving the engineering entrance problems. For example, if there is a theory like the 'Newtons second law of motion', Pradeep's will define the theorem, probably have a proof for it, and have some solved examples to make the student understand (numericals.... thats what the students like the most). With this, the student starts solving some new type of problems which he has never solved before. So the feeling after reading Pradeep's is good.
But this is not sufficient when it comes to the engineering level. Foreign author books on the other hand, like 'Resnick and Halliday', 'University Physics' and 'Sears and Zamansky' (Complete list will be given in my other posts) will have a very practical approach to explaining the same theorems. With the help of very practical situation examples (like 'when sachin tendulkar's bat hits the ball, the impulse of the bat gets transferred to the ball'), and real life figures (of rocket launch or a car skidding on the road, etc) the author is able to EXPLAIN and make the student really UNDERSTAND the theorems. The idea is not to just 'get marks'. Idea is to GRASP the concept, so that the student never, ever forgets.
I mean, how can anyone forget what one has understood?? I can definitely forget someones name or a formula, but I can never forget the answer to a question like 'why moon revolves around the earth' (once i have understood the concept of gravitation).
2. Books are only a medium to deliver knowledge and concepts. But the most important thing in preparation for competitions is the application (in the form of problems). The problems that will be asked in IITJEE this year will be completely new. No student would have seen the problems anywhere in any book or course material. Even the best of the best teachers can never predict what problems will come in IITJEE.
So the idea is not to know more in terms of concepts or knowledge (formulae, tricks, etc). What is needed is the answer to ‘How to solve any new problem?’. The answer to this question is the key. The students who are able to crack this are the winners.
The key lies in trying every problem for as long as possible without looking at the solution or asking anyone. This looks like the most difficul! t thing to do when you read it the first time. But it’s actually the only way to succeed. Let me explain…
I remember the time when I was in class XII and was preparing for IITJEE myself. I had read the entire trigonometry, read all the solved examples from my book, and then started attempting the unsolved questions in M.L. Khanna. The came across the following problem:Q. Prove that in any
ABC, 
.I tried everything possible in my knowledge, in terms of approach, concepts, tricks, everything. I could not go anywhere in this problem. At the end of the first hour, I was over with whatever I knew myself. I started to get frustrated. I was tempted to look at the solutions, but I didn’t. I then thought maybe I must have missed something in the theory. So I opened my books again. I first opened the books I had read from. So I went over everything I had learnt so far again, thoroughly, as if to punish myself over having forgotten something just because I was unable to solve this one little problem. Two hours had gone by.! I then opened the other books I had not read so far for trigonometry (there are plenty of other good books like S.L. Loney). I went through each of them one-by-one. That took a good 4 hours of my time. In these four hours, I learnt so many new things which I had never known after reading the refreshers I usually referred to (M.L. Khanna, etc). I mean, I got to know things like why
or why 
.These are simple things that most of the students do not know. Their proofs might not be important at all, but as science students, we must know the how and why of everything. Not just this, I came to know a lot of other stuff.
A total of six hours gone and I still could not solve this problem. I knew that now since I have already ‘wasted’ six hours on this problem, I might as well spend some more time. So what more could I do with this problem I wondered. ‘How can I solve this?’, ‘Since there is a problem, there must be a solution!’, ‘Just like a proton has a corresponding thing called electron, happiness has sadness, if there is a friend there is a enemy, ! so a problem must have a solution!’. THINK LIKE THIS!! I just kept thinking and applying the new knowledge from the books. I tried this, I tried that. I kept failing. And got frustrated more and more with every passing moment. At the back of my head was also a thought, ‘How will a guy like me make it to IIT if I am not even able to solve one problem even after trying for 8 consecutive hours!!’.
I then decided to find similar problems related to trigonometry in other chapters. I went through chapters I had already studied, like quadratic, progressions, etc. Read the whole thing again. Thoroughly. Each and every problem in those chapters, solved as well as unsolved. Six more hours went by. I still could not move the problem. After a frustrating 16 hours, I gave up. 16 hours of non-stop problem solving!! I thought to myself, ‘I have failed, I will not be able to make it to IIT for sure. A guy like ! me deserves to be nowhere’. I looked up the solution, an! d what I saw blew my mind. The required concept was a concept out of a XIIth class topic called ‘Application of Derivatives’ which I had not studied till then :).
So what this tells is:
a) Since I had spent 16 hours only on trigonometry, and other chapters I had already studied, I never had to study them again. They were THOROUGH in my head till IITJEE got over. No revision was required in any manner ever for the entire year for these chapters.
b) Since the solution to the problem required concepts from some o! ther completely different chapter, I understood that WYSIWYG (What You See Is What You Get) is not applicable in IITJEE. The problem looks like a trigonometry problem to anyone. But its actually not. So after that day, I stopped using the WYSIWYG approach to IITJEE problems.
c) I understood so many new ways of tackling a problem during this 16 hour period. My brain muscles were getting a workout. It felt exactly like one feels after coming out of a gym after a workout.
d) ! I had not failed. I was a big success. This new thing of ‘being at it’ got me into IIT finally.
Application of Derivatives Solved Problems
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