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All questions of Non-Verbal Reasoning for Class 10 Exam

A cube of side 10cm is coloured green with a 2 cm wide red strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size then how many cubes are without any colour?
  • a)
    4
  • b)
    8
  • c)
    27
  • d)
    64
Correct answer is option 'C'. Can you explain this answer?

Hridoy Iyer answered
Understanding the Cube Dimensions
The original cube has a side length of 10 cm. It is painted with a 2 cm wide red strip along all edges of each face.
Calculating the Inner Dimension
- The red strip removes 2 cm from each side of the cube.
- Since the strip is painted on all sides, we need to subtract 4 cm (2 cm from each side) from the original dimension.
- Thus, the dimension of the unpainted inner cube is:
- 10 cm - 4 cm = 6 cm.
Volume of the Smaller Cubes
- The cube is divided into 125 smaller cubes.
- Since 125 is equal to 5^3, each smaller cube has a side length of:
- 10 cm / 5 = 2 cm.
Determining the Number of Unpainted Cubes
- The unpainted inner cube has dimensions of 6 cm, and since each smaller cube has a side of 2 cm, we can determine how many smaller cubes fit within the unpainted area:
- Number of smaller cubes along each dimension = 6 cm / 2 cm = 3 cubes.
- Therefore, the total number of smaller cubes that are completely unpainted is:
- 3 x 3 x 3 = 27.
Conclusion
The total number of smaller cubes without any color is 27. Thus, the correct answer is option C.

A cube painted blue on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?
  • a)
    6
  • b)
    4
  • c)
    8
  • d)
    12
Correct answer is option 'A'. Can you explain this answer?

Aditi Sharma answered
The cubes having only one face painted are the cubes which lie at the centre of each face of big cube. There are 6 faces of a cube. So, required no. of cubes having one face painted = 6 

In the given figure, which number lies at the bottom face in position B?
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?

Meera Rana answered
From positions A and B we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions A and B we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6. Thus, 2 lies opposite 4, 1 lies opposite 6 and consequently 5 lies opposite 3.
2 lies at the bottom face in position B.

In the given figure find the number of dots on the face opposite the face having 3 dots.
  • a)
    4
  • b)
    5
  • c)
    6
  • d)
    2
Correct answer is option 'C'. Can you explain this answer?

Radha Iyer answered
From figures (i), (ii) and (iii), we conclude that 3, 4, 6 and 1 dots appear adjacent to 2 dots. Therefore, 5 dots appear opposite 2 dots. Now, from figures (i) and (iii), we conclude that 2, 4 and 1 dots appear adjacent to 3 dots. Therefore, either 5 or 6 dots appear opposite 3 dots. Since, 5 dots appear opposite 2 dots, it follows that 6 dots appear opposite 3 dots.

How many dots are there on the dice face opposite the one with three dots? 
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    6
Correct answer is option 'C'. Can you explain this answer?

Aditi Sharma answered
From    figures (i), (ii), (iv) we observe    that     6, 4, 3, 1 lie adjacent to 2. Hence the number 5 will appear on the face showing 2.

Two positions of a block are given below. When 1 is at the top, which number will be at the bottom? 
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    6
Correct answer is option 'D'. Can you explain this answer?

Meera Rana answered
2 is common to the two positions of the dice. If the dice in figure (i) is rotated so that 2 remains on the top face and the numbers 3 & 6 move to the face hidden behind 5 & 1 respectively. 5 lies opposite to 3 and 6 lies opposite to 1.

Three different positions X, Y, Z of a dice are as shown below. 

Which number lies opposite to 6?
  • a)
    1
  • b)
    2
  • c)
    4
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?

Meera Rana answered
From positions X and Y we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions Y and Z we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6.

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