Hello Akshaya!! Yes, we do have colleges in India which offers Integrated MSC courses. So you can have a look at the list of the colleges. 

Go through below links to get the list of colleges which offers Integrated MSC courses and it's a big list.

https://www.careers360.com/question-top-universities-offering-bscmsc-physics-integrated-program

https://www.careers360.com/question-msc-or-integrated-msc-phd-medical-microbiology-goverent-colleges-in-india

Good Luck!!

Dear aspirant,

Colleges offered 5 year integrated M.Sc Courses are-

All the IIT's
IISER's
NISER, Bhubhaneswar
Amity School of Arts and Science
BITS, Pilani
Indian Institute of Science Bangalore
 University of Mysore
University of Mumbai

 VIT Business School (Chennai)

Hope this helps.

Good luck.