Amrita School of Engineering, Amrita Vishwa Vidyapeetham - Bengaluru Campus

It will cost you around 85k per year for the academics plus hostel if you opt for that.

The tution fee is INR. 2,10,000 per annum, and if you require bus and hostel, it would cost you INR. 50,000 more. So, in total it would be near about INR. 3,00,000.

Amrita School of Engineering has the best faculty for Mechanical engineering. I'm unaware of MIT Pune.

Yes, management quota is available in Amrita School of Engineering, but it is necessary to attend the entrance exam, and also you should clear the minimum marks required in boards.

Yes you can but for this you have to give GATE exam in ECE only for VLSI Degin Master course. Just prepare for GATE for ECE branch. You can check the syllabus of GATE ECE you will find some of the subject are common in EE and ECE and remaining you can prepare in less time also. Just go with the concepts the branches are not too different. All institute in government allow Master in VLSI to ECE branch only not EE. Hope it solved your query. Best of luck.
For any further query please feel free to ask me.

Being a student from Tier-2 college, I can tell you that the following companies generally come for placements:
-Caterpillar (offered Highest package during my college time )
-Mahindra and Mahindra
-Tata motors
-L&T
-Wheels India
-Bosch
-Suzlon
-Flowserve
-Ucal fuel systems
-Hyundai motors
-Ford India
-Blue Star
- Elgi
Apart from these, there will be software companies for recruitment.

I doubt you can get a seat from counselling. You could try for a management seat.

Yup, you can definitely get a seat in EEE or EIE.

SRM University, Chennai offers better placements for B.Tech and if you want to know the placement about any other branch, then kindly mention it.

Hello Gopa, please use Shiksha compare college: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.