could you please suggest the most effective methods of studying and preparing for the jee mains and the jee advanced ....

The main deciding factor in all the competitive exams is the time management so first thing you should keep in mind is the time 

You must solve as many questions as you can with a thinking in mind that you are in the exam hall.

This improves the question solving skills and also there is less wastage of time.

Along with this you should concentrate on your studies constantly throughout the year i.e. you have to make a time table for studies and must allot at least 6-7hrs per day for self studies.

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AND BEST OF LUCK FOR JEE 2013 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I think the jee mains and jee advanced needs the same old method of iit jee preparations.