Is iim amritsar worth joining at the age of 21?

The younger you are, the more opportunities you will receive. So don’t let the age factor discourage you. It’s highly possible that the old IIMs did not consider you. Think of the bright side. You are young and you have multiple CAT opportunities.

What you can do is work somewhere and gain experience. This might upgrade your profile. Inculcate extracurricular skills and prepare yourself well for the next batch of CAT aspirants. Keep trying till your dream comes true.