Nice. Except that Mode X was not usually called 13h. The former would be 320x240 and the latter 320x200. Technically X would be a variant of the 13h, though.
And actually, INT 13h is the BIOS interrupt to access block-based disk I/O functions (like sector read, track format, etc.). The INT used for mode-setting is 10h (with AH=00h and AL=13h as mode for 320x200 at 256 colors).