Hello Arpit, 

Yes IITs do allow students the day scholar facility but it is only in cases of dire neccessity.  You will have to explain the reasons for your applying to be a day scholar to the concerned HOD and if the HOD approves of your reason as legitimate, you will be allowed to be a day scholar. 

IITs are now allowing day scholars to apply for PHD and B.Tech courses as well. 

Hope this helps :)