Is it possible to have two virtual directories under the same website in IIS but have the virtual directories be using different versions of the .net framework?
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It depends if you mark them as "applications". Application virtual directories can use different framework. Make sure you associate them to different application pools. Never mix two .NET framework versions in one application pool.
One important note: if you create a virtual directory as an application, you don't share session state and other application related objects. Also Server.MapPath("~") and other ServerURL related methods an properties will point to the physical directory of the virtual directory and not to the main root.