Quantitative Aptitude - Arithmetic Ability Questions

What is the value of [sin (90– 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?

What is the area (in sq cm) of an equilateral triangle of side 6 cm?

Point P is the midpoint of segment AB. Co-ordinates of P are (3 , 1) and B are (5, -4). What are the co-ordinates of point A?

An octahedron has 6 vertices. How many edges does it have?

If the perimeter of a semicircle is 108 cm, then find its area (in cm²).

The mean of 12 observations is 15. One more observation is included and the new mean becomes 16. The 13th observation is

The sum of present age of father and his son is 60 yrs. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?

A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity and during the fifth hour it was only one -third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?