Let $$x * y = {x^2} + {y^3}$$ and $$(x * 1) * 1 = x * (1 * 1)$$.

Then a value of $$2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2} \over {{x^4} + {x^2} + 2}}} \right)$$ is :

The sum of all the real roots of the equation

$$({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$$ is

Let the system of linear equations

x + y + $$\alpha$$z = 2

3x + y + z = 4

x + 2z = 1

have a unique solution (x$$^ * $$, y$$^ * $$, z$$^ * $$). If ($$\alpha$$, x$$^ * $$), (y$$^ * $$, $$\alpha$$) and (x$$^ * $$, $$-$$y$$^ * $$) are collinear points, then the sum of absolute values of all possible values of $$\alpha$$ is

Let x, y > 0. If x³y² = 2¹⁵, then the least value of 3x + 2y is