Hi Ron,
Yes it can be done, in fact you can arbitrarily have any question set to what you want it to be and any others to be randomized. The way I know how to do it needs to have the questions in two question separate banks, and set the quiz Layout > Question Order to As shown on the edit screen. Do NOT set it for shuffled randomly.
Put your first question in one question bank (no shuffle), plus any others you might want to set to show up as a particular question, like your first one.
Put all other questions in another question bank (shuffled.) You seperate the banks so that you do not accidentally have your first question show up as one of your randomized questions.
Create your quiz, and as mentioned in the quiz Edit settings, set Layout > Question Order to As shown on the edit screen. Question behavior > Shuffle within questions can be set to Yes or No, whichever you prefer.
Now, switch to Edit quiz. Under Question bank contents, Select a category: select your No Shuffle question bank and pick the question you want to be first and add to the quiz like your normally do.
NOTE: At the top of the Editing Quiz page, make sure you are on the tab for Editing quiz.
For your second and subsequent questions, you will add them to the test by clicking the button that is on the quiz page, named Add A Random Question. In the pop up window change the Category to your shuffled question bank, then click the Add Random Question button. Repeat until you have as many questions as you want in the quiz.
As mentioned before, at any point, instead of adding another question using the Add Random Question button, you can select from your non shuffled question bank like you did for the first one.
Check here for more info: http://docs.moodle.org/26/en/Building_Quiz#Adding_a_random_question
HTH,
AL