Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :

Let $$\alpha$$, $$\beta$$ be two roots of the

equation x² + (20)^1/4x + (5)^1/2 = 0. Then $$\alpha$$⁸ + $$\beta$$⁸ is equal to

The probability that a randomly selected 2-digit number belongs to the set {n $$\in$$ N : (2ⁿ $$-$$ 2) is a multiple of 3} is equal to :

Let $$A = \{ (x,y) \in R \times R|2{x^2} + 2{y^2} - 2x - 2y = 1\} $$, $$B = \{ (x,y) \in R \times R|4{x^2} + 4{y^2} - 16y + 7 = 0\} $$ and $$C = \{ (x,y) \in R \times R|{x^2} + {y^2} - 4x - 2y + 5 \le {r^2}\} $$.

Then the minimum value of |r| such that $$A \cup B \subseteq C$$ is equal to