The sum of the co-efficients of all even degree terms in x in the expansion of
$${\left( {x + \sqrt {{x^3} - 1} } \right)^6}$$ + $${\left( {x - \sqrt {{x^3} - 1} } \right)^6}$$, (x > 1) is equal to:

The area (in sq. units) of the region
A = { (x, y) $$ \in $$ R × R|  0 $$ \le $$ x $$ \le $$ 3, 0 $$ \le $$ y $$ \le $$ 4, y $$ \le $$ x² + 3x} is :

Let ƒ : [0, 2] $$ \to $$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $$ \in $$ (0, 2). If $$\phi $$(x) = ƒ(x) + ƒ(2 – x), then $$\phi $$ is :

The sum of the squares of the lengths of the chords intercepted on the circle, x² + y² = 16, by the lines, x + y = n, n $$ \in $$ N, where N is the set of all natural numbers, is :