I graduated from IIT Madras in July 2002 with a B.Tach in Materials Scinece and Metallurgical Engg. I would have the following things to say regarding any aspring candidate who wants to study in any of the IITs.
1.Firstly if you really want to be there, then you have to stop thinking as to what would happen in case you dont qualify the exam. Positive thinking helps big-time and along with it comes also the determination to work harder.
2.You should make sure that you do-not linger on any problem for days while preparing. remmember this is only an entrance exam and no research confrence or something. You aim is to get into these institutions and not to research things before you did so. I never spent more than a couple of days if I got stuck on any problem, . and this itself was quite rare.
I did not take a clssroom coaching, but I do not say that they are bad. You have only to be sure that you are choosing the right one. I would strongly not recommend you to leave your home and stay somewhere outside when you are preparing. Staying at home and preparing is the best way to do so. However incase there is no other way and you HAVE to leave your house and stay somewhere else in order to prepare for this exam then do so. But think about this well before you take this step.
Finally on the D-Day, try to solve the easier questions before you jump to the harder ones. Doesnt matter the easier ones come later. Your aim is to get maximum points and not to write a thesis.
Guess the above suggestions help. Good Luck.