Before I answer this question, I would like you to know that I am not from one of the premier institutes in India.
What I say henceforth is largely from a view point of an average Indian pursuing his/her graduate studies in the United States. I will warn you that this is going to be a subjective analysis.
It is exaggerated and generalized.
You see, if we Indians remotely understood the concept of subtlety, I wouldn’t be writing this post today.
The following is more like a session given when tripping on some high quality LSD, things that will not be openly told to you on that ‘incoming students’ group on Facebook.
The usual advice about education and research is towards the end. Skip and help yourself.