1.How do you communicate bad news/project delays to team / upper management and customer? 
2. How do you handle an unhappy / disgruntled team member? 
3. If top management asks you to deliver a project within unrealistic time-lines, how do you handle the scenario? 
4. How do you handle conflicts between two team members?
5. What is your style to track the progress of a project? 
6. Have you ever failed in a project? How did you manage the failure? 
7. Some high level questions on Budget management and Risk Management 
8. Explanation of standard project management terms like SOW,WBS, Activity time estimate, Three point estimate, critical path. 
9. How do you convince your management for taking certain direction or action relating to project? 
10. You might be asked some PMI concepts from PMIBOK