Can we apply for Adsense without sending Sitemap to webmaster tools ?
Here are the published AdSense requirements, policies, and terms. The word "sitemap" never appears. Nor does a sitemap seem to have any obvious relevance to AdSense, since the ads are based on the pages the ads appear in not some overall spidering of the site.
Your demand for "100% correct knowledge" suggests you have some doubts about this. Maybe you should explain why you're asking in your question.