There are two things, Minor exams and a Minor degree.
I suppose you mean a Minor Degree here. Yes, some IITs offer a choice of additional courses along with the depth subjects which you can take up after the 2nd semester. If you're able to clear a certain minimum of credits with courses of a department, you will get a Minor degree in the same. But there are some conditions on that like you need to get atleast a C in the additional to get it counted for the minor. And you have to take care that your additionals donot clash with the depth courses' slots.