Do students in IITM have to stay in the college hostel or can stay at home?

IITM students have the option of being residential students or day scholars. Generally, students are expected to seek accommodation in hostels but, students who wish to seek exemption from residence in the hostels, can apply separately every semester to be a day scholar. They shall have to submit an application online, in the prescribed format (as found here) to the Dean of Students.

The exempted students, however, are expected to pay Hostel Establishment "A" (the patient health insurance which varies from year to year) to the Institute. Married students / research scholars / QIP scholars have the opportunity to avail quarters in the campus, rather than staying in the hostel. For such cases, rental/establishment charges may be paid to the Institute.

So, there is no compulsion to staying in a hostel. But, the benefits in doing so are many, such as having more peer interaction and easier access to institute facilities.