1. "How would you investigate a technology without letting anyone know you were investigating it?"
This is a tough question. Apple doesn't want people to know what it's planning, sosecrecy is key.
2. "Describe the manufacturing process for some of the components in an iPhone."
You'll need some seriously technical expertise for certain engineering jobs.
3. "How do you test the prototype of the vending machine?"
This prospective engineer was asked to solve a problem: "If vending machine takes 1$ bill and gives 75 cents worth product. But it doesn't give out change. How do you analyze what has gone wrong. You don't have any access to internals of the vending machine."
4. "Why aren't you going to work at the place where you interned?"
5. "Write a function that calculates a number's factorial using recursion."
6. "In a stream of integers from 1 to n, only one number will be repeated. How can you tell what that number is?"