JAVASCRIPT

can we add jquery in chrome extension js code

You can just put jquery.js into extension folder and include it in the manifest:

{
  "name": "My extension",
  ...
  "content_scripts": [
    {
      "matches": ["http://www.google.com/*"],
      "css": ["mystyles.css"],
      "js": ["jquery.js", "myscript.js"]
    }
  ],
  ...
}
You don't need to worry about conflicts with jQuery on a parent page as content scripts are sandboxed.

Add jquery in extension

{
  "name": "MyExtension",
  "version": "0.1",
  "description": "blah blah",
  "background_page": "background.html",
  "content_scripts": [
    {
      "matches": ["http://*/*","https://*/*"],
      "css": ["extension.css"],
      "js": ["jquery-1.4.2.js", "extension.js"]
    }
  ]
}

jquery extension

<script src="jquery-1.9.1.min.js"></script> <!-- REPLACE THE SRC DEPENDING ON THE VERSION YOU HAVE DOWNLOADED -->