In which of the following cases, is the construction of a quadrilateral ABCD not possible ?

A parallelogram is a quadrilateral in which:

The number of diagonals in a hexagon is :

ABCD is a trapezium in which BC || AD and AC = CD. If ∠ABC = 54° and ∠BAC = 60°, then what is the measure of ∠ACD (in degree)?

ABCD is a trapezium in which BC || AD and AC = CD. If ∠ABC = 19° and ∠BAC = 137°, then what is the measure of ∠ACD (in degree)?

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and $$\angle ADC = 140^\circ.$$ 
Then $$\angle BAC$$ is equal to:

If  $$(x_1, y_1)$$​ is the solution of the pair of equations: $$\frac{x}{10} + \frac{y}{5} - 1 = 0$$​ and$$\quad \frac{x}{8} + \frac{y}{6} = 15 \\$$ 
and $$y_1 = \lambda x_1 + 5,$$​ then the value of $$\lambda$$​ is:

The number of real solutions of the equation x² − 3|x| + 2 = 0 is:

The interior angles of a polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

ABCD is a trapezium in which BC‖AD and AC=CD. If ∠ABC=40° and ∠BAC=120°, then what is the measure of ∠ACD (in degree)?

For a regular polygon, the sum of the interior angles is 250% more than the sum of its exterior angles. Each interior angle of the polygon measures x°. What is the value of x?