The distance of line $$3y - 2z - 1 = 0 = 3x - z + 4$$ from the point (2, $$-$$1, 6) is :

The numbers of pairs (a, b) of real numbers, such that whenever $$\alpha$$ is a root of the equation x² + ax + b = 0, $$\alpha$$² $$-$$ 2 is also a root of this equation, is :

Let P₁, P₂, ......, P₁₅ be 15 points on a circle. The number of distinct triangles formed by points P_i, P_j, P_k such that i +j + k $$\ne$$ 15, is :

The range of the function,

$$f(x) = {\log _{\sqrt 5 }}\left( {3 + \cos \left( {{{3\pi } \over 4} + x} \right) + \cos \left( {{\pi \over 4} + x} \right) + \cos \left( {{\pi \over 4} - x} \right) - \cos \left( {{{3\pi } \over 4} - x} \right)} \right)$$ is :