The main objective is to have a good conversation and highlight your intellectual capacity and curiosity. Thus:
It is ok to ask:
- Questions that cause positive emotions and highlight consulting pros (e.g. Mck people, getting industry knowledge, becoming an expert in something, building a great network, etc)
- Questions on the topics you are excited about (e.g. data science, digital, etc)
- Topics related to the industry in which the interviewer specializes (hint: think of the most common industries in the particular office, go to the company's website and read the recent articles about these industries to come up with the good questions)
- Non-business questions (e.g. team retreats, office traditions and celebrations)
It's not ok to ask:
- Questions that can cause negative emotions (e.g. work hours, most difficult project, etc) - you don't want to finish on a negative note, right?
- The information you should learn before the interview (e.g. typical career path, etc)
- Questions that may show that you are unfamiliar with consulting work ("Will I be able to work specifically on strategic projects?")
Be prepared and good luck!