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Category pages are not intended to be exhaustive lists. They are navigation aids; merely groupings of related, existing English Wikipedia pages.
To categorize an article, first make sure it actually belongs to the category. Then, go to the article and add the category at the bottom of the page. Once published (saved) the blue-linked name of the article will automatically appear on the category page. To remove an article from appearing on a category page, edit the article and remove the category. Note, if there is no existing WP article on the subject, then there is nothing to categorize and therefore nothing to do as far as categorization is concerned.
In this particular case, we have the disambiguation page Nallur, but the town in question is not listed as an existing Wikipedia article, i.e. there is no WP article for Nallur, Karnataka or Nallur, Davanagere. So indeed there is nothing to categorize and nothing more to do here. Sorry, probably not what you wanted to hear, but I hope this helps in your understanding of the situation.