Yes, you can take admission in private colleges. There are many private colleges who consider JEE marks to provide admission and provide good placements as well.

You can check the list of colleges below

https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-India-accepting-jee-main-score

You should always keep many options with you. Appear for other exam as well apart from JEE like BITSAT, VIT, Amrita, Manipal and COMEDK. These are top private colleges and provide excellent placements.

Getting a good package depends on many factors like skill, talent, knowledge and college. Make sure you choose a college with good placements whether it is government or private for that you really need to work hard as there is lot of competition.

Good luck!!

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