How to use latest jquery version on specific page or code?
There are several ways to do it. If you want to update  jquery, you can use jquery update moudle. 

Second thing is you can use, drupal_add_js() function to include the jquery file to particular node.

Third thing is you can use the js, that is used in all the page in template.php or in theme.info file. I hope you are looking for second method. Also, this question will help you much. 

Updating jquery