Let P be the point of intersection of the common tangents to the parabola y² = 12x and the hyperbola 8x² – y² = 8. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio :

If $$\int\limits_0^{{\pi \over 2}} {{{\cot x} \over {\cot x + \cos ecx}}} dx$$ = m($$\pi $$ + n), then m.n is equal to

The number of solutions of the equation
1 + sin⁴ x = cos²3x, $$x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} \right]$$ is :

The equation |z – i| = |z – 1|, i = $$\sqrt { - 1} $$, represents :