In how many ways can cells in a 3 ร 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 ๐ number of balls are picked simultaneously, what is the smallest value of ๐ 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?
Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of oneโs love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
(i) In Elvesland, one always declares oneโs love by gifting a white flower.
(ii) In Elvesland, all emotions are declared by gifting flowers.
(iii) In Elvesland, sometimes one expresses oneโs anger by gifting a flower that is not yellow.
(iv) In Elvesland, sometimes one expresses oneโs love by gifting a white flower.