Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real solution.

The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ..............

If $$2 + i\sqrt 3 $$ is root of the equation $${x^2} + px + q = 0$$, where p and q are real, then (p, q) = (..........,....................).

The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x \right| + 2 = 0$$ is