On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
In how many ways can cells in a 3 Γ 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.
There are 4 red, 5 green, and 6 blue balls inside a box. If π number of balls are picked simultaneously, what is the smallest value of π that guarantees there will be at least two balls of the same colour?
One cannot see the colour of the balls until they are picked.
Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?
