Hello Kiran,


Some of the to universities are,

• Indian Institute of Science
• Indian Institute of Technology, Bombay
• Indian Institute of Technology, Roorkee
• Indian Institute of Technology, Delhi
• Indian Institute of Technology, Kanpur
• Indian Institute of Technology, Kharagpur
• Savitribai Phule Pune University
• Amrita University
• Banaras Hindu University
• Indian Institute of Technology Guwahati
• Indian Institute of Technology Madras
• Jadavpur University
• Panjab University
• Birla Institute of Technology and Science

Hope this helps.
All the Best.

Hello there you write gate or national eligibility test(Net) for getting admission in PhD..

So coming to good college I better suggest you to opt iits and nits. Colleges like iit bombay, Kanpur, madras, karagpur, Delhi and niits like surathkal are best and there are some private university like biits 

Hey,
Since you haven't mentioned the subject you want to do your  Phd in so it's bit confusing to tell the names of the colleges as it generally depends on the programme you want to pursue.
The basic eligibility criteria is graduation degree and post graduation degree.
GATE or NET exams are the gateway to Phd.
Here is the list of some of the colleges that offer
Phd degree:

• University of Delhi
• Jamia Millia Islamia University
• Calicut University
• Banaras Hindu University
• CSJM Kanpur University
• Banasthali Vidyapith
• Rabindra Bharat University
• University of Calcutta

Hope this helps.