This code show how to Get Search Results with Default Search Scope using SharePoint 2010 Search web Service.
//_vti_bin/search.asmx
SearchSoapClient soc= new SearchSoapClient ();
soc.ClientCredentials.Windows.ClientCredential.Domain ="XYZ";
soc.ClientCredentials.Windows.ClientCredential.Password ="xxxxx";
soc.ClientCredentials.Windows.ClientCredential.UserName ="xxxxx";
StringBuilder queryXml = new StringBuilder(); ;
queryXml.Append("<QueryPacket>");
queryXml.Append("<Query>");
queryXml.Append("<Range>");
queryXml.Append("<Count>50</Count>");
queryXml.Append("</Range>");
queryXml.Append("<Context>");
queryXml.Append("<QueryText type='STRING'>");
queryXml.Append("products:\"XYZ\" path:\"http://www.c-sharpcorner.com/code/create.aspx?CodeId=535\"");
queryXml.Append("</QueryText>");
queryXml.Append("</Context>");
queryXml.Append("</Query>");
queryXml.Append("</QueryPacket>");
soc.Query(queryXml.ToString());