It is possible to run asp.net 2.0 applications on the same server as asp.net 1.1 applications for as long as we follow a few simple rules:

1. We can select the version of asp.net runtime to use from the asp.net property tab using Internet Infomration Services Manager.
2. ASP.NET 2.0 applications will not run under ASP.NET 1.x runtime. ASP.NET 1.x applications might run under ASP.NET 2.0 runtime.
3. You cannot have a sub application running under ASP.NET 1.x runtime while the root app runs under ASP.NET 2.0 runtime. An ASP.NET applications inherits the web.config from its parent; ASP.NET 1.x runtime cannot process the ASP.NET 2.0 web.config in the parent directory.
4. You might run an ASP.NET 1.x appplication under ASP.NET 2.0 runtime. You might have to fix a few things. This is what I have done in one of my apps:

 <location path="Projects/DataGridHelper">
  <system.web>
   <pages pageBaseType="System.Web.UI.Page" />

   <httpModules>
    <remove name="UrlRoutingModule" />
   </httpModules>
   
   <httpHandlers>
    <remove verb="GET" path="FtbWebResource.axd" />
   </httpHandlers>
  </system.web>
 </location>

Specifically, I removed some unwanted httpModules and httpHandlers and reset the attributes on the Pages element that cannot be used in ASP.NET 1.0 application. One might also need to add the following in the httpHandlers section:
<add path="WebResource.axd" verb="GET" type="System.Web.Handlers.AssemblyResourceLoader" validate="True" />