I know in my brother's university (IT-BHU), they put caste names next to students' names. And this was a top-tier government university at that!

In my University (IIT-D), I believe certain scholarship announcements revealed details about students' categories, ie whether they were SC/ST/OBC/General. Especially if it were a means scholarship.

Worse case, professors in India have zero personality training, and will casually ask such questions of their students.