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All questions of Cube & Dice for UPSC CSE Exam
The cube of any multiple of 2 is always divisible by- a)16
- b)12
- c)8
- d)14
Correct answer is option 'C'. Can you explain this answer?
The cube of any multiple of 2 is always divisible by
a)
16
b)
12
c)
8
d)
14
|
Ishita Reddy answered |
Cube of multiple of 2 is divisible by 8
eg:
eg:
Cube of a natural number will never end with the digit- a)0
- b)1
- c)3
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Cube of a natural number will never end with the digit
a)
0
b)
1
c)
3
d)
none of these
|
Arun Sharma answered |
There'd no such digit which can't end in a cube of a natural number. Hence a cube of a natural number can end with any digit.
1³= 1 (ends with 1)
2³= 8 (ends with 8)
3³= 27 (ends with 7)
4³= 64 (ends with 4)
5³= 125 (ends with 5)
6³= 216 (ends with 6)
7³= 343 (ends with 3)
8³= 512 (ends with 2)
9³= 729 (ends with 9)
0³= 0 (ends with 0)
Hence the last digits are 0,1,8,7,4,5,6,3,2,9
Therefore we see every digits are last digits of these cubes. Hence a cube of a natural number can end with any digit.
1³= 1 (ends with 1)
2³= 8 (ends with 8)
3³= 27 (ends with 7)
4³= 64 (ends with 4)
5³= 125 (ends with 5)
6³= 216 (ends with 6)
7³= 343 (ends with 3)
8³= 512 (ends with 2)
9³= 729 (ends with 9)
0³= 0 (ends with 0)
Hence the last digits are 0,1,8,7,4,5,6,3,2,9
Therefore we see every digits are last digits of these cubes. Hence a cube of a natural number can end with any digit.
What is the smallest number by which 3600 be divided to make it a perfect cube?- a)9
- b)50
- c)300
- d)450
Correct answer is option 'D'. Can you explain this answer?
What is the smallest number by which 3600 be divided to make it a perfect cube?
a)
9
b)
50
c)
300
d)
450
|
Raghavendra Sharma answered |
3600=23 X 52 X 32 X 2
To make it a perfect cube it must be divided by
52 X 32 X 2=450
Cube of 0.2 is- a)0.8
- b)0.08
- c)0.008
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Cube of 0.2 is
a)
0.8
b)
0.08
c)
0.008
d)
none of these
|
Ishani Rane answered |
(0.2)3 = 0.2 x 0.2 x 0.2 = 0.008
Therefore, cube of 0.2 is 0.008
Which symbol will be on the face opposite to the face with symbol * ?
- a)@
- b)$
- c)8
- d)+
Correct answer is option 'C'. Can you explain this answer?
Which symbol will be on the face opposite to the face with symbol * ?
a)
@
b)
$
c)
8
d)
+
|
Alok Sen answered |
- The symbols of the adjacent faces to the face with symbol * are @, -, + and $.
- Hence the required symbol is 8.
Two positions of dice are shown below. How many points will be on the top when 2 points are at the bottom?
- a)6
- b)5
- c)4
- d)1
Correct answer is option 'D'. Can you explain this answer?
Two positions of dice are shown below. How many points will be on the top when 2 points are at the bottom?
a)
6
b)
5
c)
4
d)
1
|
Janhavi Mishra answered |
In these 2 positions of a dice, one common face having points 3 is in the same position. Hence according to rule (3), there will be 4 points on the required face.
Two positions of a dice are shown below. Which number will appear on the face opposite to the face with the number 5?
- a)2/6
- b)2
- c)6
- d)4
Correct answer is option 'C'. Can you explain this answer?
Two positions of a dice are shown below. Which number will appear on the face opposite to the face with the number 5?
a)
2/6
b)
2
c)
6
d)
4
|
|
Rajveer Ghoshal answered |
According to the rule no. (3), common faces with number 3, are in same positions. Hence the number of the opposite face to face with number 5 will be 6.
Directions to SolveThe figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed.Question - 
- a)1 and 2 only
- b)2 and 3 only
- c)1, 2, 3 and 4
- d)2 and 4 only
Correct answer is option 'C'. Can you explain this answer?
Directions to Solve
The figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed.
Question -
a)
1 and 2 only
b)
2 and 3 only
c)
1, 2, 3 and 4
d)
2 and 4 only
|
Nilanjan Biswas answered |
C
Directions to Solve The figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed. Question - 
- a)2 and 3 only
- b)1, 3 and 4 only
- c)2 and 4 only
- d)1 and 4 only
Correct answer is option 'B'. Can you explain this answer?
Directions to Solve
The figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed.
Question - a)
2 and 3 only
b)
1, 3 and 4 only
c)
2 and 4 only
d)
1 and 4 only
|
Kiran Reddy answered |
As, shown in figure, these are opposite of each other. Thus, option (2) is correct.
The smallest number by which 5400 must be multiplied so that it become a perfect cube, is- a)2
- b)10
- c)5
- d)3
Correct answer is option 'C'. Can you explain this answer?
The smallest number by which 5400 must be multiplied so that it become a perfect cube, is
a)
2
b)
10
c)
5
d)
3
|
Manoj Ghosh answered |
Find prime factors of 5400
5400=2x3x3x3x2x2x5x5
If we group them in the group of 3
5400=(2x2x2)x(3x3x3)x5x5
Here to make group of 3 for 5
We have to multiply 5400 by 5.
Answer is 5
A cube of side n is painted green on all its sides. It is then cut into n3 identical cubes. How many of the smaller cubes will have three of its sides painted?- a)4
- b)6
- c)8
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
A cube of side n is painted green on all its sides. It is then cut into n3 identical cubes. How many of the smaller cubes will have three of its sides painted?
a)
4
b)
6
c)
8
d)
Cannot be determined
|
Talent Triumphacademy answered |
Since, all the sides of the cube is painted, the cubes cut out from the corners will have three of its faces green. Since there are 8 corners for a cube, there will be 8 such cubes.
Two positions of dice are shown below. How many points will appear on the opposite to the face containing 5 points?
- a)3
- b)1
- c)2
- d)4
Correct answer is option 'D'. Can you explain this answer?
Two positions of dice are shown below. How many points will appear on the opposite to the face containing 5 points?
a)
3
b)
1
c)
2
d)
4
|
|
Amar Chavan answered |
In these two positions one of the common face having 1 point is in the same position. Therefore according to rule (2). There will be 4 points on the required face.
Cube of all even natural numbers is- a)even
- b)odd
- c)even or odd
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Cube of all even natural numbers is
a)
even
b)
odd
c)
even or odd
d)
none of these
|
S.v. Reddy answered |
Any even number to power 2 will have unit digit number
Example : 2^8=16÷8=2
16÷2=8
Example : 2^8=16÷8=2
16÷2=8
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7. Question - If the dice (I), (II) and (III) have even number of dots on their bottom faces, then what would be the total number of dots on their top faces?- a)7
- b)11
- c)12
- d)14
Correct answer is option 'B'. Can you explain this answer?
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7.
If the dice (I), (II) and (III) have even number of dots on their bottom faces, then what would be the total number of dots on their top faces?
a)
7
b)
11
c)
12
d)
14
|
|
Anjali Nair answered |
No. of dots on the top faces of dice (I), (II) and (III) are 5, 1 and 5 respectively.
Required total = 5 + 1 + 5 = 11
Two positions of a cube with its surfaces numbered are shown below. When the surface 4 touch the bottom, what surface will be on the top?
- a)1
- b)2
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
Two positions of a cube with its surfaces numbered are shown below. When the surface 4 touch the bottom, what surface will be on the top?
a)
1
b)
2
c)
5
d)
6
|
|
Rajveer Ghoshal answered |
In these 2 positions one common face with number 1 is in the same position. Hence according to the rule number (3), 2 is opposite 6 and 3 is opposite to 5. Therefore opposite to 4 is 1.
Directions to Solve Six dice with upper faces erased are as shows.The sum of the numbers of dots on the opposite face is 7. Question - If even numbered dice have even number of dots on their top faces, then what would be the total number of dots on the top faces of their dice?- a)12
- b)14
- c)18
- d)24
Correct answer is option 'C'. Can you explain this answer?
Directions to Solve
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7.
If even numbered dice have even number of dots on their top faces, then what would be the total number of dots on the top faces of their dice?
a)
12
b)
14
c)
18
d)
24
|
|
Amar Chavan answered |
Even numbered dice are: (II), (IV) and (VI)
No. of dots on the top face of (II) dice = 6
No. of dots on the top face of (IV) dice = 6
and No. of dots on the top face of (VI) dice = 6
Therefore Required total = 6 + 6 + 6 = 18
Here two positions of dice are shown. If there are two dots in the bottom, then how many dots will be on the top?
- a)2
- b)3
- c)5
- d)6
Correct answer is option 'C'. Can you explain this answer?
Here two positions of dice are shown. If there are two dots in the bottom, then how many dots will be on the top?
a)
2
b)
3
c)
5
d)
6
|
|
Snehal Nambiar answered |
Here the common faces with 4 dots are in same positions.
Hence 2 will be opposite to 5.
From the four positions of a dice given below, find the color which is opposite to yellow ?
- a)Violet
- b)Red
- c)Rose
- d)Blue
Correct answer is option 'A'. Can you explain this answer?
From the four positions of a dice given below, find the color which is opposite to yellow ?
a)
Violet
b)
Red
c)
Rose
d)
Blue
|
|
Amar Chavan answered |
The colours adjacent to yellow are orange, blue, red and rose. Hence violet will be opposite to yellow.
Cube root of 0.064 is- a)0.04
- b) 0.004
- c)0.4
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Cube root of 0.064 is
a)
0.04
b)
0.004
c)
0.4
d)
none of these
|
Sameer Rane answered |
0.064 = 64/1000= 4^3 / 10^3 =(4/10)^3= (2/5)^3
taking cube root of 0.064= 2/5=0.4
Which number is on the face opposite to 6?
- a)4
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
Which number is on the face opposite to 6?
a)
4
b)
1
c)
2
d)
3
|
|
Mansi Kumar answered |
As the numbers 2, 3, 4 and 5 are adjacent to 6. Hence the number on the face opposite to 6 is 1.
Two positions of a cubical block are shown. When 5 is at the top which number will be at bottom?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
Two positions of a cubical block are shown. When 5 is at the top which number will be at bottom?
a)
1
b)
2
c)
3
d)
4
|
|
Amar Chavan answered |
In these 2 positions one common face with number 3, is in same position. Hence according to rule (3), 1 is opposite to 6 and 4 is opposite to 2. Therefore 5 is opposite to 3.
The figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed. Question - 
- a)1 only
- b)2 only
- c)3 only
- d)4 only
Correct answer is option 'A'. Can you explain this answer?
The figure given on the left hand side in each of the following questions is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed.
Question - a)
1 only
b)
2 only
c)
3 only
d)
4 only
|
Dishani Sengupta answered |
The pattern on fig. (X) and also the fact that the faces are rectangle, indicate that only fig. (1) can be obtained by folding fig. (X).
How many points will be on the face opposite to in face which contains 2 points?
- a)1
- b)5
- c)4
- d)6
Correct answer is option 'D'. Can you explain this answer?
How many points will be on the face opposite to in face which contains 2 points?
a)
1
b)
5
c)
4
d)
6
|
Sravya Deshpande answered |
In first two positions of dice one common face containing 5 is same. Therefore according to rule no. (3) the face opposite to the face which contains 2 point, will contains 6 points.
Directions to Solve Six dice with upper faces erased are as shows.The sum of the numbers of dots on the opposite face is 7. Question - If the odd numbered dice have even number of dots on their top faces, then what would be the total number of dots on the top faces of their dice?- a)8
- b)10
- c)12
- d)14
Correct answer is option 'A'. Can you explain this answer?
Directions to Solve
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7.
If the odd numbered dice have even number of dots on their top faces, then what would be the total number of dots on the top faces of their dice?
a)
8
b)
10
c)
12
d)
14
|
|
Rajveer Ghoshal answered |
Odd numbered dice are : (II), (III) and (V)
No. of dots on the top faces of these dice are 2, 2 and 4 respectively.
Required total = 2 + 2 + 4 = 8
Two positions of a dice are shown below. When number '1' is on the top. What number will be at the bottom?
- a)3
- b)5
- c)2
- d)6
Correct answer is option 'B'. Can you explain this answer?
Two positions of a dice are shown below. When number '1' is on the top. What number will be at the bottom?
a)
3
b)
5
c)
2
d)
6
|
|
Amar Chavan answered |
According to the rule (2) when 'one' is at the top, then 5 will be at the bottom.
Here 4 positions of a cube are shown. Which sign will be opposite to '+' ?
- a)%
- b)-
- c)x
- d)$
Correct answer is option 'C'. Can you explain this answer?
Here 4 positions of a cube are shown. Which sign will be opposite to '+' ?
a)
%
b)
-
c)
x
d)
$
|
|
Anjali Nair answered |
From position I and III common face with % is in the same position. Hence according to rule (3) opposite is X.
Which symbol will be on the face opposite to the face with symbol * ?
- a)@
- b)$
- c)8
- d)+
Correct answer is option 'C'. Can you explain this answer?
Which symbol will be on the face opposite to the face with symbol * ?
a)
@
b)
$
c)
8
d)
+
|
Luminary Institute answered |
The symbols of the adjacent faces to the face with symbol * are @, -, + and $. Hence the required symbol is 8.
Directions to Solve
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7.
Question -
If the even numbers of dice have odd number of dots on their top faces and odd numbered dice have even of dots on their bottom faces, then what would be the total number of dots on their top faces?
- a)12
- b)14
- c)16
- d)18
Correct answer is option 'C'. Can you explain this answer?
Directions to Solve
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7.
Question -
If the even numbers of dice have odd number of dots on their top faces and odd numbered dice have even of dots on their bottom faces, then what would be the total number of dots on their top faces?
a)
12
b)
14
c)
16
d)
18
|
|
Lakshmi Nair answered |
No. of dots on the top faces of the dice (II), (IV) and (VI) are 1, 1 and 1 respectively.
No. of dots on the top faces of the dice (I), (III) and (V) are 5, 5 and 3 respectively.
Required total = 5 + 5 + 3 + 1 + 1 + 1 = 16
Directions to Solve Six dice with upper faces erased are as shows.The sum of the numbers of dots on the opposite face is 7. Question - If dice (I), (II) and (III) have even number of dots on their bottom faces and the dice (IV), (V) and (VI) have odd number of dots on their top faces, then what would be the difference in the total number of top faces between there two sets?- a)0
- b)2
- c)4
- d)6
Correct answer is option 'D'. Can you explain this answer?
Directions to Solve
Six dice with upper faces erased are as shows.
The sum of the numbers of dots on the opposite face is 7.
If dice (I), (II) and (III) have even number of dots on their bottom faces and the dice (IV), (V) and (VI) have odd number of dots on their top faces, then what would be the difference in the total number of top faces between there two sets?
a)
0
b)
2
c)
4
d)
6
|
|
Lakshmi Nair answered |
No. of faces on the top faces of the dice (I), (II) and (III) are 5, 1 and 5 respectively.
Therefore, Total of these numbers = 5 + 1 + 5 = 11
No. of dots on the top faces of the dice (IV), (V) and (VI) are 1, 3 and 1 respectively.
Therefore, Total of these numbers = 1 + 3 + 1 = 5
Required difference = 11 - 5 = 6
Which digit will appear on the face opposite to the face with number 4?
- a)3
- b)5
- c)6
- d)2/3
Correct answer is option 'A'. Can you explain this answer?
Which digit will appear on the face opposite to the face with number 4?
a)
3
b)
5
c)
6
d)
2/3
|
|
Shivam Malik answered |
Here the common faces with number 3, are in same positions. Hence 6 is opposite to 2 and 5 is opposite to 1. Therefore 4 is opposite to 3.
How many points will be on the face opposite to the face which contains 3 points?
- a)2
- b)4
- c)5
- d)6
Correct answer is option 'C'. Can you explain this answer?
How many points will be on the face opposite to the face which contains 3 points?
a)
2
b)
4
c)
5
d)
6
|
Dipika Dasgupta answered |
The adjacent faces to the face which 3 points have 2, 1, 4 and 6 points. Hence on the face which is opposite to the face which contains 3 points, there will be 5 points.
When the digit 5 is on the bottom then which number will be on its upper surface?
- a)1
- b)3
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
When the digit 5 is on the bottom then which number will be on its upper surface?
a)
1
b)
3
c)
4
d)
6
|
|
Rajveer Ghoshal answered |
According to the rule no. (3), common faces with number 2 are in same positions. Hence when the digit 5 is on the bottom then 1 will on the upper surface.
Chapter doubts & questions for Cube & Dice - CSAT Preparation 2025 is part of UPSC CSE exam preparation. The chapters have been prepared according to the UPSC CSE exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for UPSC CSE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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