A square piece of paper is folded three times along its diagonal to get an isosceles triangle whose equal sides are 10 cm. What is the area of the unfolded original piece of paper?

a, b, c are integers, |a| ≠ |b| ≠ |c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?

The difference between the area of the circumscribed circle and the area of the inscribed circle of an equilateral triangle is 2156 sq. cm. What is the area of the equilateral triangle? Assume that π = 22/7

Each day on Planet M is 10 hours, each hour 60 minutes and each minute 40 seconds. The inhabitants of Planet M use 10 hour analog clock with an hour hand, a minute hand and a second hand. If one such clock shows 3 hours 42 minutes and 20 seconds in a mirror what will be the time…

A person standing on the ground at point A saw an object at point B on the ground at a distance of 600 meters. The object started flying towards him at an angle of 30° with the ground. The person saw the object for the second time at point C flying at 30° angle with him. At point…

Study the figure below and answer the question: (Figure: triangle ABD with C on AD between A and D, and segment BC.) [Figure: see page 17 of source PDF] Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person t…

For two positive integers a and b, if (a + b)^(a+b) is divisible by 500, then the least possible value of a × b is:

Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in 60 : 40 ratio. The initial investment of Rs. 100,000 on infrastructure is borne entirely by ABC whereas the running cost of Rs. 400 per student is…

Pradeep could either walk or drive to office. The time taken to walk to the office is 8 times the driving time. One day, his wife took the car making him walk to office. After walking 1 km, he reached a temple when his wife called to say that he can now take the car. Pradeep figu…