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Hi Vishal,
Yes AIME is recognised internationally. An AMIE degree is recognized as equivalent to an engineering degree by AICTE, UPSC, SSC, central govt. Departments and state governments etc. AMIE degree holder can write examinations like civil services, Indian engineering services, GATE, GRE, etc.
Requirements are you should have a good bachelors degree or an engineering degree in the relevant field, some university might ask for GRE score however TOEFL / IELTS is must to showcase you English skills some courses are taught in German language also.
BITS Pilani is one of the most reputed institutes of India and the degree that you've mentioned in your query is with par that of IITs.
It's valid as a graduation degree across the globe for any kind of Job (Govt. & Pvt.) and higher studies.
While selecting the best, you need to check some of the important parameters such as recognition, year of establishment, batch size, syllabus, faculty, fees, placements etc.
Hope it helps. Please feel free to revert. Click on the thumbs up or mark it as the best, if you found this useful.
Wish You Luck!

CBS is one of the best college in Eastern India after that of IIMs . Very few Business Schools in India will be able to match Calcutta Business School's world-class faculty in terms of academic and industrial background, collective knowledge, research experience, sheer number (which is very much beyond the regulatory requirement of 15:1 student : faculty ratio) and international exposure.Many of the faculty members at Calcutta Business School are erstwhile IIM Directors, have taught at IIMs, XLRI and many other nationally and internationally reputed institutions or have been CEOs / Directors of reputed corporate organizations.
now the choice is yours.
All the best.