Like this :
string ext = System.IO.Path.GetExtension(this.File1.PostedFile.FileName);
string contenttype = String.Empty;
OR
string ext = Path.GetExtension(filename);
switch(ext)
{
case ".doc":
contenttype = "application/vnd.ms-word";
break;
case ".docx":
contenttype = "application/vnd.ms-word";
break;
case ".xls":
contenttype = "application/vnd.ms-excel";
break;
case ".xlsx":
contenttype = "application/vnd.ms-excel";
break;
case ".jpg":
contenttype = "image/jpg";
break;
case ".png":
contenttype = "image/png";
break;
case ".gif":
contenttype = "image/gif";
break;
case ".pdf":
contenttype = "application/pdf";
break;
}