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MCA through distance mode is valid but not worthy as it is a technical course and you need to attend regular classes for better learning and labs for practical work. If you merely want degree then you can go for a distance mode MCA but if you want to do job and want better career growth then you should do MCA through regular mode. You will find many good colleges for Regular MCA. Regular has more value than distance mode.

No, for UPSC you have to only qualify your graduation after that you are eligible but a regular degree is slightly better than an open degree because in a regular college you have social interaction interactions with professors. You have ample opportunity to refine yourself through college society extra circular activities which experience not only help in the interview but throughout your UPSC preparation.

No, I think it's not possible to continue in regular college parrell to articleship.

For MBA the best B-School preferred is IIM-Ahmedabad but it only accepts students at 90-99 percentile. If you are unable to fall under this category you can go for NMIMS Mumbai, Symbiosis Pune, etc. Also for regular or executive MBA yoh can go for executive MBA but it's not necessary that all the colleges provide it. So if you get a chance for executive MBA just do it as it will save your time and energy both.

Yes, recently there was some law which allows 2 degree simultaneously. Refer UGC Guidelines for pursuing two degrees simultaneously, rules and process explained
UGC has allowed students to pursue two degrees at the same time. Students will be given a choice to pursue the degrees in physical mode, hybrid mode or online mode. Students will also be allowed to choose from a variety of disciplines. The complete guidelines have now been issued by UGC.

Hi dear, Can you please tell me which state/college you want information about?

Hi. Here is the list of colleges you can look for-
Yashvantrao Chavan Maharashtra Open University YCMOU, Nashik
BJB Autonomous college - (BJB), Bhubaneswar
Madhya Pradesh Bhoj Open University - (MPBOU), Bhopal
Krishna Kanta Handiqui State Open University - (KKHSOU), Guwahati.

You can get to know about the admission here-
https://www.shiksha.com/university/jamia-millia-islamia-Delhi-843/course-master-of-business-administration-mba-190341

You can refer to the link given below-
https://www.shiksha.com/mba/articles/top-mba-colleges-accepting-mat-score-blogId-6056

Course Details:
Master of Business Administration (M. B.A) is a full-time two-year postgraduate Management Department course and it is offered by the Acharya Nagarjuna University, Guntur.