Site: This restricts the results to those websites in the given domain. For instance, [help site:www.microsoft.com] will find pages about help within www.microsoft.com. [help site:com] will find pages about help within .com urls.
Cache: The query [cache:] will show the version of the web page that Google has in its cache. For instance, [cache:www.microsoft.com] will show Google’s cache of the Microsoft homepage. [cache:www.microsoft.com web] will show the cached content with the word “web” highlighted.
Info: The query [info:] will present some information that Google has about that web page. For instance, [info:www.microsoft.com] will show information about the Microsoft homepage.
Link: [link:www.microsoft.com] will list webpages that have links pointing to the Microsoft homepage.
Related: This will list web pages that are “similar” to a specified web page. For instance, [related:www.microsoft.com] will list web pages that are similar to the Microsoft homepage
AllinURL: This will restrict the results to those with all of the query words in the url. For instance, [allinurl: live search] will return only documents that have both “live” and “search” in the url.
InURL: This will restrict the results to documents containing that word in the url. For instance, [inurl:live search] will return documents that mention the word “live” in their url, and mention the word “search” anywhere in the document.
AllinText:
AllinTitle: This will restrict the results to those with all of the query words in the title. For instance, [allintitle: live search] will return only documents that have both “live” and “search” in the title.
InTitle:
Define: This will provide a definition of the words you enter after it, gathered from various online sources. The definition will be for the entire phrase entered (i.e., it will include all the words in the exact order you typed them).
Stocks: This will treat the rest of the query terms as stock ticker symbols, and will link to a page showing stock information for those symbols. For instance, [stocks: intc yhoo] will show information about Intel and Yahoo.
FileType: This will restrict the results to pages whose names end in suffix. For example, [web page evaluation checklist filetype:pdf] will return pdf files that match the terms “web”, “page”, “evaluation”, and “checklist”. You can restrict the results to pages whose names end with pdf and doc by using the OR operator, e.g. [email security filetype:pdf OR filetype:doc].
InAnchor: This will restrict the results to pages containing the query terms you specify in the anchor text or links to the page. For example, [restaurants inanchor:gourmet] will return pages in which the anchor text on links to the pages contain the word “gourmet” and the page contains the word “restaurants”.
AllinAnchor: This will restricts results to pages containing all query terms you specify in the anchor text on links to the page. For example, [allinanchor:best museums sydney] will return only pages in which the anchor text on links to the pages contain the words “best”, “museums”, and “sydney”.
AllinText: This restricts results to those containing all the query terms you specify in the text of the page. For example, [allintext:travel packing list] will return only pages in which the words “travel”, “packing”, and “list” appear in the text of the page.
Truncation Wildcards (* or ?): The multi-character (*) and single character (?) truncation symbols can be used within and at the ends of words to search for word variants thereby broadening your search.

Reference:
Google Search Operators
Google Search Features

• Adobe – http://www.adobe.com
• Adobe Acrobat – http://www.adobe.com/products/acrobat/readstep2.html
• World Wide Web Consortium http://www.w3.org/
• Macromedia – http://www.macromedia.com
• Energy.gov – http://www.energy.gov
• Apple – QuickTime – http://www.apple.com/quicktime/
• Keio University – http://www.keio.ac.jp
• National Aeronautics and Space Administration – http://www.nasa.gov
• Apple Computers – http://www.apple.com
• U.S Goverment Official Portal – http://www.firstgov.gov
• Google Search – http://www.google.com
• W3C CSS Validation Service – http://jigsaw.w3.org/css-validator/
• ERCIM – http://www.ercim.org
• MIT Laboratory for Computer Science – http://www.lcs.mit.edu
• National Science Foundation – http://www.nsf.gov
• The New York Times – http://www.nytimes.com/
• Language Tools – http://www.google.com/language_tools
• The White House – http://www.whitehouse.gov
• Real Media – http://www.real.com
• The Web Standards Project – http://www.webstandards.org/
• Stat Counter – http://www.statcounter.com

PR(A) = (1-d) + d(PR(t1)/C(t1) + … + PR(tn)/C(tn))
PR(A) is the PageRank of the page you are trying to measure.
d is a damping factor considered to be about 0.85.
tn is the PR of the incoming link page.
C is the number of outgoing links from each page that has a link to you.

Pretty simple is it not ?

Either you can work upon this code and solve the mystery or use the Jvw Google Pagerank script.

Jvw Pagerank Script can generate PR (Google Pagerank) for any given URL without the help of Google Toolbar.

You just have to enter the URL in the textbox and get the resulting PR in the browser itself.

This simple and easy-to-use php script finds the Google Page Rank for any URL by requesting the PR from Google’s servers. Just upload script to your web site, enter small piece of code (less than 1Kb) to your page and you will be able to track your site’s google page rank live! Completely accurate real time google page rank info that is always available directly on your web site.