IIM-K (BMSAT) 2025 (QA) PYQs

The number of whole metallic tiles that can be produced by melting and recasting a circular metallic plate, if each of the tiles has a shape of a right-angled isosceles triangle and the circular plate has a radius equal in length to the longest side of the tile (Assume that the tiles and plate are of uniform thickness, and there is no loss of material in the melting and recasting process) is

A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 $m^{3}$. The emptying capacity of the pump is 10 $m^{3}$ per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank as to fill it. The filling capacity of the pump is

A cylindrical vessel of base radius 42 cm contains water to a certain level. A solid cylinder of height 18 cm is dropped into it and is completely submerged in water. If the level of the water in the vessel rises by 6 cm, what is the total surface area (in cm²) of the solid cylinder? (Use $\pi = \frac{22}{7}$ ) (Assuming no overflow.)