Let $a$ be an integer selected at random from the set $\{0, 1, 2, 3, \ldots, 9\}$. The probability that the equation $ax^2 - ax + 1 = 0$ has real roots is ...

The smallest positive integer $n$ for which $\dfrac{(1 + i)^n}{(1 - i)^{n-2}}$ is a real number, is ...

Four men and three women are to be arranged at a round table. The number of arrangements in which no two women are together is ....

The value of $\cos\left(\dfrac{\pi}{5}\right)$ is ...