Practice UPSC CSAT previous year questions from 2011–2026 classified underCubes and Dice. Review the original question, four options, correct answer and explanation for every PYQ.
5 questions • 2011–2026
What is the least possible number of cuts required to cut a cube into 64 identical pieces?
64 = 4×4×4. Three cuts in each of the three perpendicular directions create 4 layers along each axis, requiring 3+3+3 = 9 cuts.
125 identical cubes are arranged in the form of cubical block. How many cubes are surrounded by other cubes from each side?
A 5×5×5 block has an internal 3×3×3 block, hence 27.
A cuboid of dimensions 7cm × 5cm × 3cm is painted red, green and blue on each pair of opposite faces of dimensions 7cm × 5cm, 5cm × 3cm, 7cm × 3cm respectively. It is cut into 1cm cubes. Which statements are correct? 1. Exactly 15 small cubes have no paint. 2. Exactly 6 small cubes have exactly two faces, one blue and one green.
The unpainted core is (7−2)×(5−2)×(3−2)=15 cubes, so statement 1 is true. The blue-green intersections yield 4 cubes with exactly those two painted faces; the endpoint cubes also have a third painted face. Hence statement 2 is false and only statement 1 is correct.
A cube has all its faces painted with different colours. It is cut into smaller cubes of equal sizes such that the side of the small cube is one-fourth the big cube. The number of small cubes with only one of the sides painted is:
The large cube becomes 4×4×4 small cubes. On each face, the cubes with exactly one painted face are the interior face cells: (4−2)²=4 per face. Across 6 faces, 6×4=24.
Cube adjacency problem on PDF page 28
Each of the six different faces of a cube has been coated with a different colour i.e., V, I, B, G, Y and O. Following information is given: 1. Colours Y, O and B are on adjacent faces. 2. Colours I, G and Y are on adjacent faces. 3. Colours B, G and Y are on adjacent faces. 4. Colours O, V and B are on adjacent faces. Which is the colour of the face opposite to the face coloured with O?
The adjacency constraints force G to be opposite O; hence option C.
Attempt questions one by one with UPSC-style marking and immediate explanations.