For the following questions answer them individually
$$\left(\frac{\sin 45^\circ + \cos 45^\circ + \tan 45^\circ}{\sin 45^\circ - \cos 45^\circ - \tan 45^\circ}\right)^2 =$$
In $$\triangle ABC, \angle ABC = 45^\circ, \angle CAB = 30^\circ$$ and CD is perpendicular to AB. If CD = 100, then AB =
The progression in which the roots of the equation $$6x^3 - 11x^2 + 6x - 1 = 0$$ lie is
The quadratic expression that leaves remainders 1, 2 and 4 respectively when divided by (x - 1), (x - 2) and (x - 3) is
The number of solutions of the system $$x - y + z = -6, x + y - z = 3, -x + y - z = 6$$ is