Two numbers are selected randomly from the set $$S = \left\{ {1,2,3,4,5,6} \right\}$$ without replacement one by one. The probability that minimum of the two numbers is less than $$4$$ is

If $$P\left( B \right) = {3 \over 4},P\left( {A \cap B \cap \overline C } \right) = {1 \over 3}$$ and
$$P\left( {\overline A \cap B \cap \overline C } \right) = {1 \over 3},\,\,$$ then $$P\left( {B \cap C} \right)$$ is

The area bounded by the curves $$y = \sqrt x ,2y + 3 = x$$ and
$$x$$-axis in the 1^st quadrant is

If $$y(t)$$ is a solution of $$\left( {1 + t} \right){{dy} \over {dt}} - ty = 1$$ and $$y\left( 0 \right) = - 1,$$ then $$y(1)$$ is equal to