B.Tech Mechanical Engineering

Hello Manish, there are 2-3 entrance tests that you ought to give to secure admission in India. One of them is JEE Mains, then JEE Advance. The fees of any engineering college or university is not more than the figures you described. As far as good colleges for Mechanical Engineering are concerned, the link below has the list of them-
https://www.shiksha.com/b-tech/ranking/top-mechanical-engineering-colleges-in-india/48-2-0-0-0

Of course Germany, because Engineering is one of the hit courses in Germany. High quality of education with low education costs are one of the biggest lures for students to go to Germany.

Apply for CDS or TGC to get entry in Indian army.

Choosing mechanical is one of the best decisions as compared to other branches. You can go for RV, BMS or Dayanand Sagar or any other college.

You are advised to share your educational qualifications and interest areas for an appropriate advice.

The numerical content of a mechanical engineering degree opens up a variety of opportunities in the finance and management sectors.
Job options
Jobs directly related to your degree include:
Aerospace engineer
Automotive engineer
Contracting civil engineer
Control and instrumentation engineer
Maintenance engineer
Mechanical engineer
Nuclear engineer
Jobs where your degree would be useful include:
Corporate investment banker
Mining engineer
Patent attorney
Production manager
Technical sales engineer
Water engineer

Dear Sreeram,
Please understand that there is no difference in PGDM and MBA other than course name. PGDM is equivalent to MBA and syllabus of both are almost same.
Maths is an essential subject in both. There are subjects like Quantitative Techniques , Business Maths / Statistics or etc in both PGDM and MBA.
If you are interested in Mechanical Eng., you can specialize in Production Engineering, Automobile Engineering, and Advanced Automotive Design Engineering etc. at PG level.