These are more personal questions and she'll enjoy talking about them. If you have friends in common, this is an easy place to start the conversation.
Questions about these topics make excellent icebreakers, they're natural questions to ask — not too personal or invasive — and they easily lead to an in-depth conversation. Just commit to your answer, use it as an example and let her talk. Choosing a college major is, for a lot of people, one of the only big decisions they make on the basis of passion. Although everyone could talk about work all night, we don't usually want to; we like to leave the office behind at the end of the day. That number has only increased since then. More than that, you need to know what makes a question good, so you can come up with your own questions spontaneously, effectively, at the moment. Asking questions — any question — requires a certain amount of finesse.