How to pass two variables to php,mySQL using ajax jquery

You can pass the data as json,

$.ajax({
    type: "POST",
    dataType: "json",
    url: "newExam.php",
    data:  {
        name: username,
        pwd: password
    },
    success: function(data) {
        alert("Form submitted successfully");
    }
});

Also, names should match the parameters in the function.

Client Side

$("#submit_login").click(function(){

       var username=$("input[name='user_email']").val();
       var password=$("input[name='user_password']").val();

         $.ajax({
                type: "POST",
                dataType: "json",
                url: "newExam.php", 
                data: {name : username, pwd : password },
                success: function(data) {
                     alert("Form submitted successfully");
                }
              });     

   }); 

Server Side

<?php

// file : newExam.php     

// to view  post array
if(!empty($_POST))
{
   print_r($_POST);
}

// access individual element
if(isset($_POST['name']))
{
   echo $_POST['name'];
}

?>

The above representation of the data variable shows an error.

Absolutely. That is correct because there is an error. You have a variable and you are assigning a query string with : where it should be =:

data= "name="+username+"&pwd="+password;

But this is not a good idea because you have to post the values not the input objects. username is an html input element, instead you should post an object like:

$("#submit_login").click(function(){
   var username=$('input[name=user_email]').val();
   var password=$('input[name=user_password]').val();
   var data = {name:username, pwd:password};
   $.ajax({
     type: "POST",
     dataType: "json", // <---make sure you return json from the php side.
     url: "newExam.php", 
     data: data,
     success: function(data) {
         alert("Form submitted successfully");
     }
   });     
}); 

Your selectors dont look right to me.

   var username=$('input[name="user_email"]');
   var password=$('input[name="user_password"]');

Note the double quotes around the input name attributes

Can you try the below code format:

data: {name : username, pwd : password }