Is there any google API which searches the web for any given page conent and return the url of the pages if the searched content is present in those urls?
By "page content", you mean strings of text? By strings of text, you mean search queries? Then yes, there is a Google search API, at http://code.google.com/apis/ajaxsearch/, but it's a client-side API.
There is no server-side API available for searching Google.
Yes, content of the page. For ex. if I want to know that whether the content of the T&C page of my site has been copied or not, then is there any API to know that?
Take a sentence of the page, copy it, paste it into Google with quotes around it, and search. That'll give you a good idea.
But there's no API from Google that will let you do this in a server application automatically. Google doesn't want those kinds of applications built on its search engine.
Copyscape is a company that provides what you're asking about as a service.