This is a no-brainer for mass (non-count) items: Use singular.
I have no paper. I have no money. I have no trust in politicians. I have no patience with children.
For the count items, it's trickier. My gut feeling is that the concrete nouns are usually plural in that situation, and the abstract nouns are usually singular.
Again, the same principles apply. In the case of a linear equation, which has only one solution, "It has no solution." In the case of a higher order equation, which typically has more than one solution, "It has no solutions." In the general case I would use the singular.