Let the probability of getting head for a biased coin be $$\frac{1}{4}$$. It is tossed repeatedly until a head appears. Let $$\mathrm{N}$$ be the number of tosses required. If the probability that the equation $$64 \mathrm{x}^{2}+5 \mathrm{Nx}+1=0$$ has no real root is $$\frac{\mathrm{p}}{\mathrm{q}}$$, where $$\mathrm{p}$$ and $$\mathrm{q}$$ are coprime, then $$q-p$$ is equal to ________.

If A is the area in the first quadrant enclosed by the curve $$\mathrm{C: 2 x^{2}-y+1=0}$$, the tangent to $$\mathrm{C}$$ at the point $$(1,3)$$ and the line $$\mathrm{x}+\mathrm{y}=1$$, then the value of $$60 \mathrm{~A}$$ is _________.

Let $$\mathrm{S}=\left\{z \in \mathbb{C}-\{i, 2 i\}: \frac{z^{2}+8 i z-15}{z^{2}-3 i z-2} \in \mathbb{R}\right\}$$. If $$\alpha-\frac{13}{11} i \in \mathrm{S}, \alpha \in \mathbb{R}-\{0\}$$, then $$242 \alpha^{2}$$ is equal to _________.

If the line $$l_{1}: 3 y-2 x=3$$ is the angular bisector of the lines $$l_{2}: x-y+1=0$$ and $$l_{3}: \alpha x+\beta y+17=0$$, then $$\alpha^{2}+\beta^{2}-\alpha-\beta$$ is equal to _________.