Distance MBA

Yes you are eligible and shall appear for entrance exam like CMAT, MAT, CAT, XAT, SNAP. Although it is advised to go for full-time MBA programme for better paying jobs. I am sending you list for distance MBA in Delhi below.
https://www.shiksha.com/mba/colleges/distance-correspondence-mba-colleges-in-delhi-ncr

Try for executive MBA in Finance management.

The PGDM programs at SPJIMR are rigorous and thus are residential programs. We currently do not have any distance education programs

Dear Abhishek,
To pursue MBA degree, you should have completed with your graduation. Without graduation, you cannot get admission in PG courses in any form.
All the best.

No. only Regular course is available. No correspondence

MBA will be helpful after MSW if she is performing a managerial role or likely to perform managerial role in near future with a Social org / NGO/ Corporate.

congrats for 9 grade n Your que for distance MBA I suggest you to do an MBA degree regular and definitely after MBA you got much better job than now.

both are not recommend ed. IGNOU is much better. Look below for Top distance MBA colleges.
https://www.shiksha.com/top-10-institutes-for-distance-correspondence-mba-article-6301-1

You can refer this link for college information: https://www.shiksha.com/Sgvude-Suresh-Gyan-Vihar-University-Distance-Education-Sgvude-Jaipur-institute-college-listingoverviewtab-47867