"If you are given work from your manager that is boring and tedious, what will you do?"
This is an important question for the manager. If you are hired on as a analyst and you have to do some data entry, you might not be happy about it. But if there it has to be done, then the manager has to assign the work to someone. They want to find out if you are the type of person who is willing to work on boring and tedious things. The long answer is the answer I gave when I was asked this question.
Short Answer
"If it's helping the company in any way, I don't mind doing boring work."
"My responsibility as an employee is to help the company succeed. If the work I'm given will help the company, then I'll do the best that I can no matter if it's boring or tedious."
"I don't mind doing boring and tedious work. As long as I don't have to do it for a long duration such as six months, then I really wouldn't have a problem."
Long Answer
"I trust that management knows what is best for the project. Whatever work I'm given, I'm going to do my best knowing that it's helping the entire company. I'm more oriented towards the success of the company and I'll do whatever it takes to help out. So I wouldn't mind doing boring and tedious work for awhile."
This answer is showing loyalty and being able to sacrifice personal interest for the success of the company. Maybe it was this question that helped me pass my third interview.