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