Simple math quiz in C#
This is pretty nice. I got some comments, some of which are my personal opinion (for example how to declare variables), some are accepted conventions (naming), and some are bug fixes.

Declaring variables

While it might be more performance friendly to declare all variables from the outset, it is best practice, I think, to declare variables only within the scope they're used. This is to decrease variable pollution in bigger functions. In such a simple app, it doesn't matter. But as your application gets bigger and better you don't want too many variables in scope.

From your code: num01, num02, playeranswer, and answer are only used within the loop. So it is better to declare then inside the loop (or you might accidentally use them outside or simply crowd your intellisense).

Also, for some variables you're splitting declaration (int numofquestions;) and assignment (numofquestions = Convert.ToInt32(Console.ReadLine());), and for other you're not. I think it is better to have declaration and assignment in one line, it is terser and more readable: (int numofquestions = Convert.ToInt32(Console.ReadLine());).

Naming

.Net convention is to use PascalCase for methods and classes and the like, and camelCase for variables. So, in your code: playeranswer becomes playerAnswer, and so on. You don't have any methods defined but you need to know the convention. It makes it easier to read your code. Again, it doesn't really matter for such a short app but for bigger apps such practices are a life saver. (A crude example, but I am sure you have seen the photo where KidsExchange reads like KidSexChange due to uniform capitalization KIDSEXCHANGE.)

I also like questionCount more than numOfQuestions. Shorter and uses clearer vocab.

Using a for loop

for loops are easier for humans to process than while loops, I think. Well easier for me.

So this :

int questionCount= Convert.ToInt32 (Console.ReadLine ());
int questionLeftCount = questionCount;

while (questionLeftCount &gt; 0)
{
    // .. do stuff
    questionLeftCount --;
}


Can be better written as:

int questionCount= Convert.ToInt32 (Console.ReadLine ());

for (int questionLeftCount = questionCount; questionLeftCount &gt; 0; questionLeftCount--)
{
    // do stuff ..
}


And it is exactly the same.

Also, since questionLeftCount is only used within the for loop definition, just use i or iter for iterator. It is standard practice. (It also standard practice to increment rather decrement). I am sure you have seen something that looks exactly like this in your readings.

for (int i = 0; i &lt; questionCount; i++)
{
    // do stuff ..
}


Much shorter and nicer.

Verifying input

Your code crashes when I type something that is NOT a number. Obviously if you're shipping the app (I know you're not, but humor me), you can't have that.

The trick is to use int.TryParse to parse inputs. TryParse returns a bool to indicate whether the conversion is successful or not, and has an out variable which assigns a value to an already declared variable. The syntax is a bit weird and takes some getting used to, but it is being made nicer in C# 7.0 (not released yet).

// Usage
int playerAnswer;

if (int.TryParse (Console.ReadLine (), out playerAnswer))
{
    // do stuff with playerAnswer
}
else
{
    // show error message
}


If you want to keep asking for input until you get something valid, you can use a while loop :

 int playerAnswer;

 while (!int.TryParse (Console.ReadLine (), out playerAnswer))
 {
     Console.WriteLine ("Invalid Input. Please type a number using digits");
 }


Something of note: you need this little piece of code in two places. When you ask for the number of questions and when you ask for the answer. Instead of typing it twice, you should extract it into a method. You can easily do that in Visual Studio by selecting the code you want to extract into a method, pressing Ctrl + . or the small light bulb to the side, and selecting, well, Extract Method. It does all the thinking for you and it is fantastic.

I am not very imaginative so I just called it RequestInput. 

static int RequestInput ()
{
    int playerAnswer;

    while (!int.TryParse (Console.ReadLine (), out playerAnswer))
    {
        Console.WriteLine ("Invalid Input. Please type a number using digits");
    }

    return playerAnswer;
}


Final result

class MainClass
{
    public static void Main ()
    {
        var rand = new Random ();

        Console.Write ("How many questions would you like to answer? ");

        int correctCount = 0;
        int questionCount = RequestInput ();

        for (int i = 0; i &lt; questionCount; i++)
        {
            int num01 = rand.Next (11);
            int num02 = rand.Next (11);

            Console.Write ($"What is {num01} times {num02} ?");

            int playerAnswer = RequestInput ();

            if (num01 * num02 == playerAnswer)
            {
                Console.WriteLine ($"{playerAnswer} is correct!");
                correctCount++;
            }
            else
            {
                Console.WriteLine ($"{playerAnswer} is incorrect!");
            }
        }

        Console.WriteLine ($"You got {correctCount} of {questionCount} correct.!");
        Console.ReadKey ();

    }

    static int RequestInput ()
    {
        int playerAnswer;
        while (!int.TryParse (Console.ReadLine (), out playerAnswer))
        {
            Console.WriteLine ("Invalid Input. Please type a number using digits");
        }

        return playerAnswer;
    }
}


I did a few other things I like but that are just style choices and mild annoyances (for me). Using var instead of Random, for example, makes it easier for me to read, since Visual Studio has the same coloring for keywords like var and int but different for class names like Random. I also removed Console.ReadKey () from within the loop because it annoyed me when trying out your app. I removed Try Again because you didn't actually let me try again the same question. You could make it possible to try until you get the right answer in a similar pattern to the one dome earlier when verifying input. Finally, I used string interpolation syntax (introduced in C# 6.0) which is much, much, more pleasant to use.

Bonus, how to set a timer

There is a Timer class, which I have never used. (I am a beginner myself, mind you). There is also System.Diagnostics.StopWatch, which as you can tell is used for diagnostics.

Here is the code with Stopwatch. Mind that you'll need using System.Diagnostics at the top of the file.

class MainClass
{
    public static void Main ()
    {
        var rand = new Random ();

        Console.Write ("How long do want to play in seconds?");

        var ts = TimeSpan.FromSeconds(RequestInput ()); // type is System.TimeSpan

        int correctCount = 0;
        int questionCount = 0;

        var sw = Stopwatch.StartNew ();

        while (sw.Elapsed &lt; ts)
        {
            // .. same old
            questionCount++;
        }
        sw.Stop ();

        Console.WriteLine ($"You got {correctCount} of {questionCount} correct in {sw.Elapsed}.!");
        Console.ReadKey ();

    }
}


You will notice I used Stopwatch.StartNew() which is a static method that creates a new instance of Stopwatch and starts it immediately. You could also do var sw = new Stopwatch(); sw.Start();

Edit: i realized there was a bug in my original implementation because I didn't understand how the TimeSpan struct works. I think it should work as expected now for longer times that 1 minute. Make sure to check the MSDN documentation 

Let me know in the comments if there is anything unclear.

Edit : On the other answer, I think creating new classes for a simple console app is overkill, but it is definitely good practice for larger apps and it allows you to extend your game more flexibly.