Number Logic Puzzle: Identifying the Outlier
This problem asks us to identify which number among the given options does not share a common characteristic with the others. This type of question tests our ability to recognize patterns and logical connections between numerical values.
Analyzing the Options
Let's examine each number provided in the options:
- Option 1: $123$
- Option 2: $213$
- Option 3: $212$
- Option 4: $312$
Finding the Underlying Pattern
To find the number that does not belong, we can investigate the properties of the digits within each number:
- The number $123$ is composed of the digits $1$, $2$, and $3$. All these digits are distinct (unique).
- The number $213$ is composed of the digits $2$, $1$, and $3$. All these digits are also distinct.
- The number $212$ is composed of the digits $2$, $1$, and $2$. Notice that the digit $2$ appears twice; it is a repeated digit.
- The number $312$ is composed of the digits $3$, $1$, and $2$. All these digits are distinct.
From this analysis, we can see a clear distinction. The numbers $123$, $213$, and $312$ are all formed using three unique digits. In contrast, the number $212$ uses the digit $2$ more than once.
Conclusion: The Number That Does Not Belong
The defining characteristic that separates the numbers is the uniqueness of their digits. Since $123$, $213$, and $312$ all contain unique digits, while $212$ contains a repeated digit, $212$ is the number that does not belong to the group.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
