When am accessing my dedicated server with root passwrod and using the following command then error appears:
LSNRCTL> start
Starting /opt/oracle/product/10.2/db_1/bin/tnslsnr: please wait...

TNS-12546: TNSermission denied
TNS-12560: TNSrotocol adapter error
TNS-00516: Permission denied
Linux Error: 13: Permission denied

can you please help me out.

thanks & regards

This isn't a "Linux Error" but rather a series of "Oracle Errors" all telling you the same thing: You don't have permission to do what you are trying to do.

You need to insure:
a) There is a single owner/group for the files in the directory (e.g. oracle/dba - see "man chown")
b) The owner at least has permissions to read and execute the files. (see "man chmod).
c) That you are starting your processes as the user in the first item (e.g. oracle) so that the user has the correct permissions.

I'm not a DBA but on quick Google see people have gotten this error on HP-UX, Solaris and other UNIX/Linux variants so we know it is not specific to Linux. You should always look at the first error line rather than the last one when troubleshooting. That is to say the TNS... messages are the cause of the "Error 13" later rather than vice versa.

Also note that Oracle has its own security configuration so it may be something within your Oracle configuration files rather than file permissions generating the error. I can't offer any guidance on that because I'm not a DBA.