Irrlicht Engine

How can we convert a 2d coordinate say mouse pointer coordinates to 3d world coordinates and from world coord to mouse cursor cord.

Have a look at the API, in particular at the ISceneCollisionManager.
This class (for which a pointer can be received via the ISceneManager)
provides all methods you need for this tasks.
For example, you can use getScreenCoordinatesFrom3DPosition() to
transform 3d coordinats into 2d screen coordinates.

i know this but how can i perform vice versa

I don't think you can do that(2D to 3D). Why would you want to do anyway. If you're trying select something on the screen there are tutorials for that. I'm not sure where though.

for 2d to 3d, look at the mouse picking section in the wiki-
http://www.irrforge.org/index.php/Mouse_Input
you don't need to use collision, you could just pick a set distance along the ray given by getRayFromScreenCoordinates