I'm not entirely sure that I'm interpreting what you mean by "perplexity" correctly (I think I am..), but I tend to think that among the many different types of causes of anxiousness (which can sometimes be blurred, in terms of definition, with "anxiety"), there's a good chance that "perplexity" causes the "anxiousness", rather than the other way around.
The world/life is full of so many different types of situations, it's kind of difficult to zero in on real "precise-ness" here, but I think a complicating factor can be if a person brings a little anxiety to the situation in the first place.
There are people who are (for lack of more polite terms in one case) too young, too immature, too inexperienced, or just too stupid (that's the "case" I was referring to) to to even bring any anxiety to the situation that, maybe, should involve more caution. Then you have people who are certainly skilled and experienced and probably should not be anxious, but there are also people who are skilled and experienced who are going to take something to "the next level" and things get more iffy with regard to how much caution/risk (of one kind or another) even that person should take.
Getting the matter of anxiety out of the way and getting back to "anxiousness", the person who isn't quite sure of what he should be doing, or of how, exactly, to move forward (even from a place of little or no anxiety at the start) (in other words, what I think you mean by "perplexity") would, I think, most likely get at least a little anxious. Maybe people who don't know they don't really know what they're doing would not experience being anxious, but I think people who know they don't know what they're doing would a) benefit from taking their anxiousness as a sign that they need to learn more skill/have more information/more equipment (in other words, a sign that they're not ready for/capable of doing something; or b) ask them-self if they brought in some kind of anxiety at the start (and whether they should have, and/or what that was/is "all about"); and whether or not what appears to be (or even may be) simple anxiousness over some actual "next step"/accomplishment (in site of adequate skill, equipment,information, etc.) would call for ironing out any "original anxiety" before moving ahead.
Sometimes a situation doesn't allow "the luxury" of not moving at all or not trying to move ahead with some aim/goal.