Question

why mountain areas have less population density and plain areas have high​

Answer 1

Answer:

Because just about anything you might want to do is harder and more expensive in the mountains, compared to the plains: moving around, building houses ior infrastructure, growing crops, you name it. In sufficiently steep and high mountains, all those things are effectively impossible.

Answer 2

Answer:

Because mountainous areas are less accessible, making it harder and more expensive to construct buildings, infrastructure and to provide services and amenities. There is also less likelihood of there being enough access to fertile land in order to sustain any amount of animals or crops.