The area (in sq. units) of the region

A = {(x, y) : (x – 1)[x] $$ \le $$ y $$ \le $$ 2$$\sqrt x $$, 0 $$ \le $$ x $$ \le $$ 2}, where [t]

denotes the greatest integer function, is :

Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set
C = {f : A $$ \to $$ B | 2 $$ \in $$ f(A) and f is not one-one} is ______.

If $$\alpha $$ and $$\beta $$ are the roots of the equation,
7x² – 3x – 2 = 0, then the value of
$${\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}}$$ is equal to :

If L = sin²$$\left( {{\pi \over {16}}} \right)$$ - sin²$$\left( {{\pi \over {8}}} \right)$$ and
M = cos²$$\left( {{\pi \over {16}}} \right)$$ - sin²$$\left( {{\pi \over {8}}} \right)$$, then :