This is a thorny issue. It comes down to copyright and license, and, particularly, what is and isn't copyrightable. If the problem is not copyrightable, then you can do whatever you wish. If the problem is copyrightable, you should assume it is copyrighted, which means you can't use it unless you have a licence to do so. The only way you are guarantee that you have a licence is to use that book in your course. If you require your students to purchase the book, then they are purchasing the license to use all of that content. You can then use the same content with them. Even providing a reference is not good enough if the material is copyrighted, and you don't have the licence.
If the problem is fundamental or factual, then it's probably not copyrightable unless there is something peculiar about the wording. Thrse questions can be complex. For example, the following would not be copyrightable:
What is the derivative of x3 + 4x?
What is the major product of the reaction between calcium carbonate and sulfuric acid?
Write the time-independent wavefunction for the electron in a ground state hydrogen atom. Then, provide the eigenvalues for this wavefunction with the kinetic energy operator.
Draw a simple set of supply and demand curves for a generic free market for a manufactured product. Describe or draw the effects of each of the following changes on the market: 1) discovery of a cheaper method of production, 2) closing of a plant, 3) government enforcement of a maximum price.
I'm having trouble coming up with a question that is copyrightable. Feel free to add one to my answer.