If y² + log_e (cos²x) = y,
$$x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$, then :

$$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx} $$ is equal to :

Consider the two sets :
A = {m $$ \in $$ R : both the roots of
x² – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?

Let P be a point on the parabola, y² = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is $${4 \over 3}$$, then :