Let S be the set of points where the function, ƒ(x) = |2-|x-3||, x $$ \in $$ R is not differentiable. Then $$\sum\limits_{x \in S} {f(f(x))} $$ is equal to_____.

If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c $$ \in $$ R are non-zero distinct; has a non-zero solution, then:

Let $$\alpha $$ and $$\beta $$ be two real roots of the equation
(k + 1)tan²x - $$\sqrt 2 $$ . $$\lambda $$tanx = (1 - k), where k($$ \ne $$ - 1) and $$\lambda $$ are real numbers. if tan² ($$\alpha $$ + $$\beta $$) = 50, then a value of $$\lambda $$ is:

A vector $$\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k\left( {\alpha ,\beta \in R} \right)$$ lies in the plane of the vectors, $$\overrightarrow b = \widehat i + \widehat j$$ and $$\overrightarrow c = \widehat i - \widehat j + 4\widehat k$$. If $$\overrightarrow a $$ bisects the angle between $$\overrightarrow b $$ and $$\overrightarrow c $$, then: