Applying 'Uncle Bob's Clean Code' on this small exercice
CreateArray1to30() could be renamed to CreateQuestions()
ReturnAllCombinationsOfInputtedList() could be renamed to Combinations() or QuestionCombinations()
ReturnAllCombinationsOfInputtedList() does too much. The call to .Distinct() is unecessary, and can be replaced with correct indices in the first place. Furthermore, the aTest array is entirely useless and could be replaced by using firstQuestion and secondQuestion directly.
Strings are a non ideal data structures for the exams, as you use a different format when printing them out

using System;
using System.Collections.Generic;
using System.Linq;


namespace ConsoleAppHelpingAlexWithExercices
{
    struct ExamTicket {
        public int Question1, Question2;
        public ExamTicket(int Question1, int Question2) {
            this.Question1 = Question1;
            this.Question2 = Question2;
        }
    }
    class Program
    {
        //**************************************************************************
        // How many different exam tickets with two different questions can be made, 
        // from a syllabus with 30 questions
        //**************************************************************************
        static void Main(string[] args)
        {
            int[] questions = CreateQuestions();
            var combinations = new List&lt;ExamTicket&gt;(Combinations(questions));
            foreach (var combination in combinations) {
                Console.WriteLine($&quot;{combination.Question1} and {combination.Question2}&quot;);
            }
            Console.WriteLine(&quot;Total unique combinations: {0}&quot;, combinations.Count);
        }

        static IEnumerable&lt;ExamTicket&gt; Combinations(int[] questions)
        {
            for (int i=0;i&lt;questions.Length;++i) {
                for (int j=i+1;j&lt;questions.Length;++j) {
                    yield return new ExamTicket(questions[i],questions[j]);
                }
            }
        }

        static int[] CreateQuestions()
        {
            return Enumerable.Range(1, 30).ToArray();
        }
    }
}