Let X₁, X₂, ......., X₁₈ be eighteen observations such
that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $$\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90$$, where $$\alpha$$ and $$\beta$$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of | $$\alpha$$ $$-$$ $$\beta$$ | is ____________.

Let a be an integer such that all the real roots of the polynomial
2x⁵ + 5x⁴ + 10x³ + 10x² + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equal to ___________.

Let L be a common tangent line to the curves

4x² + 9y² = 36 and (2x)² + (2y)² = 31. Then the

square of the slope of the line L is __________.

Draw the output signal Y in the given combination of gates.