The Following code sample shows how to get selected text out from ASP .NET Drop Down List.
<script type="text/javascript">
function GetSelectedText() {
var ddlID = '#' + '<%= ddlEmployees.ClientID %>';
var selectedText = $(ddlID + " option:selected").text();
return selectedText;
}
</script>
<asp:DropDownList ID="ddlEmployees" runat="server">
<asp:ListItem Text="Employee Name 1" Value="1"></asp:ListItem>
<asp:ListItem Text="Employee Name 2" Value="2"></asp:ListItem>
<asp:ListItem Text="Employee Name 2" Value="2"></asp:ListItem>
</asp:DropDownList>
Source: https://www.nilebits.com/blog/2010/05/how-to-get-dropdownlist-selected-text-in-asp-net-by-using-jquery/