How to hide the "Add comment" link in the teaser? I don't want the Add comment link displayed in the teaser. But the comment form should be displayed along with the content of the node which forms a part of a page.

Edit:  I don't have access to the php code. I want to do it through the admin console. Is there a way I can uncheck "Add comment" from appearing in the teaser and instead appear in the full content node which forms a part of a page?
You can accomplish this with a custom module, as I found here https://drupal.org/node/1257788

Here is the code you'll need:

function MODULE_node_view_alter(&amp;$build) {
  if ($build['#view_mode'] == 'teaser') {
    // remove "add comment" link from node teaser mode display
    unset($build['links']['comment']['#links']['comment-add']);
    // and if logged out this will cause another list item to appear, so let's get rid of that
    unset($build['links']['comment']['#links']['comment_forbidden']);
  }
}