Google ranks a page based on several criteria that will be covered. The most important part of a page being ranked is the relevance. read more on wikipedia
Page Rank is one of the important factors in Google's SERP rankings. To increase the PageRank of a website, get back links from popular, relevant niche sites. Where links from the relevant niche sites helps in getting good rank in SERP, there the back links from the high PR sites help in attaining high PageRank.
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