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WordPress' standard pages, such as the Search Page, the error/404 page and Archive pages will display the default Image Set you have selected under the "Settings" tab. At the moment it is not possible to have a specific image set for these.
You can override this default Image Set per: Post, Page, Category and/or Tag.
For an individual post, simply select that post and there will be a "Background" box in the main (wide) column. If it is not showing, ensure the appropriate box is ticked/checked on the "Screen Options" tab for the post (upper-right corner). Overriding a page is done the same way - simply select the page, edit it and select the Image Set, Overlay and Background Color in the "Background" box.
Overriding a Category or Tag is done slightly differently. You do this from within an Image Set itself. So let's say you'd like to have the Image Set "Pears and Apples" appear on all posts tagged "Fruit". Go to the Image Sets tab, select the "Pears and Apples" Image Set, and in the right-hand column, add "Fruit" to the "Override by Tag" box. Then save the Image Set. From now on, any time a post with the tag "Fruit" is encountered, it will use the "Pears and Apples" Image Set.
Hope this helps!