Hello.
As you see , the courses that you are talking about here are two different courses and each have their own benefits and cons. And you have to look at different factors before you choose a College or a course. However, Amruta Coimbatore Is a very good and well reputed college that provides quality education and BITS Mesra too is an institute with a reputation of providing quality education as well as good placements. So it is a little difficult to make a choice because while making a choice there are a lot of things that you must consider. Here is a link that you can visit for further details:-
https://www.careers360.com/university/birla-institute-of-technology-mesra/btech-biotechnology-engineering-course
https://www.careers360.com/university/amrita-vishwa-vidyapeetham-coimbatore
Dear candidate out of the two options chosen by you, let us analyse BIT Mesra first, overall it is a very renowned institution because of its sophisticated infrastructure, top notch faculties and academic environment. However the placement records would not satisfy you after your B.Tech Biotechnology degree, it's true that big companies do recruit from the campus but the rate is moderate.
On the other hand if you consider Amrita Institute, the campus life is very strict there, your academic career would be embraced because of their discipline. After your Mechanical Engineering degree you would receive satisfying jobs with packages around 5-7 LPA. Their Faculties are quite experienced and their class notes are updated as per the curriculum, that would help you during the Semesters.
Good luck!!
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