Which system database of which we can't take the backup?

We can't take the backup of the tempdb database and the tempdb database is a universal "scratch" area within SQL Server. The SQL Server engine utilizes tempdb as a temporary storage area when doing sorting and aggregation operations. Applications can also utilize tempdb through the use of temporary tables, procedures, and cursors. You can look at tempdb as serving a function similar to the paging file within Windows. Anything created within tempdb, by its very nature, is temporary. When you restart a SQL Server instance, tempdb is wiped out and re-created.

You should never create any object that is required to be persistent within tempdb, because you will lose anything stored in tempdb when the instance is restarted.

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