Hi Poonam123,
I will recommend you to use AutoComplete feature which can populate the DropDownList options dynamically.
It will be too complicated to load the options by dragging the scrollbar.
For example you need to decide how many items need to be added when dragging the scrollbar onetime, you still need to redraw the List every time which may consume lots of resources.
Another issue is suppose users have to select the last option then unless user scroll and loads all the data can't able to select the option.
Again another issue is suppose user clicked outside the DropDownlist then loaded data will lost and users have to load it again and again.
So my suggestion is to use AutoComplete TextBox so that user is able to type the letters and quickly select the option.