There are several cases that could be discussed here. There could be a drop-down with no scrolling set, thus when expanded, it would make the page higher. Another case would be a drop-down with scrolling. In this case the user could scroll down the drop-down items. If your concern is that there is no visual indicator for more items downwards in the drop-down, you could overcome that by setting such height to the dropdown so that there is a partially visible item at the bottom when expanded. This approach is used in the Google Chrome browser settings drop-down, for example. Again, initially not visible scrollbars is the default mobile browsers behavior.
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