curiousThe best students are the ones who are curious about everything.
inquisitiveShe's such an inquisitive little girl!
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.