Correct option (C) Distant
Far off :
It can't be used in place of 'aloof' as far off' means long-long ago. Hence, incorrect alternative .
It means 'self-centred', Hence, It is an incorrect alternative.
This is an appropriate word because one of the meaning of 'aloof' is distant also while keeping distance between two nouns.
(it means 'hopeless') Hence, quite irrelevant.