out of problem和out of the problem的区别我记得有一个是"没问题"的意思,另一个是"不知道"的意思,但是搞不清楚

out of question:没问题
out of the question:有问题,不行
巧记:有the的有问题,没the的没问题

question是一个多义词,其中一个是:"something about which where is discussion; something which needs to be decided".
out of the question 的解释: "impossible or not to be discussed at all"
eg: --How would you feel about postponing the announcement?
--It's out of the question. (不可能,不行)
eg: Privately I admitted that the trip was out of the question, for my money was almost gone.
eg: Of course it is out of the question to expect that we could achieve complete success in this week.

question的另一个意思是:"(the putting forward of )doubt, objection."
out of question: "certainly or undoubtedly."
eg:His courge and integrity is out of question.(他的勇气和正直是无可怀疑的)
out of question
= above all question
=beyond question
=past question
eg: My courage is beyond question.

你可能记错了,应该是 out of question 毫无疑问
out of the question 不可能

no problem：没问题
表示“不知道”好像与problem搭配的没有见过。