Hello aspirant,

Some of the IIMs like IIM-A, IIM-C provide courses in which you will be able to study one year in India and around 6 months in other countries, but please note that these are only students exchange programs, where few students of a college abroad will come to India and study in your college and you will study in theirs, and this is not necessary for every students studying in such colleges to go, it depends on number of students the college sends and is mostly on the basis of merit and willingness to represent their colleges. Not just IIMs but few private universities also runs this students exchange programs.

I hope this helps