I'm assuming you're trying to find problems to solve so as to start a business. This seems like a fine thing to do. Your approach could be a bit better, though.
1. You're asking about "unsexy industries." The people who work in those industries might care quite a lot about their job, so your description isn't going to be appealing.
2. You're implicitly insulting any developer who works there, based on how you define such industries: you're saying they're probably not talented.
3. You're asking in the wrong place.
4. The term "sexy" is going to turn a bunch of people off regardless of where they work.
5. Your phrasing makes this sound like an exam or a test.