Specify Scope in Search Box Web Part

How to specify the scope to be used in the Search Box Web Part and hide the drop down.

Put the search scope into its own Display Group.

In order to specify the scope, you have to select the “Show scopes dropdown”. To hide the dropdown, fix the dropdown width to 1 pixel.

To set the scope, in the Miscellaneous group, set the Scope display group to the group created.