<ASP:dropdownlist id="ddlLastName" runat="server" bla bla></asp:dropdownlist>

 

<input type=button value="clear" onclick="Clear_ddls()">

-------------------------------------------------------------------------

-- you need to use the ClientId property of the controls to know the name. try:
-------------------------------------------------------------------------
function Clear_ddls()
{
document.getElementById('<%=ddlLastName.ClientId%> ').selectedIndex =
0;
}

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