What topics should I prepare before a month if I am going to Narayana IIT Academy without any foundation course? There will be many students ahead of me who would have done basics of 11 and 12 earlier. How should I cope up ?

dear soumya 
donot worry about that , u have 2 years in your hand . 
before going prepare the following topics to gain the maximum 
1- make sure 1 trigo chapter in class 10^th are clear to you , thats the foundation . 
2- do the carbon and compounds chapter of clss 10^th , thats the besics of class 11^th organic . 
3- alongwith that update a little bit about the periodic table element and their trends in atomic radii , ionisation enthalpty etc . 
4- make sure the unit conversion are clear to you of physics , 
5- learn that parallel and series configuration , ohms law , with full concentration 
all the best 
regards