Both questions are alternatives; you answer ........ one ........ the other
Answer Details
The correct phrase is "either/or".
"Either/or" means you have two options, and you must choose one of them. For example, "Do you want to have pizza or burgers for dinner?" Here, you have to choose either pizza or burgers, not both or neither.
"Neither/nor" means you have two options, but you reject both of them. For example, "I don't like neither pizza nor burgers." Here, you are rejecting both options, and you do not want either one.
"Either/nor" is not a commonly used phrase, so it's best to avoid it.