In no particular order:
- Why do you think you need a CTO? Why me?
- What is the business plan?
- What's the plan when the current idea fails and we need to change?
- What's the current funding runway?
- Why are you trying to solve this problem?
- What customers do you already have lined-up to pilot the solution?
- What's your plan for further funding if we're not sustainable before the runway runs out?
- What constraints have current investors applied to the business?
- What percentage of the business has been sold to angel/VC investors? How much more can/will be sold as the need arises to fund the business until it's profitable?
- What's the business' exit strategy (be bought, go public, stay private...)?
- Who's already on the team - and why?
- What leeway will I, as CTO, have to make hire/fire decisions for my team(s)?