I have an old laptop which I carried from India to the US & has an export certificate with it(so it's duty-free). Can I buy the laptop in the US and bring both the laptops, duty-free into India?
If your export certificate correctly lists the earlier laptop with serial number, then items on it will not be counted against any limits.
The new laptop will fall into the category of one duty-free laptop and can be brought in without any duty.
Moreover, it is very common to bring in two laptops (one personal and one company) while travelling from the US to India and this is not practically questioned. Of course if questioned one has to somehow show the work laptop belongs to their company, but that is the default assumption made by customs.
Transfer of residence limits will not be needed for this, also if possible this privilege should be saved for when you actually have to transfer residence, perhaps at the end of your course.