Central University of Haryana, Mahendergarh: One of the 15 central universities established by MHRD, it is fully funded by the UGC. It is highly competitive and offers a host of courses across disciplines to choose from.
University of Mumbai: One of the largest universities in the world, it has so many different departments including for sciences that you'll never be short on options.
Indian Institute of Technology: Not only does one of India's premier institute for engineering have option for science stream, you can get PhD in Humanities and Social Sciences. Choose the city you want!
University of Delhi: It has so many different departments, centres and colleges, that whatever you want to study, it is available here. Beware of those high cut-offs though!
Jadavpur University, Kolkata: This university is great for Humanities and Social Sciences students, and is one of the most competitive universities in India.