curiousThe best students are the ones who are curious about everything.
inquiringThe organization tries to encourage inquiring and analytical young people to go into the sciences.
nosydisapproving"Did her spouse leave her?" "Well, aren't you rather nosy!"
prurientformaldisapprovingThat reporter has a reputation for being prurient and asking questions that are too invasive.
inquisitorialformaldisapprovingThe inquisitorial nature of his questions did not set his guest at ease.