I am not sure if many candidates appear in M.Sc & Ph.D simultaneously in India. In foreign, this is a popular option & most of the science graduates are preparing for integrated Ph.D.
In India following institutes provide M.Sc & Ph.D Courses:
IIT Bombay - Go read [IIT JAM exam 2018] Brocedure
Department of energy science & engineering
University of Birmingham
Geographic Data Science lab
Culham Centre for Fusion Energy
Faculty of Rehabilitation Medicine
You can discuss any other reputed M.Sc & Ph.D courses here in this thread. This will help Students to grab the opportunities available within country & even abroad.