In the given reaction,

The number of $$\pi$$ electrons present in the product 'P' is _________.

Let $$\alpha$$ be a root of the equation 1 + x² + x⁴ = 0. Then, the value of $$\alpha$$¹⁰¹¹ + $$\alpha$$²⁰²² $$-$$ $$\alpha$$³⁰³³ is equal to :

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $$-$$ 1) $$-$$ arg(z + 1) = $${\pi \over 4}$$ intersect :

The value of $$\mathop {\lim }\limits_{x \to 1} {{({x^2} - 1){{\sin }^2}(\pi x)} \over {{x^4} - 2{x^3} + 2x - 1}}$$ is equal to: