Let $$\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}$$ and $$\mathrm{a}< \mathrm{b}< \mathrm{c}$$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $$9,25, a, b, c$$ be 18, 4 and $$\frac{136}{5}$$, respectively. Then $$2 a+b-c$$ is equal to ________

The number of distinct real roots of the equation $$|x+1||x+3|-4|x+2|+5=0$$, is _______

If $$\int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} \mathrm{~d} x=\mathrm{A}\left(\frac{\alpha x-1}{\beta x+3}\right)^B+\mathrm{C}$$, where $$\mathrm{C}$$ is the constant of integration, then the value of $$\alpha+\beta+20 \mathrm{AB}$$ is _________.

Let $$\mathrm{S}$$ be the focus of the hyperbola $$\frac{x^2}{3}-\frac{y^2}{5}=1$$, on the positive $$x$$-axis. Let $$\mathrm{C}$$ be the circle with its centre at $$\mathrm{A}(\sqrt{6}, \sqrt{5})$$ and passing through the point $$\mathrm{S}$$. If $$\mathrm{O}$$ is the origin and $$\mathrm{SAB}$$ is a diameter of $$\mathrm{C}$$, then the square of the area of the triangle OSB is equal to __________.