I want ListBox/DropDownList to keep its value when SelectedIndexChanged.The problem is when page is refreshed it goes back to the top of index.

It is happening because you are loading the dropdownlist/Listbox every time when page is called.You have to use ISpostback property i.e. You have to load dropdownlist for the first time when page is called.
Write the below code in pageload event

Page_load Event ()
{
if (!ispostback)
{
load your dropdownlist /Listboxlist
}
}

I think this should work . Try and let me know

Here is a small example that you could follow

<asp:dropdownlist id="DropDownList1" runat="server" xmlns:asp="#unknown">
onselectedindexchanged="DropDownList1_SelectedIndexChanged" AutoPostBack="true">


Following is in .cs

public partial class DropDownListSelectedIndex : System.Web.UI.Page
    {
        protected void Page_Load(object sender, EventArgs e)
        {
            if (!IsPostBack)
            {
                DropDownList1.DataSource = DataClass2.getData();
                DropDownList1.DataTextField = "s";
                DropDownList1.DataValueField = "s2";
                DropDownList1.DataBind();
            }

        }

        protected void DropDownList1_SelectedIndexChanged(object sender, EventArgs e)
        {
            DropDownList dptList = (DropDownList)sender;
            Label1.Text = dptList.SelectedIndex.ToString();
        }
    }
//Following class is used just to get the data
    public class DataClass2
    {
        public string s { get; set; }
        public string s2 { get; set; }
        public static List<dataclass2> getData()
        {
            List<dataclass2> dataLst = new List<dataclass2>();
            for (int i = 1; i <= 5; i++)
            {
                DataClass2 data = new DataClass2();
                data.s = "S" + i;
                data.s2 = "M" + i;
                dataLst.Add(data);
            }
            return dataLst;
        }
    }</dataclass2></dataclass2></dataclass2>

Thank You all for Your response but i figured out the most suitable technique... I just needed to create a new eventhandler aftr page load referrenced to DropDownlist Selectedindexchanged event and Set DropDownlist Autopostback Proprty to True..


Ex:

Page_load()
{
if(!IsPostback)
{
//Some Code//
//Databound //
}

DropDownList1.SelectedIndexChanged += new EventHandler(DropDownList1_SelectedIndexChanged);
}