Let a circle C of radius 5 lie below the x-axis. The line L₁ : 4x + 3y + 2 = 0 passes through the centre P of the circle C and intersects the line L₂ = 3x $$-$$ 4y $$-$$ 11 = 0 at Q. The line L₂ touches C at the point Q. Then the distance of P from the line 5x $$-$$ 12y + 51 = 0 is ______________.

Let S = {E₁, E₂, ........., E₈} be a sample space of a random experiment such that $$P({E_n}) = {n \over {36}}$$ for every n = 1, 2, ........, 8. Then the number of elements in the set $$\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}$$ is ___________.

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :

The distance of the Sun from earth is 1.5 $$\times$$ 10¹¹ m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :