\(x^2(a - b) + a^2(b - x) + b^2(x - a)\) is factored as

The parallel sides of a trapezium shaped field are 25 m and 10 m and non parallel sides are 14 m and 13 m. What is the area (in m\(^2\)) of the field?

Three fair dice are thrown simultaneously. What is the probability that the sum of numbers on their tops, is at least 6?

If a person travels at a speed of 40 km/h he will reach his destination on time. He covered half the journey in \(\frac{2}{3}\) of the time. At what speed (in km/h) should he travel to cover the remaining journey to reach the destination on time?

Six dice are stacked on the floor as shown in the figure below. On each dice, the sum of numbers on opposite faces is 7, i.e., if 1 written on one face then 6 is written on the face opposite it and so on. [Figure: six dice stacked in steps on the floor - a column of three dice on…

Four pipes A, B, C and D can fill a tank with water in 15, 20, 30 and 60 hours respectively. Pipe A is opened at 4 a.m., B at 5 a.m., C at 6 a.m. and D at 7 a.m. When is the tank filled up completely?

A and B are inversely proportional to each other and are positive. If A increases by 100%, then B decreases by

Twelve men and 5 women can complete a work in 2 days whereas 4 men and 3 women can complete the same work in 5 days. In how many days can 8 men complete the work?

In a 120 litre of solution of Acid and water, acid is 75%. A person takes out 20 litres of this solution and added 16.2 litres of acid and 3.8 litres of water in the remaining solution. What is the percentage of water in the final solution?