Hello there,
You haven't mentioned your category, and your home state. So, I'm assuming that you are from the general category, and do not fall under Home State Quota.

Now, to get government colleges, you need to have 3000 rank approximately. The cut-off ranks change every year depending on the difficulty of the paper, and the number of students appearing for it.

For a rank of 3000, you need to have 97+ percentile in your JEE Mains paper 2.

You can check the government colleges, their cut-off ranks, along with their fee structure from the link given below:
https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?ownership=Public/Government&degree=B.Arch&branch=Architecture%20Engineering&exam=JEE%20Main

Hope this answer helps you.
Good luck!!

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