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You stand good chance of getting admission in Germany universities provided you are able to obtain two recommendation letters from internationally renowned faculties from your engineering college.

Refer to this article, it has details of all entrances exams for HM:
https://www.shiksha.com/popular-hotel-management-entrance-exams-in-india-article-6838-1

Yes, it's equivalent to B.Tech and is completely valid for pursuing Masters degree and even for applying for government jobs.

There will be less number of seats for management quota.

Any should give you a job, as early as possible or you should get a research opportunity. Subjects like English and economics are better for you. MA should not be a fancy qualification. It should lead you to a job.

There is no entrance exam in Loyola for M.Sc in mathematics.

Computer engineering will be better option.

You can do 2 years of ITI or 3 years of polytechnic Diploma. You will become technician/engineer in the fields like:
1. Electronics.
2. Electrical.
3. Mechanical.
4. Construction.

Hello! The registrations have started for SNAP, last date to apply is 22nd November http://snaptest.org/Best-MBA-college-in-Pune-siib.html

If you have a deep desire to become a mechanical engineer and have maths as one of three optional in your B.Sc then you can do 3 year B.Tech in mechanical engineering or M.Sc in electronics or MCA.

You can do MBA through CAT, MAT, XAT, CMAT, ATMA, etc. after B.Com.

As you are not interested in teaching jobs, don't go for M.Tech. First, you need to analyse your skills, if you are good at managing people, MBA is the best option. You should opt for MBA in operations management as you are a BE graduate.

All private universities allow lateral entry in 2nd year of B.Tech if they have vacant seats.

JIGSAW Academy and Simplilearn are the best.

Go for B.Tech CSE. It will help you to get a decent job and better opportunities. Computer engineering is a discipline that integrates several fields of electrical engineering and computer Science required to develop computer hardware and software. A few good institutes offering these courses are:
IITs, IIITs, NITs. Lovely Professional University, Jalandhar
Delhi Technological University, Delhi
Amrita School of Engineering, Coimbatore
Birla Institute of Technology
Vellore Institute of Technology.

Analytics plays an important role these days, and even corporate companies are preferring the people who have knowledge of business analytics.

If you want to learn cyber security you can enroll for any of the training programs by http://pune.cssrl.in. The training is possible in regular classroom or in online mode. The career options in the field of cyber security are growing a lot these days.