In the Chinese book for beginners by Bellassen, it is stated that 国 cannot be used alone: it doesn't have a meaning on its own, and thus the word country/fatherland is 国家 and not 国.
However... I am surprised by the question 你是哪国人? (still in Bellassen's book). Would it be possible to ask 你是哪国家人吗? Are there other uses where 国 can be used alone, while still meaning country?
edit: the word country/fatherland is indeed 国家 as stated in the answer below, and not 家国 as I first wrote.