Hello Aspirant,
The government engineering colleges are run solely by the government. While private aided colleges are run by trusts but they receive funds from the government. Private engineering colleges are run entirely by private trusts.
Coming to engineering, I would recommend LPU in private universities and IITs in public universities in India.
LPU offers engineering in CSE, EE, ECE, ME, CE, Automobile, Chemical, Aerospace, Biotechnology, etc. I recommended my cousin to do B.Tech from LPU itself.
The maximum package availed for the Engineering programme is 42 LPA.
Scholarships/Financial Assistance: You can get scholarships based on LPUNEST, JEE (Main), Toppers of Education Board., Financial Aid - Need-Based, Financial Aid for Serving/ Retired Defence/ CAPF/ Para- Military Personnel and their dependents., Financial Aid to Orphans, Financial Aid to Persons with Certain Disabilities.
I'm available if you need help with this.
All the best!!
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