Question

which metals does not produce hydrogen gas when added to acid

Answer 1

All the metals having their activity level lower than the hydrogen don't produce hydrogen with acids.
Simply, in order to produce hydrogen from acid, a metal has to be above from the hydrogen in the electrochemical series(metal has to react more vigorously or more reactive).

So the metal like gold, silver, copper ,platinum etc don't produce hydrogen with acids as they can't able to replace the hydrogen in the reaction. 

hope this will helps you.

Answer 2

These metals are those metals that are below hydrogen in the electrochemical series. Some examples of such metals are copper, mercury, gold, and platinum. They do not liberate hydrogen when they react with dilute acids. In electrochemical series, the elements are arranged in the decreasing order of potential values.