Is it permissible for a woman to travel alone by plane for a limited number of hours to attend a necessary exam, given that her husband is unable to accompany her? And is the prohibition related to time or distance?

The prohibition of a woman traveling without a mahram (unmarriageable kin) is supported by authentic, explicit, and unconditional proofs from the Sunnah. These proofs are not conditioned by a state of fear or otherwise. More than one scholar has narrated a consensus on the unlawfulness of her traveling without a husband or mahram for purposes other than Hajj and Umrah. Every instance that is considered "travel" is forbidden for a woman without a husband or mahram, whether it be for a day, a night, or less or more.