11. (15 points) In a math competition, answering a mandatory question correctly earns 3 points, and answering it incorrectly deducts 2 points; answering a selective question correctly earns 5 points, and answering it incorrectly earns 0 points. Xiao Ming answered all the questions and got 15 of them correct, scoring a total of 49 points. How many mandatory questions were there in the math competition?
【Analysis】First, assume all questions are multiple-choice questions, and solve based on the difference in quantity.
【Solution】Solution: According to the problem, we know:
Assume the math competition consists entirely of multiple-choice questions, then Xiao Ming scores $5 \times 15=75$ points for answering 15 questions correctly; and replacing a multiple-choice question with a mandatory question, regardless of whether it is answered correctly or not, reduces Xiao Ming's score by 2 points. Therefore, the number of 3-point mandatory questions is ( $75-49) \div 2=13$ (questions).

Answer: There are 13 mandatory questions in the math competition.