The sum of the cubes of all the roots of the equation

$${x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0$$ is _________.

There are ten boys B₁, B₂, ......., B₁₀ and five girls G₁, G₂, ........, G₅ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B₁ and B₂ together should not be the members of a group, is ___________.

Let the common tangents to the curves $$4({x^2} + {y^2}) = 9$$ and $${y^2} = 4x$$ intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and l respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $${l \over {{e^2}}}$$ is equal to ______________.

Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $$\int\limits_{ - 6}^0 {f(x)dx} $$ is equal to __________.