Let Z be the set of integers.
If A = {x $$ \in $$ Z : 2^{(x + 2) (x2 $$-$$ 5x + 6)} = 1} and
B = {x $$ \in $$ Z : $$-$$ 3 < 2x $$-$$ 1 < 9},
then the number of subsets of the set A $$ \times $$ B, is

If the function f given by f(x) = x³ – 3(a – 2)x² + 3ax + 7, for some a$$ \in $$R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $${{f\left( x \right) - 14} \over {{{\left( {x - 1} \right)}^2}}} = 0\left( {x \ne 1} \right)$$ is :

The integral $$\int {{{3{x^{13}} + 2{x^{11}}} \over {{{\left( {2{x^4} + 3{x^2} + 1} \right)}^4}}}} \,dx$$ is equal to : (where C is a constant of integration)

Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor axis. If $$\Delta $$S'BS is a right angled triangle with right angle at B and area ($$\Delta $$S'BS) = 8 sq. units, then the length of a latus rectum of the ellipse is :