The XFX Radeon r7-240a-clh4 and XFX Radeon r7-250a-zlh4 video cards do not seem to be able to generate 3840x2160 @ 30 Hz video modes over HDMI, even though I believe their hardware is supposed to be capable of this (~299 MHz pixel clock).
At least with my se39uy04 39" Seiki television, the Radeon X.org driver happily passed through the five 3840x2160 @ 24-30 Hz that the television's advertises in its EDID modes to xrandr, meaning that driver thinks it can support those video modes, but, if I select any of them, the telvision just says "mode not support." In comparison, if I make a custom video mode for 3840x2160 @ 15Hz, the 4k TV displays that fine.
I observed this problem with the r7-240 and r7-250 on Linux 3.13.0-x86_64, and with the r7-250 on Linux-3.14-rc3-x86_64 (I haven't tried the r7-240 on it).
I am reporting this bug now primarily in the hopes that doing so might eventually benefit other users. As for my own use, it looks like I'm probably not going to use either of these video cards anyhow, because they appear not to support dual link, contrary to Tiger Direct's description fo the r7-250 card, by the way (yes, I tried faking dual link connector information in atombios.c). That said, I am happy to do further experiments with these cards if that would be helpful.
Adam Richter