Hello, 

There are various centeral and government university in which you can take admissions. Some of the name of government universities are as follows:

1. University of delhi

2. Banaras Hindu University

3. Jawaharlal Nehru University

4. Jamia mila University 

Above University provides bsc psychology course and in some university admission is based on the 12th board result and some university conducts there own entrance exam for admission.

All the best. Hope this will help you.