D.Ed

Yes, you can do so. Since 2013, UGC has approved two degrees simultaneously, one preferably a distance education and other regular one. In your case, B.Sc from SOL and D.Ed are allowed and both will be a valid degree in same time frame.

It will be held in the month of June.

Hi Rockstar,
As per UGC, students can pursue two-degree programmes simultaneously. Therefore, you can pursue the two courses. The students can get enrolled in a regular full-time degree programme to pursue one more additional degree programme simultaneously on open/distance learning mode from the same university or another institution.
For more details, please follow the link:
http://www.ugc.ac.in/pdfnews/0367166_morethanonedegree.pdf

No, you can pursue either B.Sc or B.Ed at same time, you cannot do simultaneously.