Enable Disable Validators based on DropDownList selection in ASP.Net

I have tested it and its working fine here.

Please run this code in a new website.

HTML

<table border="0" cellpadding="0" cellspacing="0">
    <tr>
        <td>
            Validation required
        </td>
        <td>
            <asp:DropDownList ID="ddlTypes" runat="server" AutoPostBack="true" OnSelectedIndexChanged="Types_OnSelectedIndexChanged">
                <asp:ListItem Text="Select" />
                <asp:ListItem Text="City" />
                <asp:ListItem Text="Name" />
            </asp:DropDownList>
        </td>
    </tr>
    <tr>
        <td>
            Name
        </td>
        <td>
            <asp:TextBox ID="txtName" runat="server" />
            <asp:RequiredFieldValidator ID="rfvName" ErrorMessage="Name is required" ControlToValidate="txtName"
                runat="server" />
        </td>
    </tr>
    <tr>
        <td>
            City
        </td>
        <td>
            <asp:TextBox ID="txtCity" runat="server" />
            <asp:RequiredFieldValidator ID="rfvCity" ErrorMessage="City is required"
                ControlToValidate="txtCity" runat="server" />
        </td>
    </tr>
</table>
<asp:Button Text="Submit" runat="server" />

C#

protected void Page_Load(object sender, EventArgs e)
{
    //If you want by default name TextBox shold be enabled
    this.rfvName.Enabled = true;
    this.rfvCity.Enabled = false;
}

protected void Types_OnSelectedIndexChanged(object sender, EventArgs e)
{
    string code = this.ddlTypes.SelectedItem.Text;
    switch (code)
    {
        case "Name":
            this.rfvName.Enabled = true;
            this.rfvCity.Enabled = false;
            break;
        case "City":
            this.rfvName.Enabled = false;
            this.rfvCity.Enabled = true;
            break;
        default:
            this.rfvName.Enabled = false;
            this.rfvCity.Enabled = true;
            break;
    }
}