Hello student home state quota is quota reserved for students who passed their class 12 from the state where the iiits/college is. Or their family must be a citizen of that state.
And other state quota is open for all students across the India for that college.
Like you mentioned you're from Delhi then 50%of seats are reserved for you in every college like DTU, NSIT, IIIT.

You can easily calculate your rank by using this formula (100-your total percentile) 869010 /100
In your case your rank must be around 2800.
With this rank you can get easily into IIIT DELHI.

You can also use college predictor to predict college on careers360 by clicking on the link mentioned below its very user friendly and very helpful.
https://engineering.careers360.com/jee-main-college-predictor

Feel free to comment if you have any doubt
Good luck

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