Let f be a polynomial function such that

f (3x) = f ' (x) . f '' (x), for all x $$ \in $$ R. Then :

A square, of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30^o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :

A line drawn through the point P(4, 7) cuts the circle x² + y² = 9 at the points A and B. Then PA⋅PB is equal to :

If    $$\int\limits_1^2 {{{dx} \over {{{\left( {{x^2} - 2x + 4} \right)}^{{3 \over 2}}}}}} = {k \over {k + 5}},$$ then k is equal to :