Quantitative Aptitude - Arithmetic Ability Questions

What is the area (in sq cm) of a regular hexagon of side 9 cm?

What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is -13 and the 6th term is -4?

If 493/29 = 17, then 4.93/0.0017 = ?

A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?

If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?

If 3+12=x+3y, then the x+y is 

The co-ordinates of the centroid of a triangle ABC are (3,-2). What are the co-ordinates of vertex C if co-ordinates of A and B are (-2,5) and (6,-2) respectively?

In the given figure, ABCD is a square of side 14 cm. E and F are mid points of sides AB and DC respectively. EPF is a semicircle whose diameter is EF. LMNO is a square . What is the area (in sq.cm) of the shaded region?