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Incidentally, this year's batch has atleast 3 or 4 electrical engineers and 2 people are from IIT! If economics is of interest to you, nothing wrong in switching to this stream! 2-3 months of preparation should be good enough. Do Varian + Varian workbook (definitely can be done on your own!). I also see coursera.org offering some econ courses, which I'm doubly sure, will be of help! For macro, I'd recommend starting off with Mankiw, but looking to say, Macro economic theory by Branson, for a slightly more mathematical (and slightly more extensive) treatment. Try doing questions from the MIT OCW courses. Some universities in the US also have a lot of their assignments out in the open. Google's your best bet.
You won't have too much of a problem with Math and Stat (look at prev year papers. More than enough of them around!). Also, going by the trend over the past 3 years, there are a significant number of questions from econometrics. Some online lectures (Khan academy, Yale lectures on Udemy etc) and other websites should help you out with that.
Good luck!
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