Thank you again for your help.
It seems that LimeSurvey can do this using Expression Manager. Very easily too.
It was actually the link just below the one you sent me earlier that provides the correct information:
docs.limesurvey.org/Expression+Manager+S...e_Question_Per_Group
In short:
i. Set up a question group before the question group you want to randomly select one question from.
ii. In that question group place an equation question - call it ask1 (see relevance equation below)
iii. Set this as the equation {floor(rand(1,3.9999))} (3.9... for three options, 4.9... for 4, etc.)
iv. hide the question so participants don't see it
v. Then for each of the questions you want LimeSurvey to randomly select from set a relevance equation: ask1 == 1 [1-3]
Thanks.