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I am trying to figure out whether to use Google App Engine or other available PaaS. During my research, I am trying to figure out if a particular website using google app engine or not - Is there any known method to figure this out ?
Sorry for the basic question, but appreciate any help. Thanks.

You can recognize a GAE-based site based on the server's domain:
*.appspot.com - default domain of standard GAE apps
*.appspot-preview.com - default domain of newer flex GAE apps
custom domains mapped to ghs.google.com or ghs.googlehosted.com. See step 5 in the Adding a custom domain for your application procedure and how does ghs.google.com work?. Note that I'm unsure if this doesn't also apply to other Google products, not only to GAE.
There may be other such domains as well.
You can also check the Server header in the responses coming from the site. From Headers added or replaced:
Server
Set to Google Frontend. The development server sets this to
Development/x, where x is the version number.

ping the domain and if you have something with ghs.googlehosted.com:
PING ghs.googlehosted.com (216.58.213.147): 56 data bytes
It's a GAE application. You can also check the headers in requests from your browser's dev tools.