InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
How many cubes have only one coloured face each ? |
| Answer» 8 from (I) and 8 from (II) Therefore 8 from each. | |
| 2. |
What is the number of cubes with at least one green face each ? |
| Answer» 24 from (I) and 14 from (II) | |
| 3. |
How many cubes have two red and one green face on each ? |
| Answer» None from (I) and 4 from (II) | |
| 4. |
How many cubes have no coloured face at all ? |
| Answer» There is no such cube in all, where all the faces are unclosured. | |
| 5. |
How many cubes have each one red and another green ? |
| Answer» 16 from (I) and 8 from (II) | |
| 6. |
How many cubes have at least two coloured red faces each ? |
| Answer» 64 and 64 cubes of both types of cubes are such who have at least two coloured faces red each. Therefore, total number of the required cubes is 128. | |
| 7. |
What is the total number of red faces ? |
| Answer» No. of red faces among first 64 cubes = 128 No. of red faces among second 64 cubes = 192 Therefore, total number of red faces = 128 + 192 = 320 | |
| 8. |
How many cubes have two adjacent blue faces each ? |
| Answer» Second 64 cubes are such each of whose two faces are blue. | |
| 9. |
How many cubes have only one red face each ? |
| Answer» Out of 128 cubes no cube have only one face is red | |
| 10. |
Which two colours have the same number of faces ? |
| Answer» First 64 cubes are such each of whose two faces are green and second 64 cubes are such each of whose two faces are blue. Therefore, green and blue colours have the same number of faces. | |
| 11. |
The upper face is _________ |
| Answer» | |
| 12. |
How many small cubes are there where one face is green and other one is either black or red ? |
| Answer» Number of small cubes having one face green and the other one is either red or black = 8 x 2 = 16 | |
| 13. |
How many small cubes are there whose no faces are coloured ? |
| Answer» Number of small cubes having no face coloured = (x - 2)3 = (4 - 2)3 = 8 | |
| 14. |
How many small cubes are there whose 3 faces are coloured ? |
| Answer» Number of small cubes having three faces coloured = 1 at each corner = 1 x 8 = 8> | |
| 15. |
How many small cubes are there whose only one face is coloured ? |
| Answer» Number of small cubes having only one face coloured = 4 from each face = 4 x 6 = 24 | |
| 16. |
How many small cubes have only one face coloured ? |
| Answer» Number of small cubes having only one face coloured = (x - 2)2 x No. of faces = (4 - 2)2 x 6 = 24 | |
| 17. |
How many small cubes have no faces coloured ? |
| Answer» Number of small cubes having only one faces coloured = (x - 2)3 Here, x = side of big cube / side of small cube x = 4 /1 x = 4 Required number = (4 -2)3 = 8 | |
| 18. |
How many small cubes are there whose three faces are coloured ? |
| Answer» Number of small cubes having three faces coloured = No. of corners = 8 | |
| 19. |
How many small cubes are there whose two adjacent faces are coloured red ? |
| Answer» Number of small cubes having two adjacent faces coloured red = (x - 2) x No. of edges = (4 - 2) x 12 = 24 | |
| 20. |
How many small cubes will have will have three faces coloured ? |
| Answer» Such cubes are related to the corners of the cuboid and in the cuboid there are 8 corners. Hence, the required number of small cubes is 8. | |
| 21. |
How many small cubes are there whose at the most two faces are coloured ? |
| Answer» Number of small cubes having two faces coloured = 8 + 8 + 4 + 4 = 24 and Number of small cubes having only one face coloured = 4 x 6 = 24 and Number of small cubes having no face coloured = 4 + 4 = 8 Therefore, total number of small cubes whose at the most two faces are coloured = 24 + 24 + 8 = 56. | |
| 22. |
How many small cubes will have only two faces coloured ? |
| Answer» Number of small cubes having only two faces coloured = 6 from the front + 6 from the back + 2 from the left + 2 from the right = 16 | |
| 23. |
How many small cubes have three faces coloured ? |
| Answer» Such cubes are related to the corners of the cuboid and there are 8 corners. Hence, the required number is 8. | |
| 24. |
How many small cubes will have no face coloured ? |
| Answer» Number of small cubes have no face coloured = (4 - 2) x (3 - 2) = 2 x 1 = 2 | |
| 25. |
How many small cubes will have only one face coloured ? |
| Answer» 2 from the front + 2 from the back + 3 from the left + 3 from the right + 6 from the top + 6 from the bottom = 22 | |
| 26. |
How many small cubes will have no faces coloured ? |
| Answer» Required number of small cubes = (5 - 2) x (4 - 2) x (3 - 2) = 3 x 2 x 1 = 6 | |
| 27. |
How many small cubes will have two faces coloured with red and green colours ? |
| Answer» Required number of small cubes = 6 from the top and 6 from the bottom = 12 | |
| 28. |
The face opposite to brown is _________ |
| Answer» | |
| 29. |
Which face is opposite to green ? |
| Answer» | |
| 30. |
How many small cubes will be formed having only one face coloured ? |
| Answer» No. of small cubes having only one face coloured = (5 - 2)2 x 6 = 9 x 6 = 54 | |
| 31. |
How many small cubes will be formed having no face coloured ? |
| Answer» No. of small cubes having no face coloured = (x - 2)3 = (5 - 2)3 = 27 | |
| 32. |
How many cubes having red, green and black colours on at least one side of the cube will be formed ? |
| Answer» Such cubes are related to the corners of the cuboid. Since the number of corners of the cuboid is 4. Hence, the number of such small cubes is 4. | |
| 33. |
How many small cubes will be formed ? |
| Answer» Number of small cubes = l x b x h = 6 x 4 x 1 = 24 | |
| 34. |
How many cubes will have 4 coloured sides and two non-coloured sides ? |
| Answer» Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 non-coloured sides. | |
| 35. |
How many cubes will have green colour on two sides and rest of the four sides having no colour ? |
| Answer» There are 16 small cubes attached to the outer walls of the cuboid. Therefore remaining inner small cubes will be the cubes having two sides green coloured. So the required number = 24 - 16 = 8 | |
| 36. |
How many cubes will remain if the cubes having black and green coloured are removed ? |
| Answer» Number of small cubes which are Black and Green is 8 in all. Hence, the number of remaining cubes are = 24 - 8 = 16 | |