Let the points of intersections of the lines x $$-$$ y + 1 = 0, x $$-$$ 2y + 3 = 0 and 2x $$-$$ 5y + 11 = 0 are the mid points of the sides of a triangle $$\Delta $$ABC. Then, the area of the $$\Delta $$ABC is _____________.

Let f(x) be a polynomial of degree 3 such that
$$f(k) = - {2 \over k}$$ for k = 2, 3, 4, 5. Then the value of 52 $$-$$ 10f(10) is equal to :

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two R appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is ___________.

Let $$\overrightarrow a = 2\widehat i - \widehat j + 2\widehat k$$ and $$\overrightarrow b = \widehat i + 2\widehat j - \widehat k$$. Let a vector $$\overrightarrow v $$ be in the plane containing $$\overrightarrow a $$ and $$\overrightarrow b $$. If $$\overrightarrow v $$ is perpendicular to the vector $$3\widehat i + 2\widehat j - \widehat k$$ and its projection on $$\overrightarrow a $$ is 19 units, then $${\left| {2\overrightarrow v } \right|^2}$$ is equal to _____________.