My daughter is giving her 12th CBSE Boards from Oman. She would like to pursue B.A with Psychology or B.M.M. Does any college have NRI quota

Hii

Yes she can pursue her College in India after completing her 12th class. A number of colleges provide NRI quota including the University of Mumbai too.
Mumbai university has decided last year to prepare a single window body to provide help to all the international students. Edulab Educational Exchange Pvt. Ltd has been identfied by the university as the Service Provider to provide all the services petaining to admissions of international students at all the affiliated college and university departments of the university of mumbai.
So as you want your daughter to study in the university of mumbai being an NRI student, you are supposed to contact Edulab Education Pvt Ltd for all the admission formalities as now the college or even the university departments are not allowed to provide direct admission to International students.

You need to contact the following people regarding the admission procedure -
Dr. Sunil Patil - Director , department of students' development & university information bureau And foreign Students'ss advisor.
Contact -> 022- 22042859
He would be the Coordinator for the admission process of international students.
Mr Pratic Gandhi - Chief Executive officier, Edulab Education pvt ltd.
Contact -> 022 - 26879696, 022- 26879697
He would be the student coordinator ( international admissions)

Hope this helps
Thanks!!