hi jeevasri,

No, 2581 rank will not fetch you a seat in IIT Madras through IIT Jam. With the rank of 2581 you can't IIT Madras even if you have sc quota. If you have st quota then you can get top old IITs like IIT delhi, madras with this rank.

For detailed cutoff for all IITs in IIT Jam, I am attaching a pdf file. You should check it here : Click Here (https://jam.iitk.ac.in/doc/JAM2019_cutoffRound3.pdf)

I hope this answer will help.
All the best for the future!!