If you are ineligible, a law or rule says you are not allowed to have or do something. You are ineligible for the prize if you work at the company. You may be ineligible to vote, to play, to apply, or to receive the discount. The door is closed by the rule, not by your skill. It is mainly an adjective. The same French word also gave English a noun — an ineligible, meaning a person who does not qualify — but you will almost always see the adjective. Formal to neutral; very common on forms, in sports, and in elections. Everyday speech often prefers “you don’t qualify” or “you can’t apply.”

無資格的、不符合資格的（不是「沒能力」；也可當名詞「無資格者」，但很少見）