The target search results page is */_layouts/OSSSearchResults.aspx*. In Site Actions >Search Setting> selected Show, do not include contextual scopes for Site collection Search Dropdown Mode. It is not displaying contextual scope in the search box but in target results page, it adds the contextual scope 'This Site: SiteTitle'
Env: SharePoint Server 2010
Pls let me know if anyone has solution for it.