export data from oracle 10g
Unfortunately not, you cannot export from a 10g database with the 11g client. You can, though, use a dump file from a 10g database (exported with the 10g client) to import into an 11g database (with the 11g client).

Alternatively you can use the newer datapump functionality, and if you create a database link from 11g to 10g you can even transfer the data directly between them without needing to create an intermediate dump file at all.