Let *, ▢ $$\in$${$$\wedge$$, $$\vee$$} be such that the Boolean expression (p * $$\sim$$ q) $$\Rightarrow$$ (p ▢ q) is a tautology. Then :

The number of real roots of the equation

$${e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0$$ is :

The sum of 10 terms of the series

$${3 \over {{1^2} \times {2^2}}} + {5 \over {{2^2} \times {3^2}}} + {7 \over {{3^2} \times {4^2}}} + ....$$ is :

Let the equation of the plane, that passes through the point (1, 4, $$-$$3) and contains the line of intersection of the
planes 3x $$-$$ 2y + 4z $$-$$ 7 = 0
and x + 5y $$-$$ 2z + 9 = 0, be
$$\alpha$$x + $$\beta$$y + $$\gamma$$z + 3 = 0, then $$\alpha$$ + $$\beta$$ + $$\gamma$$ is equal to :