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When using the Generate Page specific javascript option in HTML settings, wanted to know about it more detailed I mean when should we use it and when we shouldn't use it.

Most importantly wanted to know does it effect a Master Page and the menu.

This is from the help:

Generate external JS file for page specific scripts.
Enable this option to generate a separate JS file with the script used by a page. The name of the file will be the same as the page name. So 'index.html' will generate a 'index.js' file.

Whether or not you enable this, is a personal preference.