Annamalai University

Dear,
Yes, you can pursue two different programmes from two different universities in distance mode as per the UGC guidelines.
But you need to manage the time table for both the courses.
All the best.

Yes, it is a good institute to pursue MBA.While joining MBA in distance mode, make sure that you are into the relevant specialization in which you have appropriate work experience so that it can enhance your employ ability and professional skills. If you are not working, it is always better to pursue regular MBA than the former one.

The University Grants Commission, India) (UGC) canceled the recognition of the Annamalai DDE courses in 2015. Annamalai authorities approached the Madras high court which has as of now stayed the UGC's cancellation order. The matter is still pending in Madras High Court. Therefore, as of day degrees awarded by DDE of University are valid.

From my point of view, GITAM University would be a better option for you.

Yes, it is a UGC approved university. So, there is a scope in both government and private sector.

ICFAI is better and more relevant to the current industry. The ICFAI has a better record than Annamalai. You should go for ICFAI, though is a little tough to get admission in the same.