B.Tech Computer Science and Engineering

Yes, for sure.
You don't even need to opt for dual degree course, you can get CSE in non-integrated course too, I guess.

It is approx 2.2 lakh rupees per annum without hostel charges.

Hi Ram, check
RWTH Aachen
Passau University
ULM University
Hasso-Plattner-Inst. Potsdam
Jacobs University Bremen
TU Kaiserslautern
and
University of Gttingen

check the complete detail related to college and CSE branch in the link provided
https://www.shiksha.com/university/jaypee-institute-of-information-technology-noida-20383

Hello Varun,
For admission into any government colleges, you need to write any entrance and score well in that, however regarding donation, no government colleges offer admission via management quota.

Computer science engineering (CSE) is one of the popular courses among engineering aspirants which focuses on the basic elements of computer programming and networking. Students pursuing computer science courses will gain knowledge of design, implementation and management of information system of both hardware and software. Going by the name, CSE course deals primarily with the theory of computation and design of computational systems. The course is offered across the globe in technical institutions at undergraduate as well as postgraduate levels awarding B.Tech and M.tech degrees, respectively.