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Hi Meena,
Some institutes that might interest you are:
Dresden University of Technology
Dresden International Graduate School for Biomedicine and Bioengineering
University of Cologne:
Fast Track Master's / Doctoral Program in Biology at the Graduate School for Biological Sciences in Cologne
University of Gttingen:
GGNB Biomolecules: Structure-Function Dynamics (PhD)
University of Gttingen:
GGNB Molecular Biology - International Max Planck Research School (MSc / PhD)
University of Gttingen:
GGNB Molecular Biology of Development and Interaction between Organisms (PhD)
Max Planck Institute of Biochemistry, Neurobiology:
International Max Planck Research School for Molecular and Cellular Life Sciences, IMPRS-LS
University of Leipzig:
Leipzig School of Natural Sciences - Building with Molecules and Nano-objects
University of Dsseldorf
NRW Research School BioStruct - Biological Structures in Molecular Medicine and Biotechnology
University of Heidelberg:
The Hartmut Hoffmann-Berling International Graduate School of Molecular & Cellular Biology (HBIGS)
University of Constance:
Chemical Biology; PhD Graduation Program
Ruhr University Bochum:
Chemistry and Biochemistry (Graduate School) (GSCB)
Hannover Medical School:
PhD Program: Molecular Medicine
In order to pursue your Phd. you need to submit your research topic along with the LOR to the relevant department for their consideration.
Also I would like to say that education in Germany is a good option as it is govt. funded so you may have to give a very minimal fee ranging between 140- 500 euros.
For more details, I would request you to visit the nearest DAAD office. DAAD is officially authorized to provide information about education in Germany. They have offices in major cities in India.
http://www.daad.de
If possible go for a German language course as it will help you find a part time job. A student in Germany can work 90 full days or 180 half days.
Hope this helps
All The Best!

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Richa there are many more institutes who provide engg degree in Mechanical. like IIT, NIT and some state govt. colleges. these are best for this course. and to get admission in these colleges u need to appear an entrance exam for each institutes. for iit, IIT JEE is conducted in every year. for NIT u need to appear AIEEE and for state Govt college U need to appear State technical university's entrance exam in every year.
finally there are also some different private university's who provides these courses also.
Kindly revert for any further queries, also if you liked this answer then rate it 'Best answer' or give a 'Thumbs Up' rating. thnxx.