An example of an extremely common question: “Write a function to check if a binary tree is a binary search tree.”
Yes you can memorize an answer here, and the implementation of a binary tree - I think most people just do that. Knowing the inns and outs of a binary tree is probably useful if you're writing a database, or a compression format. If they're hiring someone with the capability to write a database, or compression format, this question makes plenty of sense. It also makes sense if your criteria for hiring is "did they study and understand an algorithms course?". It doesn't make much sense if they're looking for someone who can do the actual job, in my opinion.