Hello,

First of all the eligibility criteria for BEd is passed graduation or post graduation in any discipline from a recognized university with 50% or above aggregate, there is relaxation of 5% for reserved category, even for MSc the eligibility criteria is passed bachelor's degree in relevant discipline from a recognized university with 50%-60% aggregate, the aggregate factor varies as per norms of the university and so does the admission process which can be done through entrance test or it's simply based on the merit of the qualifying examination

now, coming to your question UGC has allowed candidates to pursue two degree programs simultaneously but the only condition is one is to be done through regular mode and another through distance mode. some of the top colleges to pursue BEd are RIEs which are premier educational institutes for which admission is done through entrance test named CEE conducted by NCERT, other than this application forms of DU, BHU to name a few are yet to be out, for MSc you haven't mentioned you want to do in which subject, but you may consider appearing for IIT JAM, that's a gateway for admission into top institutions IITs, NITs, IISc, IISER etc, you can check out the entire list of MSc Colleges by filtering information as per your preference such as subject, state/city, ownership, gender diversity, study mode etc at https://engineering.careers360.com/colleges/list-of-msc-colleges-in-india

Also, check out the entire list of BEd colleges at https://university.careers360.com/colleges/list-of-bed-universities-in-india