No no. You're not understanding the DX concept. DX is released based on the operating system. XP was DX9, Vista was DX10, W7 is DX11, W8 is DX11.1, W8.1 is DX11.2 and W10 is DX12. If you have a GPU that supports the latest DX version, you'll be able to run games in that version. If not, you'll still be able to play the game (if supported) but in an older version of DX.
While possible, you don't typically change the DX version you want to play a game in. For example, Civilization 5 allows people to choose between DX 9 or DX10/11 depending on OS and GPU.
Because the 275 only runs up to DX10, native, all games will run in DX10 if they support it.