B.Tech

Dear Rohit,
As per AICTE norms, BE/BTech courses can't be done through distance education,
Although considering your graduation, you can proceed for an MBA degree which will give you a more detailed knowledge and skill sets on management.

Do not restrict yourself to the specialisation before exploring all the fields. It is true that operations is the optimal choice given your background but you may want to consider other choices as well because your background has a very little role to play in your MBA.

Yes, you can do B.Tech Dairy Technology. For engineering PCM are compulsory. So you are eligible for that. Given below is the link for Dairy Science College, Bangalore. Check it out for more information:
http://www.kvafsu.kar.nic.in/dairy college.htm
https://www.shiksha.com/college/dairy-science-colle

Eligibility for M.Sc. in Artificial Intelligence
Candidates wishing to apply for the course need to meet the following minimum eligibility criteria:
A minimum aggregate score of 55% at the level of graduation in B.Sc. or B.E./B.Tech. or an equivalent degree with Mathematics as one of the main subjects

The chances of you getting placed will be doubled if you do your M.Tech or MS in material sciences or metallurgy. The demand for metallurgical engineers is growing these days. Government organisations like DRDO, DRDL, etc. offer a wide range of opportunities. Also, private companies like shell, Line

Follow the link below for all the details:
https://www.shiksha.com/b-tech/course/b-tech-lateral-entry-government-college-of-engineering-amravati-gcoea-239643

You can go for MBA majors with marketing and minor with HR. Quantum University is one of the best universities in north India for MBA scholars.
http://quantumuniversity.edu.in/mba

For B.Tech/BE through lateral entry (direct second year admission) from a government college, you have to appear for state LEET examination and score well in the same

Please refer to the link provided below for an exhaustive list of colleges which offer medical courses in India. You can download their brochures which contains all important information like course eligibility, admission criteria etc.
https://www.shiksha.com/medicine-health-sciences/colleges/mbbs-c