will a google search query increase page rank? for example if i search "ycombinator startup" then google (PR10) will produce links (no rel=nofollow in <a href>

will a google search query increase page rank? for example if i search "ycombinator startup" then google (PR10) will produce links (no rel=nofollow in <a href>) i think that will increase search volume index in google trend, but not sure about page rank