Actually i just wanna ask about the core i3 HD graphics on intel DH55TC motherboard does this processor support shader 3.0 on games ??

Hi.
Yes, you have an i3 processor, which allows for blazing fast gaming graphics with the graphics media accelerator.
It supports directx 11, and has pixel shader 3.0 support as well.
It allows the processor to offload the graphics signal to the graphics portion of the motherboard, allowing the processor to work way more efficiently
It has support for vertex shaders as well as the normal pixel shaders, so graphics come alive.

Just check which type of graphic chipset that you have, and download the latest drivers for it.
Some have intel chips, some have ati, and others have nvidia.

They all work equally well for the most part, for games it seems that the nvidia chips appear to work a little smoother than the ati, but the ati has it's pluses as well. The ati chips can run at a faster overall speed.
Make sure that you set the AGP aperture to the maximum amount available in your bios settings