I thought that it is aspirated because of the rule of aspiration : the stops like /p t k/ become aspirated when they occur in the word initial position OR in the onset position of the stressed syllable. But the answer was "unaspirated" because /k/ is not in the stressed syllable even though it occupies the word initial position. Is the answer correct?
It's aspirated, since it's at the beginning of a syllable. The aspiration is less prominent if the syllable does not have stress, but it's still aspirated. Compare the "t" of "tomorrow" or "today", where "t" is before the schwa of an unstressed syllable, yet has clearly discernible aspiration (at least for many people -- there could be exceptions).