Should wife take permission from husband?

Was this discussed before marriage (that she'd appear for exam and may work away from her matrimonial town)?

Discuss and come to a conclusion on what you both want.

If she's adamant on her exam and going from you, take preemptive legal action (consult a lawyer for this).

No point in living separate in the fear of law or in the name of women empowerment.

her getting Govt job is ultimately going to enahance financial status of your family and you are just going on hunting spree.

some person have had very sad and bitter expereince from mariage and they have developed such feeling that all wives are villians.  There is no justification of forcing action re-play of their life in your life.