If we need to remove the Core.CSS, Core.JS and related files just do the following steps
1)keep the links a) and b) in a ContentPlaceHolder named "PlaceHolderAuthendicatedLinks" and keep the ContentPlaceHolder visible=false
a)<sharepoint:csslink runat="server" />--->For Core.CSS and Related CSS files
b)<sharepoint:scriptlink language="javascript" runat="server" name="core.js" defer="true" />----->For Core.JS and Related Files
<asp:contentplaceholder id="PlaceHolderAuthendicatedLinks" runat="server" visible="false">
<sharepoint:csslink runat="server"></sharepoint:csslink>
<sharepoint:scriptlink language="javascript" runat="server" name="core.js" defer="true"></sharepoint:scriptlink>
</asp:contentplaceholder>
2)if we need the Core.CSS and Core.JS files with any of a condition, just set the visible as true
3)For an example i dont want to load these files for anonymous users and i need these files for authenticated users
4)For that i did as default ContentPlaceHolder visible=false and set the visible=true in page load event using C# inline code
<script runat="server">
void Page_load(object sender, EventArgs e)
{
if (HttpContext.Current.Request.IsAuthenticated)
{
PlaceHolderAuthendicatedLinks.Visible = true;
}
}