We have recently set up a DR site for our Oracle 11g database server at a remote location as a standby database.
How do I verify that the archive logs are being applied to the standby database and what is the last one thats been applied?
Check out these links from the 11g Data Guard Concepts and Administration (you don't need Data Guard to be configured for these to be useful):
If you have Grid Control, it's even easier. There's a link under Maintenance that allows you to maintain your Data Guard configuration, including a graphical display of transport and apply lag times, last log received/applied, and other goodies.
You can use the following query on the Primary database
and on the standby database
If the result is same it means your standby database is in sync with the primary database.