This way.
HTML
<link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script type="text/javascript" src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
<div class="panel-group" id="accordion" role="tablist" aria-multiselectable="true">
<div class="panel panel-default">
<div class="panel-heading" role="tab" id="headingOne">
<h4 class="panel-title">
<a data-toggle="collapse" data-parent="#accordion" href="#collapseOne" aria-expanded="true"
aria-controls="collapseOne">Header 1 </a>
</h4>
</div>
<div id="collapseOne" class="panel-collapse collapse in" role="tabpanel" aria-labelledby="headingOne">
<div class="panel-body">
Content 1
</div>
</div>
</div>
<div class="panel panel-default">
<div class="panel-heading" role="tab" id="headingTwo">
<h4 class="panel-title">
<a class="collapsed" data-toggle="collapse" data-parent="#accordion" href="#collapseTwo"
aria-expanded="false" aria-controls="collapseTwo">Header 2 </a>
</h4>
</div>
<div id="collapseTwo" class="panel-collapse collapse" role="tabpanel" aria-labelledby="headingTwo">
<div class="panel-body">
Content 2
</div>
</div>
</div>
<div class="panel panel-default">
<div class="panel-heading" role="tab" id="headingThree">
<h4 class="panel-title">
<a class="collapsed" data-toggle="collapse" data-parent="#accordion" href="#collapseThree"
aria-expanded="false" aria-controls="collapseThree">Header 3 </a>
</h4>
</div>
<div id="collapseThree" class="panel-collapse collapse" role="tabpanel" aria-labelledby="headingThree">
<div class="panel-body">
Content 3
</div>
</div>
</div>
<br />
<br />
<asp:Button ID="Button1" Text="Submit" runat="server" CssClass="btn btn-primary" />
<asp:HiddenField ID="PaneName" runat="server" />
</div>
<script type="text/javascript">
$(function () {
var paneName = $("[id*=PaneName]").val() != "" ? $("[id*=PaneName]").val() : "collapseOne";
//Remove the previous selected Pane.
$("#accordion .in").removeClass("in");
//Set the selected Pane.
$("#" + paneName).collapse("show");
//When Pane is clicked, save the ID to the Hidden Field.
$(".panel-heading a").click(function () {
$("[id*=PaneName]").val($(this).attr("href").replace("#", ""));
});
});
</script>
Code
protected void Page_Load(object sender, EventArgs e)
{
if (this.IsPostBack)
{
PaneName.Value = Request.Form[PaneName.UniqueID];
}
}