The convergent boundary that would most likely create a non-volcanic mountain range is the continental/continental boundary.
At this type of boundary, two continental plates collide, which can lead to the uplift of rock material and the formation of mountain ranges. An example of this is the Himalayas, which were formed by the collision of the Indian Plate with the Eurasian Plate. This process does not typically produce volcanic activity since the crust is not subducted in the same way as it is in oceanic/continental or oceanic/oceanic boundaries, where magma can lead to volcanic eruptions.
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