The sum of the real roots of the equation
$$\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} & {x - 3} \cr { - 3} & {2x} & {x + 2} \cr } } \right| = 0$$, is equal to :

If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = $${\pi \over 2}$$ , then :

If the line ax + y = c, touches both the curves x² + y² = 1 and y² = 4$$\sqrt 2 $$x , then |c| is equal to :

The area (in sq.units) of the region bounded by the curves y = 2^x and y = |x + 1|, in the first quadrant is :