A Physics or a Mathematics UG is preferable for cosmology studies.
IIT Bombay, Delhi, Madras, Guwhati are the common choices. Delhi Technological university, National institute of technology in Calicut are the other good colleges.
Delhi Technological University has B.Tech in Engineering Physics (EP), this is a four year course. Admission is selected via a joint counselling, you can check the details.(https://jacdelhi.nic.in/publicinfo/Handler/FileHandler.ashx?i=File&ii=153&iii=Y)
National Institute of Technology Calicut has a Engineering Physics UG course. You can contact the registrar (firstname.lastname@example.org) or visit the website.
You can also take time to visit and browse through the various courses offered by School of Physical Sciences, National Institute of Science Education and Research. This institute is well known for advanced research. (http://www.niser.ac.in).
JEE Advanced is good enough for this line of preparation for cosmology.