You dropped this link in a previous exercise : http://prirucka.ujc.cas.cz/?id=ono&dotaz=je&ascii=0 in which jej is in the same cell as nej. So why isn't jej one of the options either?
The versions beginning with "n" are used after prepositions. See VladaFu's reply below or, for example, Personal Pronouns at: https://en.wikipedia.org/wiki/Czech_declension#Personal_pronouns. Note especially... "In 3rd person (singular and plural) j-forms are used without prepositions, n-forms are used after prepositions."