First of all I can say that if u want to get in to IIT u want to get  through  JEE.For that u must be strong in maths bcz there is a minimum cut off for each subject and it requires a strong conceptual n problamatic skills in P.C.M .

 

Comming to the infrastructure n Faculty that is IIT my dear n there is no nead to worry abt them . 

 

as far as my knowledge IIT-K is good for research