I want OS for Beagleboard which can support HARD REAL TIME OS Feature. is Ubuntu HARD Real time OS ?
Ubuntu uses Linux, which is not a real time kernel. Although you might be able to start from an Ubuntu system and modify the kernel so that it does meet real time guarantees, I don't think it would be correct to say that Ubuntu is a real time OS.
See How can I install a realtime kernel? which is a related question on modifying Ubuntu to run a Linux kernel that has been modified to add real time features.