India

Please refer to the link provided below for an exhaustive list of colleges which offer courses via distance mode for M.Sc. maths in Delhi. You should be able to navigate to a college and course of your choice using the filters on the webpage.
https://www.shiksha.com/science/colleges/distance-correspondence-m-sc-colleges-delhi-ncr

Hi,
Some of the leading management institutes offering Distance MBA programs are SymbiosisCenter for Distance Learning, Narsee Monji Institute of Management Studies School for Continuing Education, Sikkim Manipal University Directorate of Distance Education, ICFAIUniversity and IGNOU among others. You can plan your admission by checking out this list of Institutes offering Distance MBA programs across India. You can sort them course-wise and city-wise to suit your requirement.

Yes, it will. the only difference is that your domicile will be of Jharkhand.

Check the below link for post graduate colleges for Hospital Management -
https://www.shiksha.com/medicine-health-sciences/public-health-management/colleges/hospital-healthcare-management-colleges-india

In India, it is having a very less scope. You will have to spend at least 10 to 15 years in research and study. But I think working and studying abroad will be the best option for you as it has a great future and scope in research-oriented nations.

You have to practice mock test of last year's paper and you may also go to coaching regularly because they will help you study in a flow. Also, there are a number of Youtube channels that you can check and follow to get help like Study IQ, GK Today, Jagran Josh and so on and use the legal aptitude book by RS Aggrawal and so on and read a newspaper daily so that your knowledge increases automatically. Above all, the most important thing is doing practice daily so that you can crack the exam in the first attempt. All the best.

Please refer to the link provided below for a list of colleges which offer courses in M.Sc. chemistry. You should be able to navigate to a college of your choice using the filters on the web page. Additionally, you can download their brochure which contains important information like course eligibility, admission process, application dates, forms, placement information, fee structures etc.
https://www.shiksha.com/science/colleges/b-sc-chemistry-colleges-maharashtra