The code uses nowdoc syntax, which means the content inside TEXT will be treated as a plain string, and variables will not be parsed. Thus, the value of `$world` will not be interpolated into the string, and `hello $world` will be output literally.

In PHP, when an object is cast to an array, only the public properties of the object are included in the resulting array with their respective keys. Private properties are excluded. In the given code, class Bar has a private property $a and a public property $c. When the object of class Bar is cast to an array, only the public property $c will be part of the array with the key 'c'. The array will not include the private property $a. As a result, checking if the key 'a' exists in the array will return false, and checking if the key 'c' exists will return true. Therefore, the output is false-true.