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Dear Aspirant,
With only 66.26 percentile in jee mains and a high rank of 45523 in KCET, it is extremely unlikely or rather not possible to get into government engineering colleges of Karnataka.
Your chances of getting into a good engineering college rests only on the private institutes. You should look for top private institutes that provide good placement scenario and excellent packages l, astute teaching faculty, skill oriented education, infrastructure, etc. If no option provides you a seat in good private engineering college, there is always Management Quota.
In order to know what colleges you might get based on your JEE main rank, you are suggested to go through this link:-
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
If you want to know what colleges you might get through KCET with KCET rank, you may click on this link:-
https://www.careers360.com/kcet-college-predictor?ici=cp-listing_root&icn=KCET-College-Predictor
This shall also give you a list of colleges that shall be enough for you with respect to your rank.
If you want to compare the colleges and find out which one is better, you may click on this link:-
https://www.careers360.com/compare-colleges
This shall serve as a good comparison tool.
Good luck.
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