There are a few state governments which provide free laptops during your btech years. As in case of state of chhattisgarh provide free laptops to all the engineering students of every engineering college of the state. These laptops are of the range 20k rupess noramally from hp company. These are provided in the last year of engineering.

Most colleges do not provide free laptops to students as they do not have a sufficient budget. You should go to electronic stores and claim a student discount on laptops. Most companies offer from 5% - 25% off on various laptops for student use. You only have to show your college ID and you can avail the discount.

Firstly,  you can't get a laptop totally free of cost. Though a ver few no. Of scholarships provide a free laptop to students who have passed 12th .
Some engineering colleges provide laptops, but they are not free of cost. Apparently, it seems that they are giving it free of cost. But the price is included in the fees you pay. For example, MIT manipal.