Final answer:
The correct preposition to complete the sentence is 'for', which indicates the purpose or role for which the post is being advertised by the government of Assam in the department of education.
Step-by-step explanation:
Prepositions and post positions, together called ad positions (or broadly, in traditional grammar, simply prepositions), are a class of words used to express spatial or temporal relations (in, under, towards, ago) or mark various semantic roles (of, for). A preposition or postposition typically combines with a noun phrase, this being called its complement, or sometimes object. A preposition comes before its complement; a postposition comes after its complement.
The correct preposition to fill in the blank in the given sentence would be 'for'. Therefore, the sentence should read: "The post for the government of Assam in the department of education has been advertised." This is because the word 'for' is typically used to indicate the purpose or destination of something. In this case, it indicates the purpose or the role for which the government of Assam is advertising.