What is the ruling on competitions that rely on mentioning a word from the Quran and asking for the verse in which it appeared, or posing a religious question and answering it, then posing another question?

Posing questions for benefit and studying knowledge is permissible. Imam Bukhari titled a chapter in his Sahih, "Chapter: The Imam Posing a Question to His Companions to Test What They Have." Ibn Hajar reconciled this hadith with the hadith prohibiting "difficult or perplexing questions" (al-ughlutat) by interpreting the prohibition as applying to questions that offer no benefit, or those posed with the intent to vex or incapacitate the addressed person. Based on this, there is no harm in this type of competition as long as the intention is to discuss religious matters; rather, it is considered a good deed.