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Hello Aspirant,
Since you have not mentioned your category so considering it as General, if wrong then kindly correct me in the comment section below.
As per your percentile in JEE-Main 2022,
>>>>> your CRL rank is expected around 419430 - 471500 .
Now on such rank and category you can have chances in following colleges based on your JEE-Main rank :-
Note that the above prediction is made on the basis of latest cut-offs and the cut-offs are bound to change every year depending upon various factors such as the number of candidates appearing in an examination, the number of candidates qualifying an examination, difficulty level of the paper, and so on.
B.Tech/B.Arch Admissions OPEN
To have a list of all those colleges which you can get based upon your JEE-Main rank/score you can use JEE-Main College Predictor:-
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Till now the official qualifying cut-offs have not been released and the qualifying cut-off percentiles are released along with final result of JEE-Main 2022 which will be released after both the sessions i.e. most probably in August '22.
But o n such percentile, being a General candidate you have almost no chances to qualify for JEE-Advance 2022 but still the cutoffs for this year have not released yet officially.
As the cut-offs are released along with the JEE-Main 2022 result so for now you can get an idea from JEE-Main 2021 qualifying cut-offs that are enlisted below :-
==>> Common Rank List (CRL) - 87.8992241-100.0000000 Percentile
==>> GEN-EWS - 66.2214845-87.8950071 Percentile
==>> Other Backward Classes (OBC-NCL) - 68.0234447-87.8950071 Percentile
==>> Scheduled Caste (SC) - 46.8825338-87.8950071 Percentile
==>> Scheduled Tribe (ST) - 34.6728999 87.8474721 Percentile
==>> PwD - 0.0096375-87.8273359 Percentile
Note that in above table it is not the actual cut-off for JEE-Main 2022 but previous year's cut-off.
You can check out previous year's cut-off trends from the link given below :-
https://engineering.careers360.com/articles/jee-main-cutoff
I hope this information helps you.
Good Luck!!
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