Let z = x + iy be a non-zero complex number such that $${z^2} = i{\left| z \right|^2}$$, where i = $$\sqrt { - 1} $$ , then z lies on the :

If $$\alpha $$ and $$\beta $$ are the roots of the equation
2x(2x + 1) = 1, then $$\beta $$ is equal to :

The probabilities of three events A, B and C are given by
P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5.
If P(A$$ \cup $$B) = 0.8, P(A$$ \cap $$C) = 0.3, P(A$$ \cap $$B$$ \cap $$C) = 0.2, P(B$$ \cap $$C) = $$\beta $$
and P(A$$ \cup $$B$$ \cup $$C) = $$\alpha $$, where 0.85 $$ \le \alpha \le $$ 0.95, then $$\beta $$ lies in the interval :

A Young's double-slit experiment is performed using monochromatic light of wavelength $$\lambda $$. The intensity of light at a point on the screen, where the path difference is $$\lambda $$, is K units. The intensity of light at a point where the path difference is $${\lambda \over 6}$$ is given by $${{nK} \over {12}}$$, where n is an integer. The value of n is __________.