In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is:

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is

The area of the quadrilateral bounded by the Y-axis, the line x = 5 and the lines |x − y| − |5 − x| = 2, is

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shi…

If p² + q² − 29 = 2pq − 20 = 52 − 2pq, then the difference between the maximum and minimum possible value of (p³ − q³) is

If a certain amount of money is divided equally among n persons, each one receives Rs. 352. However, if two persons receive Rs. 506 each and the remaining is divided equally among the other persons, each of them receive less than or equal to Rs. 330. Then, the maximum possible va…

Let both the series a₁, a₂, a₃, ... and b₁, b₂, b₃, ... be in arithmetic progression such that the common differences of both the series are prime numbers. If a₅ = b₉, a₁₉ = b₁₉ and b₂ = 0, then a₁₁ equals?

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing thi…

Let aₙ and bₙ be two sequences such that aₙ = 13 + 6(n − 1) and bₙ = 15 + 7(n − 1) for all natural numbers n. Then, the largest three-digit integer that is common to both these sequences is: