Hey !

The minimum rank needed differs from state to state and from category to category. And as far as i can see , you have not mentioned none out of these two , so it is hard for me to tell you the minimum rank. But still , if we see the past year records , then you can get a government polytechnic seat with a rank of even 10000 if you are a general category student , and 15000 if you belong to any reserved category. And you usually need to have a score of 250+..

Hope it helps!