Which of the following cubes can be created by folding the given figure?
Opposite surface of the open dice can be found by the below methods:
So By using the above rule we can find the opposite surface of open dice.
Below are the opposite surfaces:
As we know that, no two opposite surfaces are adjacent to each other.
So in option 1, @ and & are opposite surfaces but shown adjacent. Hence wrong.
In option 3, © and # are opposite surfaces but shown adjacent. Hence wrong.
In option 4, $ and % are opposite surfaces but shown adjacent. Hence wrong.
In option 2, no opposite surfaces are adjacent.
Hence, option 2 is correct.
Three position of a cube are shown below. Which number will be opposite to the face containing 5?
According to the given information,
‘3’ will be opposite the face containing ‘6’
‘1’ will be opposite the face containing ‘4’
And,
‘2’ will be opposite to the face containing ‘5’
Hence, ‘2’ is the correct answer.Three positions of a dice are given below. What will come opposite to the face containing ‘Black’?
The given position of dice are:
It is clear that adjacent phase of black is yellow and pink from the first position of dice.
And also from second position of dice it is clear that black phase is also adjacent to orange and blue.
So, from third position of the dice it is clear that the purple is opposite to the black.
Hence, 'Purple' is the correct answer.
Which of the cubes from the given option can be made from the given sheet of paper?
Given,
On folding the cube, the following faces are opposite to each other:
1) ‘T’ is opposite to ‘R’
2) ‘P’ is opposite to ‘S’
3) ‘U’ is opposite to ‘Q’
In option 1) ‘P’ and ‘S’ are adjacent to each other which is not possible.
In option 2) ‘T’ and ‘R’ are adjacent to each other which is not possible.
In option 3) ‘Q’ and ‘U’ are adjacent to each other which is not possible.
In option 4) It is possible that P, T and U are adjacent to each other.
Hence, Option (4) is the correct answer.
Two different position of the same dice are shown. Select the number that will be on the face opposite to the face having number '3'
As 1 is the common face on both the dice, keeping it constant and then rotating in clockwise direction, we get the faces opposite to each other.
1 
5 
3 
1 
2 
4 
So, the face opposite to the face having number '3' is ‘4’.
Hence, ‘4’ is the correct answer.
Two positions of the same dice are shown. Select the number that will be on the face opposite to the one showing 6.
Concept:
When two faces are common in two positions of the same given dices then the remaining third face of the first dice will become the opposite pair of the remaining third face of the second dice.
Explanation :
Here the face 3 and 5 is common in both the dice.
so the remaining face in the first dice is 1 and the remaining face in the second dice is 6.
They will become the opposite pair, which means 1 will be opposite to 6.
‘1’ will be on the face opposite to the one showing ‘6’.
Three position of a cube are shown below. What will come opposite to face containing A?
From second and third cube we can see Z is adjacent to B, C, F, and N so only A is left.
A is opposite to Z.
Two rotated positions of a dice are given below. Which number will be at the top if the number 1 is on the bottom of the dice?
If the following figure is folded to form a cube, then which number will be on the face opposite to the face having number '1'?
Faces opposite to each other is shown below:
So, the face opposite to the face having number '1' is ‘6’.
Hence, ‘6’ is the correct answer.
A dice with six faces is marked with six numbers 1, 2, 3, 4, 5 and 6 respectively. The dice is rolled three times and three positions are shown as:
Find the number opposite to 1?
From figure (2) and (3) we can conclude that the numbers 2, 4, 3 and 6 appear adjacent to the letter 5. Therefore the number 1 appears opposite to 5, In other words, we can say that 5 appear opposite to 1.
Hence, the correct answer is 5.
Which digit will appear on the face opposite to the face with the number 4?
According to the given figures,
‘1’ is opposite to ‘5’
‘2’ is opposite to ‘6’
And,
‘3’ is opposite to ‘4’
‘3’ will appear on the face opposite to the face with number 4.
Hence, “3” is the correct answer.
Three different positions of the same dice are shown. Select the symbol that will be on the face opposite to the one showing ‘<’.
‘<’ is present in 3^{rd} dice.
The common symbol in 2^{nd} and 3^{rd} dice is ‘%’.
So, keeping ‘%’ constant and then rotating in clockwise direction, we get the symbols opposite to each other:
% 
@ 
$ 
# 
< 
& 
So, ‘@’ is opposite to ‘<’.
Hence, ‘@’ is the correct answer.The different of the same dice are shown. Select the number that will be on the face opposite to the face showing the number '1'
By comparing fig. (1) and fig. (3)
‘2’ is opposite to ‘4’.
‘3’ is opposite to ‘5’.
And,
‘1’ is opposite to ‘6’.
Hence, “6” is the correct answer.The expanded form of a dice is given below. If it is changed to a dice after folding, then which dice can be formed?
By observing the figures it is clear that the die in figure (2) can be formed if the expanded form of the dice is folded.
Three different positions of the same dice are shown. Select the number that will be on the face opposite to the one having 2?
From the above question figure it can be concluded that:
from cube 1 and 2 : 1, 3, 6, and 5 are adjacent to 4. Therefore,2 is opposite to 4.
from cube 2 and 3: 3 is opposite 6.
Then 1 will be opposite to 5. The open cube thus formed will be as follows:
Hence, the number that will be on the face opposite to the one having 2 is 4.
as in the dice, 2 is not mentioned so we can choose 4 as its opposite side.
Concept:
If A and B are two independent events, then the probability of A and B will be
P(A∩B) = P(A) × P(B)
Calculation:
Given The dice is thrice as likely to show an odd number than an even number.
Let the odd number be event A and the even number be event B.
P(A) = 3 P(B)
let P(A) = p
P(B) = 3p
Now p + 3p = 1
p = 1/4
When thrown twice, the sum of two numbers thrown is odd when one number is even and the other is odd.
Possible chances are:
1) Even in 1st throw and Odd in 2nd throw = \(\frac {1}{4} \times \frac {3}{4} = \frac {3}{16}\)
2) Odd in 1st throw and Even in 2nd throw = \(\frac {3}{4} \times \frac {1}{4} = \frac {3}{16}\)
∴ The total probability will be:
\(=\frac {3}{16} + \frac {3}{16} = \frac {3}{8}\)
Two positions of a cube are shown below. What will come opposite to face containing ‘B’?
In the case of two dices, we’ll write the face of dices in the anticlock wise direction starting from N,
Dice 
Same face 
Opposite face 

1 
N 
S 
B 
2 
N 
T 
Q 
Hence, we can say that face ‘Q’ will be opposite to face ‘B’.
Two different positions of the same dice are shown. Select the number that will be on the face opposite to the one having '2', if the number on the face opposite to '3' is odd.
The number on the face opposite to ‘3’ is odd.
‘1’ is opposite to ‘3’
‘4’ is opposite to ‘5’
And,
‘2’ is opposite to ‘6’
Hence, “6” is the correct answer.
Based on the figures of the dice below, which number will be opposite to 6?
As you can see, the common number visible in both the dice is 4. Rotate the dice in position II by 180 degrees keeping all the 4 sides same. So we find 3 will be opposite to 6.
Hence, 3 is the right answer.Which of the cube in the given options can’t be made from the below sheet of paper?
When we will fold a given sheet of paper, then faces (1, 5), (2, 4) and (3, 6) will lie opposite to each other. But, in figure C, face 2 and 4 are lying adjacent to each other.
So, figure C can’t be made from the given sheet of paper.
Therefore, answer is figure ‘C’.