from the alternatives it is very easy to recognize option (a) as it satisfies all the conditions of a dice formation.
option (a) is clear from the alternatives.
as per the question, sum of the numbers on opposite sides or faces is always 7. Therefore
1 appears opposite 6,
2 appears opposite 5 and
3 must appears opposite of 4.
In (a) 1 cannot adjacent to 6 In (b) 3 cannot adjacent to 4 In (d) 2 cannot appears adjacent to 5 Hence only option (c) is correct.
For the better understanding take a dice and apply the same steps which is mentioned above.
as 5 is common on both the figure, and 1,2,4 and 6 are adjacent to 5. hence 3 is opposite of 5.
Number 1 is common to both the figures (i) and (ii). The dice in fig. (ii) is assumed to be rotated so that 1 dot moves to the top face i.e to the same position as in figure (i) and 2 and 4 dots move to the face behind the faces with 3 and 5 dots respectively. Clearly by combination, 3 dots lie on the face opposite the face having 2 dots. Therefore, when there are 2 dots at the bottom, the number of dots at the top will be 3.
There are 9 columns with 5 cubes = 9 × 5
There are 7 columns with 4 cubes = 7 × 4
There are 5 columns with 3 cubes = 5 × 3
There are 3 columns with 2 cubes = 3 × 2
There is one column with 1 cubes = 1 × 1
Total = 9 × 5 + 7 × 4 + 5 × 3 + 3 × 2 + 1 × 1 = 81
(iii) will be eliminated as the separation present on the two faces which is possible and option (iv) as the separation is not on the middle of the face.
As we can see that ,
The numbers 2, 4, 5 and 6 are on adjacent faces of the number 3.
Therefore, number 1 lies opposite to 3.
The numbers 2, 3 and 5 are on adjacent faces of the number 6.
Therefore, the number 4 lies opposite to 6.
Now, the number 5 lies opposite to 2.
On the basis of question figure pattern ,
The letters A, B, D and E are on the adjacent faces of face C.
Therefore, some other letter lies opposite 'C'.
The letters B, C and E are on the adjacent faces of face D.
Therefore, A lies opposite D.
On the basis of following pattern in given dices , we can say that
The numbers 1, 2, 5 and 6 are on the adjacent faces of the number 3.
So, the number 4 lies opposite 3.
On the basis of following pattern in given dices , we can say that
The numbers 1, 3, 4 and 6 are on faces adjacent to number 5.
Therefore, 5 lies opposite 2.
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