Dynamically create DropDownList on Client Side using jQuery in ASP.Net

Here I have created sample that will help you out.

HTML

<div>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
    <script type="text/javascript">
        function Add() {
            var ddlId = "ddl" + (parseInt($('[id*=hfDDLId]').val()) + 1);
            var optionList = [1, 2, 3];
            $('[id*=div1]').append(getDropDownList(ddlId, ddlId, optionList));
            $('[id*=hfDDLId]').val(parseInt($('[id*=hfDDLId]').val()) + 1);
            return false;
        }

        function getDropDownList(name, id, optionList) {
            var combo = $("<select></select>").attr("id", id).attr("name", name).attr("runat", "server");
            $.each(optionList, function (i, el) {
                combo.append("<option>" + el + "</option>");
            });
            return combo;
        }

        function Remove() {
            var ddlId = $('[id*=hfDDLId]').val();
            $('[id$=ddl' + parseInt(ddlId) + ']').remove();
            $('[id*=hfDDLId]').val(parseInt($('[id*=hfDDLId]').val()) - 1);
            return false;
        }

        function GetValue() {
            $('[id*=hfSelectedValue]').val($('[id*=ddl1]').val());
        }    
    </script>
    <div id="div1" runat="server">
    </div>
    <input type="hidden" id="hfDDLId" value="0" />
    <asp:Button Text="Add" runat="server" OnClientClick="return Add()" />
    <asp:Button Text="Remove" runat="server" OnClientClick="return Remove()" />
    <input type="hidden" id="hfSelectedValue" runat="server" />
    <asp:Button Text="Get Value" runat="server" OnClick="GetValue" OnClientClick="GetValue()" />
</div>

Code

protected void GetValue(object sender, EventArgs e)
{
    string selected = hfSelectedValue.Value;
}

Screenshot

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