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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You have to create an "application" for both of the virtual directories, and then you'd assign their ASP.NET version using the ASP.NET tab under web site properties.
Also, as @sunny mentioned, you'd need to have two different application pools, and each virtual directory would have to be pointed to a different application pool. Because different versions of ASP.NET cannot run within the same application pool.