No you are not eligible for TANCA admission because you have not appeared for that exam so I thinbk you have to wait for another 1 year to again write either gate exam olr tancet exam or search for way whether it is possible to join through mnagement quota.May helps.

You should have qualified either tancet or gate .

So hence you are not eligible for tancet counselling that is tanca admission.

There is no age limit

Visit the below link eligibility criteria

https://www.google.com/amp/s/engineering.careers360.com/articles/tanca/amp