Page 247 - Services Selection Board (SSB) Interviews

Cubes 243

2. ConCept Builder

Direction (Qs. 1-5) : 343 cubes of similar size are 11. What is the number of cubes with no face painted?
arranged in the form of a bigger cube (7 cubes on each (a) 24 (b) 36
side, i. e. , 7 × 7 × 7) and kept on the surface of a room, (c) 48 (d) None of these
all the exposed surfaces (in this case there are 5) are
painted. 12. What is the least possible number of piece which
have at most one colour on them?
1. How many of the cubes have 0 faces painted? (a) 76 (b) 44
(a) 64 (b) 150 (c) 52 (d) None of these
(c) 240 (d) None of these 13. If K is the number of cuboids which have more than
2. How many of the cubes have 2 faces painted? one face painted in the same colour then find the
(a) 23 (b) 29 maximum value of k.
(c) 44 (d) None of these (a) 24 (b) 36
3. How many of the cubes have at most faces painted? (c) 13 (d) None of these
(a) 339 (b) 244 14. What is the ratio of maximum and minimum number
(c) 342 (d) None of these of cuboids with red colour on them?
4. How many of the cubes have at least 2 faces painted? (a) 18:7 (b) 18 :5
(a) 48 (b) 44 (c) 16:5 (d) None of these
(c) 12 (d) None of these
5. How many of the cubes have 3 faces painted? 15. What is the maximum number of cuboids with only
two face painted one face is painted red and other
(a) 0 (b) 3 green?
(c) 5 (d) None of these (a) 18 (b) 16
Direction (Qs. 6-10) : 216 cubes of similar size are (c) 14 (d) None of these
arranged in the form of a bigger cube (6 cubes on each
side, i. e. , 6 × 6 × 6) one cube from a corner is removed Directions (Qs. 16-20) : 125 cubes of similar size are
and then all the exposed surfaces are painted. arranged in the form of a bigger cube (5 cubes on each
6. How many of the cubes have 0 faces painted? side, i. e. , 5 × 5 × 5). From one corner of the top layer
of this cube, four smaller cubes (2 × 2 × 1) are removed.
(a) 64 (b) 125 From the column on the opposite side, two cubes (1 × 1
(c) 27 (d) None of these × 2) are removed, and from the third corner, three cubes
7. How many of the cubes have 2 faces painted? (1 × 1 × 3) are removed and from the fourth column four
(a) 48 (b) 44 cubes (1 × 1 × 4) are removed. All exposed faces of the
(c) 45 (d) None of these block thus formed are coloured red.
8. How many of the cubes have at most faces painted? 16. How many small cubes are left in the block?
(a) 205 (b) 144 (a) 109 (b) 114
(c) 210 (d) None of these (c) 112 (d) 110
9. How many of the cubes have at least 2 faces painted? 17. How many cubes do not have any coloured face?
(a) 55 (b) 44 (a) 38 (b) 44
(c) 52 (d) None of these (c) 25 (d) 35
10. How many of the cubes have exactly 4 face painted? 18. How many cubes have only two coloured faces?
(a) 55 (b) 44 (a) 33 (b) 36
(c) 52 (d) None of these (c) 18 (d) 29
Direction (Qs. 11-15): Four colours namely Blue,
Green, Red and White are used to paint a cube such that 19. How many cubes in the top layer have three red faces
each face is painted in exactly one colour and each colour each?
is painted on at least one face. The cube is now cut into (a) 6 (b) 8
120 identical pieces by making least number of cuts. (c) 3 (d) 4