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Is there any default options or modules in Joomla 3 that allow display the select dropdown in the Category Blog page so that I can choose how many articles per page to show?
No, there isn't. The amount of articles is defined by multiple params. See ContentModelCategory line 189:
$limit = $params->get('num_leading_articles') + $params->get('num_intro_articles') + $params->get('num_links');
Required, but never shown