M.Sc

Yes, after clearing IIT JAM exam, you can pursue M.Sc from IIT. You should start your preparations, but you will be eligible in B.Sc final year to apply for IIT jam.
Best of luck.

The course fee for 2 years is Rs 4-5 lakhs.

Please refer to the link provided below where some popular M.Sc entrance exams are listed so that science aspirants should consider giving in order to secure admission in a good college. There are many good science colleges in India wherein aspirants can choose to study a specialised Master of science (M.Sc) course after securing their graduation degree.
https://www.shiksha.com/science/articles/top-bsc-msc-entrance-exams-in-india-blogId-13484

Specializations in this field:
M.Sc is a perfect option for those students looking to specialize in a Science or engineering discipline at the advanced level. Through M.Sc degree you can specialize in various fields some of them are listed here:
M.Sc in Physics
M.Sc in Economics
M.Sc in Biological Sciences
M.Sc in Chemistry
M.Sc in Mathematics
M.Sc in Information Technology
M.Sc in Clinical Psychology
M.Sc in Organisational Leadership
M.Sc in Biotechnology
M.Sc in Atmospheric Science
M.Sc in Electronics
M.Sc in Environmental Science
M.Sc in Meteorology
M.Sc in Geology
M.Sc in Zoology
M.Sc in Botany

Joint Entrance Screening Test (JEST) is considered to be a National Eligibility Test (NET) by Science & Engineering Research Board (SERB). Aspirants who are seeking admission in Ph.D or Integrated Ph.D programmes in Physics or Theoretical Computer Science or Neuroscience or Computational Biology need to give JEST exam. Indira Gandhi Centre for Atomic Research, Kalpakkam is the organising institution for JEST 2018.
https://www.shiksha.com/science/exams/jest/syllabus

M.Sc Eligibility Criteria
Basic eligibility criteria for pursuing an M.Sc course requires students to be graduates from a recognised college with a minimum cutoff percentage (as stated by the respective college/ university) preferably in Science stream. There is usually no age limit to join the course.
Students can opt to pursue M.Sc immediately after they complete their graduation or even at a later stage.
Note: M.Sc eligibility criteria might differ from college to college depending on their policy.