Hi,
It is not necessary to have maths in 12th standard as the eligibility says that you will need to attain 50% marks in aggregate in your 12th. There are independent entrance examinations for admission to UG as well.
You can refer to the colleges mentioned in the link for studying psychology.
https://university.careers360.com/colleges/list-of-psychology-universities-in-india
With psychology, the job spectrum is diverse. You can be a teacher or a professor though for being a professor you will need to do higher studies. Government sectors also open up jobs in civil services for psychology students who have pursued their masters. You can also become a subject matter expert, community relations officer, development psychologist, child support specialist, neuropsychologist, social worker, clinical psychologist etc.

Dear Rito, Maths is not necessary to study Psychology. To start with Bachelors in Psychology is 3 years and then Master's is 2 years. From there on if you want to be a Counselling Psychologist, you need to study M.Phil and then register with Rehabilitation Council of India. If you want to pursue your career in Psychology in Organisational, Educational, Research fields of Psychology, it will take you 5 years of Education after 10+2. If you have a career designation that you are interested in, please let us know and we shall help you with the career path.