The total number of possible isomers for [Pt(NH₃)₄Cl₂]Br₂ is ______.

Consider a triangle $$\Delta$$ whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of $$\Delta$$ is (1, 1), then the equation of the circle passing through the vertices of the triangle $$\Delta$$ is

The area of the region

$$\left\{ {\matrix{ {(x,y):0 \le x \le {9 \over 4},} & {0 \le y \le 1,} & {x \ge 3y,} & {x + y \ge 2} \cr } } \right\}$$ is

Consider three sets E₁ = {1, 2, 3}, F₁ = {1, 3, 4} and G₁ = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E₁, and let S₁ denote the set of these chosen elements. Let E₂ = E₁ $$-$$ S₁ and F₂ = F₁ $$\cup$$ S₁. Now two elements are chosen at random, without replacement, from the set F₂ and let S₂ denote the set of these chosen elements.

Let G₂ = G₁ $$\cup$$ S₂. Finally, two elements are chosen at random, without replacement, from the set G₂ and let S₃ denote the set of these chosen elements.

Let E₃ = E₂ $$\cup$$ S₃. Given that E₁ = E₃, let p be the conditional probability of the event S₁ = {1, 2}. Then the value of p is