During annual exam, why does doctor do tests like hold arms out straight with eyes closed? what does it mean if uneven?

Testing your balance: You might be talking about the "romberg test" that is a test of inner-ear function (ability to balance). It's not so much the arms being uneven that may indicate a problem, but the tendency to fall over!

Muscle testing: A physician usually checks the strength of your arms when he asks to hold out the arms straight ahead. A weakness could be suspected if there is a drift, asymmetry or shifting. The weakness can be focal, from a nerve injury or even from a brain condition.

Neurological exam: This refers to the pronator drift. A examination maneuver to detect subtle weakness on one side. Most people keep both arms up even with eyes closed. The neurological exam assists in localizing the problem.