Let $$\overrightarrow a = \widehat i - 2\widehat j + \widehat k$$ and $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ be two vectors. If $$\overrightarrow c $$ is a vector such that $$\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow a $$ and $$\overrightarrow c .\overrightarrow a = 0$$, then $$\overrightarrow c .\overrightarrow b $$ is equal to

The area (in sq. units) of the region

{(x,y) $$ \in $$ R² : x² $$ \le $$ y $$ \le $$ 3 – 2x}, is :

The length of the perpendicular from the origin, on the normal to the curve,
x² + 2xy – 3y² = 0 at the point (2,2) is

If $$I = \int\limits_1^2 {{{dx} \over {\sqrt {2{x^3} - 9{x^2} + 12x + 4} }}} $$, then :