What type of research questions would lead to a qualitative study? To a quantitative one?
It would be easier to answer this if we knew the general area within social sciences that you are studying. In general, however, research questions that lead to quantitative studies are ones that can be asked using phrases like "what is the correlation" and "what level of...?" Qualitative studies come out of questions like "what kind of" or "in what way do...?"
For example, a quantitative study in sociology might ask "what is the correlation between the number of years of schooling that a person has and the likelihood that they have ever been arrested?" This is clearly something that can be studied using numbers. By contrast, a qualitative study might ask "in what way does the quality of education in a community affect the life chances of the people in that community?" This sort of question cannot be so readily reduced to numbers.