Do professors in IIT teach from the very basic. Or do they teach with the preasumtion that these guys ought to know this before. Plainly, my question is how far the 11th and 12th syllabus is related with the IIT syllabis?

yes 11^th& 12^thdoes matter in you IIT’s but if someone is going into in an IIT he is already good enough because he has cleared IIT-JEE exam
but yes i have seen people you get backlogs in their first semester.Most of them are SC/ST students because they get admission on the basis of reservation with less marks but in college they have to compete with general candidates only