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.
![GATE CE 2023 Set 2 General Aptitude - Numerical Ability Question 6 English](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1lzadh0sf/c7c48431-038a-48e3-99af-62790a04b9a5/b6c20cf0-4f85-11ef-9d69-5bca4f1bb61c/file-jaoe38c1lzadh0sg.png?format=png)
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?
![GATE CE 2023 Set 2 General Aptitude - Numerical Ability Question 4 English](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1lzad6ng1/02091d17-de4d-44e7-a258-ed37da1b9c25/965bca10-4f84-11ef-9d69-5bca4f1bb61c/file-jaoe38c1lzad6ng2.png?format=png)