"Are you okay?"
I've never seen those two used together like that. Daijoubu ka or just daijoubu would be right I'm almost certain.
だいじょうぶですか for the polite version, だいじょうぶ？for the informal version (orally you would raise your intonation at the end to make it obvious that it is a question). Then there's だいじょうぶか which is also informal, but feels more "raw" and less friendly than the simple だいじょうぶ？(from a native teacher)
I tried "大じょうぶか" and was corrected that it should be "大じょうぶ？" with emphasis on the question mark, when no question mark tile exists, and my answer is perfectly acceptable. Submitting a report!
大じょうぶか is valid but very rarely used. Most people don't even consider it to be valid. 大じょうぶ? is the casual form. In casual Japanese, you can ask a full question using only one word. It just depends on your voice inflection and the situation you might be in.
元気ですか？(げんきですか？) means more of "Are you well/good?" whereas 大じょうぶ is more of "okay".
Why does DuoLingo show it in half kanji at first, then full kanji. I don't get it, at some point let's use the kanji and give hints on the hiragana "spelling", tsssss.