Prevent page reload and redirect on form submit ajax/jquery

function sendForm(){
    // all your code
    return false;
}

I was also bit engaged in finding solution to this problem, and so far the best working method I found was this-

Try using XHR to send request to any url, instead of $.ajax()...I know it sounds bit weird but try it out!
Example-

<form method="POST" enctype="multipart/form-data" id="test-form">

---

var testForm = document.getElementById('test-form');
testForm.onsubmit = function(event) {
event.preventDefault();

var request = new XMLHttpRequest();
// POST to any url
request.open('POST', some_url, false);

var formData = new FormData(document.getElementById('test-form'));
request.send(formData);

This would send your data successfully ...without page reload.

Modify the function like this:

function sendForm(e){
  e.preventDefault();
}

And as comment mentions, pass the event:

onclick = sendForm(event);

Update 2:

$('#form-button-submit').on('click', function(e){
   e.preventDefault();

   var name = $('input#name').val(),
       email = $('input#email').val(),
       comments = $('textarea#comments').val(),
       formData = 'name=' + name + '&email=' + email + '&comments=' + comments;

    $.ajax({
      type: 'post',
      url: 'js/sendEmail.php',
      data: formData,
      success: function(results) {
        $('ul#response').html(results);
      }
    });
});