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 ...

Let $x \in [0, 6\pi]$ satisfy the equation $\cos x - \sin x = -1$. If $x = k\left(\dfrac{\pi}{3}\right)$ where $k \in N$, then find the number of possible values of $k$ is .....