friends, how to check free space on L.V.M ?

That's a bit vague. LVM = Logical Volume Manager and it has components:
Volume Groups (VGs)- Type vgs to see which ones you have then you can do vgdisplay on the specific vg to determine how much space it has and how much has been allocated to Logical Volumes (LVs) and how much is free in the VG itself. If you run vgdisplay -v it will show you which physical volumes (PVs) make up the VG and which LVs exist within the VG.

You can use lvdisplay on specific LVs to determine their sizes.

Typically you layout filesystems or swap on top of LVs (or in rare occasion on Linux even use them as raw devices). Usually all the space in a specific LV is allocated to the fielsystem, swap or raw device that lives on it. You can see filesystem sizes with "df -h" and swap information with "swapon -s".

Thanks Friend for replying to my question.

Regards,
Aparna.