I am trying to pxe boot tinycore 4:-
pxelinux.cfg/default is as
kernel vmlinuz
initrd core.gz nfsmount=ip:/nfs shared cd contents

the system boots into terminal it should boot into graphical dekstop.

Have you tried typing: startx

I tried startx as normal and sudo user it show:
-sh: startx: not found

You didn't send the full iso over.

i have tried sending full iso also by using kernel memdisk append iso=tinycore.iso
it also boot to terminal
When i directly boot system using cd it boots to graphical user interface.

If the client can boot to the cd and a pxe seems to fail then we are kind of back to some basic issues.

One may be this client version or implementation of pxe. Any 2.x ought to work fine but if worse comes to worse you may need to try it with gpxe/ipxe just to check that.

Another is your tftp server. I guess it could be out of whack from (I think it is block size??) or some such setting. Can you monitor that? Is it tftp32 or what?

Another is the network or some issue with the tftp being connectionless. Again solution may be gpxe to a different transport like ftp or http or iscsi.

Another is your iso image on the host. Could there be some mistake also in your setup or pointing to or leftovers somewhere making an error?

Some memory issues with pxe where it can't free up the area.

Is this version known to be pxe bootable?

If you are at limit then that may be the issue.

If you send over the iso and get a text prompt, you should still be able to view the filesystem as it should be.

I have only tried it a few times, keep-pxe or some option like that. Never seemed to make a difference on some very old low mem systems.