Some good questions to ask are:
How do you interact with founders after investing? -you are going to benefit more from someone who want to be involved and make intros, rather than someone passive.
This also lead to asking what their bandwidth is. How many boards do they serve on?
What's your process. How do you make a decision?
Do you have the necessary relationships to help us build the syndicate for our next round of funding?
What are your return expectations? What is your exit strategy?
How many investments they have made in the past 6 months to 1 year.
What is the size of the fund you would be investing from? What is the average size of your first round of investments?
What was the toughest portfolio company experience you went through? How do you work through these tough situations?
"What specific criteria do you have for investing in a company?"