Here is how you can apply for the integrated Ph.D. program at JNCASR. 

• You can apply for the Int. P.hD. program from the official website.
• Once shortlisted, you will need to go through the written test and interview.
• Prepare well for the interview and perform well.
• They will announce the result after 15-20 days.

You can also take IIT-JAM. It increases your chances of getting selected at reputed institutes.