Distance

Yes, why not, this is absolutely possible.

No, Annamalai University does not have Master in disaster management through distance learning you can find another college for this course, if you have any questions you can ask frequently.

Dear Diksha Shukla,
In the country, best course in Maharashtra is offered by AIIMS and Apollo Hospitals as they provide the best course. Therefore, try to join with them. Correspondence course will be best from Sikkim Manipal University.
All the best.

Shubham, for a government job, you need to crack a test irrespective of the mode of degree. LPU offers approved courses through distance mode that can enable with the objectives of a particular course.
In case you are not working somewhere better would be to opt for regular MCA, so that you can get better benefits like placements, scholarships etc.

You may refer to the following link for a list of top 10 MBA colleges for distance learning: https://www.shiksha.com/mba/articles/top-10-institutes-for-distance-correspondence-mba-blogId-6301

They are not eligible unless the MBA is either part-time or a full time from an AICTE recognised university as AICTE does not recognise any distance learning program in management and engineering. However, you will be eligible to pursue PhD if your MBA is approved by distance education Bureau of UGC.