The set of all possible values of $$\theta $$ in the interval
(0, $$\pi $$) for which the points (1, 2) and (sin $$\theta $$, cos $$\theta $$) lie
on the same side of the line x + y = 1 is :

If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation,
2x²dy= (2xy + y²)dx, then $$f\left( {{1 \over 2}} \right)$$ is equal to :

Consider a region R = {(x, y) $$ \in $$ R : x² $$ \le $$ y $$ \le $$ 2x}. if a line y = $$\alpha $$ divides the area of region R into two equal parts, then which of the following is true?

Let E^C denote the complement of an event E. Let E₁ , E₂ and E₃ be any pairwise independent events with P(E₁) > 0

and P(E₁ $$ \cap $$ E₂ $$ \cap $$ E₃) = 0.

Then P($$E_2^C \cap E_3^C/{E_1}$$) is equal to :