The problem with oral exams is that they (almost surely) cannot be given simultaneously to a large group (unlike written exams). If the questions are the same and are not known in advance, then those taking the exams earlier are at a disadvantage, because those taking them later might get additional information about the questions from those who took it earlier.
Another disadvantage of oral exams over written exams is that they would take a longer time to administer. Thus the examiner will be forced to make the exam short (shorter than a corresponding written exam), that is, to use fewer questions and cover a smaller scope of topics.
One way to do tackle these two disadvantages is to have a large set of questions announced beforehand, where the actual oral exam consists of a random sample of that set. Everyone has the same information about the questions, the exam would take a shorter time to administer, and the student needs to understand or to be skilled in a wide range of topics to have a good chance of passing the test.
I would also suggest that your oral exam consist of questions that test for understanding and for skill. For example, if the topic is, say, limits, then example tasks that assess understanding could be to give a precise definition of a limit, to give some examples of practical applications that use the concept of limits, or to determine whether a given statement about limits is true or not. An example task that assesses skill would be to find the limit of a given specific function or sequence.