I have one page it is refering from master page.
Validation is working fine for textboxes and not for dropdown.
 
Please find below the html and c# code.
<asp:Content ID="Content2" ContentPlaceHolderID="ContentPlaceHolder1" runat="Server">
    <ajaxToolkit:ToolkitScriptManager ID="ToolkitScriptManager1" runat="server">
    </ajaxToolkit:ToolkitScriptManager>
    <div>
        <h2 class="title ">
            Add Supplier Details</h2>
    </div>
    <div style="margin-left: 50px">
        <div id="errorContainer">
            <p>
                 Please correct the following errors and try again:</p>
            <ul />
        </div>
        <div>
            <asp:Label ID="lbladdsupplier" runat="server" CssClass="lblmsg"></asp:Label>
        </div>
        <table>
            <tr class="row">
                <td>
                    <asp:Label ID="lblcompanyname" runat="server" Text="Company Name :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:DropDownList ID="companynameDDL" runat="server" Width="205px" CssClass="chzn-select"
                        Height="25px">
              
                    </asp:DropDownList>
                </td>
       
                <td class="gaptdwidth">
                </td>
                <td>
                    <asp:Label ID="lbladdress" runat="server" Text="Address :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd" rowspan="2">
                    <asp:TextBox ID="txtaddress" runat="server" Width="197px" CssClass="textbox" TextMode="MultiLine"
                        Height="65px"></asp:TextBox>
                </td>
            </tr>
            <tr class="row">
                <td>
                    <asp:Label ID="lblsuppliername" runat="server" Text="Supplier Name :" Width="150"
                        CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:TextBox ID="txtsuppliername" runat="server" CssClass="textbox"></asp:TextBox>
                </td>
            </tr>
            <tr class="row">
                <td>
                    <asp:Label ID="lblphonenumber" runat="server" Text="Phone No. :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:TextBox ID="txtphonenumber" runat="server" CssClass="textbox"></asp:TextBox>
                </td>
                <td class="gaptdwidth">
                </td>
                <td>
                    <asp:Label ID="lblmobilenumber" runat="server" Text="Mobile No. :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:TextBox ID="txtmobilenumber" runat="server" CssClass="textbox"></asp:TextBox>
                </td>
            </tr>
            <tr class="row">
                <td>
                    <asp:Label ID="lblemailid" runat="server" Text="EmailID :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:TextBox ID="txtemailid" runat="server" CssClass="textbox"></asp:TextBox>
                </td>
                <td class="gaptdwidth">
                </td>
                <td>
                    <asp:Label ID="lblfax" runat="server" Text="Fax :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:TextBox ID="txtfax" runat="server" CssClass="textbox"></asp:TextBox>
                </td>
            </tr>
            <tr class="row">
                <td>
                    <asp:Label ID="lbldate" runat="server" Text="Date :" Width="150" CssClass="label"></asp:Label>
                </td>
                <td class="tabletd">
                    <asp:TextBox ID="txtdate" runat="server" CssClass="textbox"></asp:TextBox>
                </td>
                <ajaxToolkit:CalendarExtender ID="CalendarExtender1" TargetControlID="txtdate" runat="server" />
            </tr>
        </table>
        <br />
        <center>
            <fieldset class="btnfieldset">
                <legend class="legend" align="center">Operations </legend>
                <table cellspacing="20px" align="center" style="height: 74px">
                    <tr>
                        <td>
                            <asp:Button ID="btnadd" runat="server" Text="Save" CssClass="button" BorderStyle="Outset"
                                OnClick="btnsave_Click" />
                        </td>
                        <td>
                            <asp:Button ID="btnreset" runat="server" Text="Reset" CssClass="button" BorderStyle="Outset"
                                OnClick="btnreset_Click" />
                        </td>
                    </tr>
                </table>
            </fieldset>
        </center>
    </div>
    <script src="Scripts/chosen.jquery.js" type="text/javascript"></script>
    <script type="text/javascript">
        //On Page Load
        $(".chzn-select").chosen();
        $(".chzn-select-deselect").chosen({ allow_single_deselect: true });
        //On UpdatePanel Refresh
        var prm = Sys.WebForms.PageRequestManager.getInstance();
        if (prm != null) {
            prm.add_endRequest(function (sender, e) {
                if (sender._postBackSettings.panelsToUpdate != null) {
                    $(".chzn-select").chosen();
                    $(".chzn-select-deselect").chosen({ allow_single_deselect: true });
                }
            });
        };
    </script>
    <script type="text/javascript">
      
        $(document).ready(function(){
           $.validator.addMethod('selectNone',function(value, element) {
              return this.optional(element) || (value.indexOf("--Select--") == 0);
          }, "Please select an option");
        $("#form1").validate({
              // This prevents validation from running on every
              //  form submission by default.
               onsubmit: false,
//                                submitHandler: function (form) 
//                                {
//                                    form.submit();
//                                },
                                rules: 
                                {
                                <%=companynameDDL.UniqueID %>: {                  
                                     selectNone: true
                                    },
//                                     <%=companynameDDL.ClientID %>: 
//                                     {
//                                      
//                                        selectNone: true
//                                     },
                                     <%=txtaddress.UniqueID %>: 
                                    {                        
                                        required: true
                                       
                                    },
                                     <%=txtsuppliername.UniqueID %>: 
                                     {                        
                                        required: true
                                       
                                     },
                                     <%=txtphonenumber.UniqueID %>: 
                                     {                        
                                        required: true
                                     },
                                      <%=txtmobilenumber.UniqueID %>: 
                                     {                        
                                        required: true,
                                        digits:true
                                     },
                                       <%=txtemailid.UniqueID %>: 
                                     {                        
                                        required: true
                                     },
                                       <%=txtfax.UniqueID %>: 
                                     {                        
                                        required: true
                                     },
                                       <%=txtdate.UniqueID %>: 
                                     {                        
                                        required: true
                                     }
                                }, 
                                messages: 
                                {
                                  
                                    <%=companynameDDL.UniqueID %>: 
                                     {
                                      
                                        selectNone: "Please select option"
                                     },
                                     <%=txtaddress.UniqueID %>: 
                                    {                        
                                        required: "Please enter address"
                                       
                                    },
                                    <%=txtsuppliername.UniqueID %>:
                                    {
                                        required:"Please enter supplier name"
                                    },
                                   <%=txtphonenumber.UniqueID %>:
                                    {
                                        required:"Please enter phone number"
                                    },
                                    <%=txtmobilenumber.UniqueID %>:
                                    {
                                        required:"Please enter mobile number",
                                        digits:"Mobile number should be numbers only"
                                    },
                                  
                                    <%=txtemailid.UniqueID %>:
                                    {
                                        required:"Please enter email address"
                                    },
                                     
                                    <%=txtfax.UniqueID %>:
                                    {
                                        required:"Please enter fax number"
                                    },
                                    <%=txtdate.UniqueID %>:
                                    {
                                        required:"Please select date"
                                    }
                                 },
                                 errorContainer: $('#errorContainer'),
                                 errorLabelContainer: $('#errorContainer ul'),
                                 wrapper: 'li'
                });
                    $("#ContentPlaceHolder1_btnadd").click(function() {
                      return $("#form1").valid();  
                    });
        });
    </script>
</asp:Content>
 
private void FillCompanyName()
{
    CompanyBLL _objFillCompanyname = new CompanyBLL();
    try
    {
        DataSet ds = new DataSet();
        ds = _objFillCompanyname.ViewCompanyDetails();
        if (ds.Tables[0].Rows.Count > 0)
        {
            companynameDDL.DataSource = ds;
            companynameDDL.DataTextField = "company_name";
            companynameDDL.DataValueField = "company_id";
            companynameDDL.DataBind();
            companynameDDL.Items.Insert(0, new ListItem("--Select--", "0"));
            companynameDDL.SelectedItem.Selected = false;
            companynameDDL.Items.FindByText("--Select--").Selected = true;
        }
        else
        {
            lbladdsupplier.Text = "Failed to Fill Company Names";
        }
    }
    catch (Exception ex)
    {
        lbladdsupplier.Text = ex.Message;
    }
}