Hello,

No, you cannot pursue BEd along with BSc ,the reason being the eligibility criteria for pursuing BEd is passed graduation or post graduation in any  discipline from a recognized University securing 50% aggregate, this may vary as per norms of universities.

UGC  has allowed candidates to pursue two degree courses simultaneously provided one is through distance mode and another through regular mode however you also need to fulfill the eligibility criteria of the course you are willing to pursue.

Based on 10+2 qualifications  you can pursue diploma in elementary education or diploma in education, or one thing you can do you can pursue MSc or BEd simultaneously after completion of graduation, but you need to follow the norms in terms of pursuing one course through regular mode and another through distance.