Hi gpiyush152,
I have created a sample which full fill your requirement
CS.aspx
<div>
    <asp:DropDownList ID="ddlCustomers" runat="server">
    </asp:DropDownList>
    <br />
    <asp:Button ID="btnSubmit" Text="Submit" OnClick="Display" runat="server" />
    <asp:HiddenField ID="hfID" runat="server" />
</div>
<div>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            $.ajax({
                type: "POST",
                url: "CS.aspx/GetCustomers",
                data: '{}',
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: function (r) {
                    var ddlCustomers = $("[id*=ddlCustomers]");
                    ddlCustomers.empty().append('<option selected="selected" value="0">Please select</option>');
                    $.each(r.d, function () {
                        ddlCustomers.append($("<option></option>").val(this['Value']).html(this['Value']));
                    });
                }
            });
            $('[id*=ddlCustomers]').change(function () {
                $('[id*=hfID]').val($(this).find("option:selected").text());
            });
        });
    </script>
</div>
CS.aspx.cs
protected void Display(object sender, EventArgs e)
{
    Response.Redirect("DisplayDetails.aspx?ID=" + hfID.Value);
}
[WebMethod]
public static List<ListItem> GetCustomers()
{
    string query = "SELECT DISTINCT CustomerId, Name FROM Customers";
    string constr = ConfigurationManager.ConnectionStrings["conString"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query))
        {
            List<ListItem> customers = new List<ListItem>();
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            con.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    customers.Add(new ListItem
                    {
                        Value = sdr["CustomerId"].ToString(),
                        Text = sdr["Name"].ToString()
                    });
                }
            }
            con.Close();
            return customers;
        }
    }
}
DisplayDetails.aspx
<div>
    <table border="0" cellpadding="0" cellspacing="0">
        <tr>
            <td>
                ID
            </td>
            <td>
                <asp:Label ID="lblID" runat="server" />
            </td>
        </tr>
        <tr>
            <td>
                Name
            </td>
            <td>
                <asp:Label ID="lblName" runat="server" />
            </td>
        </tr>
        <tr>
            <td>
                Country
            </td>
            <td>
                <asp:Label ID="lblCountry" runat="server" />
            </td>
        </tr>
    </table>
</div>
<div>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            var id = window.location.href.split('?')[1].split('=')[1];
            $.ajax({
                type: "POST",
                url: "DisplayDetails.aspx/GetCustomerDetail",
                data: "{id:'" + id + "'}",
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: function (r) {
                    $('[id*=lblID]').html(r.d[0]);
                    $('[id*=lblName]').html(r.d[1]);
                    $('[id*=lblCountry]').html(r.d[2]);
                }
            });
        });       
    </script>
</div>
DisplayDetails.aspx.cs
[WebMethod]
public static List<string> GetCustomerDetail(int id)
{
    string query = "SELECT CustomerId, Name,Country FROM Customers WHERE CustomerId='" + id + "'";
    string constr = ConfigurationManager.ConnectionStrings["conString"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query))
        {
            List<string> customerDetail = new List<string>();
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            con.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                if (sdr.Read())
                {
                    customerDetail.Add(sdr[0].ToString());
                    customerDetail.Add(sdr[1].ToString());
                    customerDetail.Add(sdr[2].ToString());
                }
            }
            con.Close();
            return customerDetail;
        }
    }
}
ScreenShot

Hope this works for you.