If $\alpha$ and $\beta$ are the distinct roots of the equation $x^2 - x + 1 = 0$, then the value of $\alpha^{200} + \beta^{206} + 2$ is equal to

The number of arrangements of the letters in the word SOLAPUR, so that consonants and vowels are placed alternately is

If $\cos 43^\circ + \sin 43^\circ = k^3$, then $\cos 2^\circ = \ldots$

If the equation $\sin 3\theta - \cos^2\theta = \dfrac{1}{4}$ and $\theta \in [0, \pi]$, then the number of solutions is...