Cubes & Dice MCQs for UPSC Prelims

45 practice questions on Cubes & Dice from the Logical Reasoning section of the UPSC Prelims syllabus. 45 come with a written explanation and 13 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

4 Easy 20 Medium 21 Hard 13 from past papers

Sample questions

Q1
Previous year question medium

Directions: Rotated positions of a single solid (a cube) are shown below. The various faces of the solid are marked with different symbols: a single dot, two dots, three dots, four dots, a cross and a line. By studying the rotated views, answer the item that follows. What is the symbol on the face opposite to that containing two dots?

  1. A Single dot
  2. B Three dots
  3. C Four dots
  4. D Line
Show answer and explanation

Correct answer: C - Four dots

A cube has three pairs of opposite faces. Tracking the symbols that appear together (adjacent) across the rotated views lets us eliminate every face that shares an edge with the two-dot face, since adjacent faces can never be opposite. Across the views, the two-dot face is seen alongside the single dot, three dots, the cross and the line, so none of these can lie opposite it. The only symbol never adjacent to the two-dot face is the four-dot face, which must therefore be its opposite. Hence the answer is Four dots.

Q2
Previous year question medium

Directions: Rotated positions of a single solid (a cube) are shown below. The various faces of the solid are marked with different symbols: a single dot, two dots, three dots, four dots, a cross and a line. By studying the rotated views, answer the item that follows. What is the symbol on the face opposite to that containing the cross?

  1. A Single dot
  2. B Two dots
  3. C Line
  4. D Four dots
Show answer and explanation

Correct answer: C - Line

From the rotated views, the three pairs of opposite faces work out so that the single dot is opposite the three dots and the two dots are opposite the four dots. That leaves only two symbols, the cross and the line, which must form the third pair of opposite faces. So the face opposite the cross is the line. This is consistent with the views, in which the cross and the line are never shown together on the cube at the same time, confirming they sit on opposite faces. Hence the answer is Line.

Q3
Previous year question hard

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?

  1. A B
  2. B V
  3. C G
  4. D I
Show answer and explanation

Correct answer: C - G

List the neighbours of each colour. From clues 1, 2 and 3, Y is adjacent to O, B, I and G, so the face opposite Y is V. From clues 1 and 4, O is adjacent to Y, B and V. Since a face touches four others and is opposite the one it never shares an edge with, O cannot be opposite Y, B or V, so O is opposite either I or G. From clues 1, 3 and 4, B is adjacent to Y, O, G and V, leaving I as the face opposite B. That uses up I as B's opposite, so the only remaining colour to sit opposite O is G. Hence the face opposite O is coloured G. (The scanned OCR dropped the fourth clue; it is restored here from the original paper.)

Q4
Previous year question medium

Rotated positions of a single solid (a cube) are shown in four views. The various faces of the solid are marked with different symbols: a single dot, two dots, three dots, four dots, a cross, and a line. By studying the four rotated views, answer the item that follows. What is the symbol on the face opposite to that containing a single dot?

  1. A Four dots
  2. B Three dots
  3. C Two dots
  4. D Cross
Show answer and explanation

Correct answer: B - Three dots

A cube has three pairs of opposite faces. By tracking which symbols appear together (adjacent) across the rotated views, the faces that share an edge with the single dot can be eliminated as its opposite. Working through the rotations, the single dot is never seen adjacent to the three dots, while it does appear next to four dots, two dots, the cross and the line; the only face it can never sit beside is three dots, so three dots must be the hidden opposite face. Hence (b) Three dots is correct.

Q5
Previous year question hard

Three views of a single cube, following a particular rotational motion, are given (the visible lettered faces in the three positions are: K with A and B; K with B and H; K with H and P, etc.). What is the letter opposite to A? (Note: this is a non-verbal cube-rotation item showing three positions of the same lettered cube.)

  1. A H
  2. B P
  3. C B
  4. D M
Show answer and explanation

Correct answer: A - H

From the first two views, A, B, H and M all appear adjacent to K, so each of them shares an edge with K and none of them is opposite K. Since A is adjacent to B and to M, the face opposite A must be one of the remaining candidates, H or M. Testing the possibilities: if M were opposite A, then H would have to be opposite B, but the third view shows H and B configured in a way that makes this impossible. Therefore H is opposite A, answer (a).

Q6
Previous year question hard

A cuboid of dimensions 7 cm x 5 cm x 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm x 5 cm, 5 cm x 3 cm, 7 cm x 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct? 1. There are exactly 15 small cubes with no paint on any face. 2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green. Select the correct answer using the code given below:

  1. A 1 only
  2. B 2 only
  3. C Both 1 and 2
  4. D Neither 1 nor 2
Show answer and explanation

Correct answer: A - 1 only

The cuboid yields 7 x 5 x 3 = 105 unit cubes. Statement 1: unpainted cubes form the inner block (7-2) x (5-2) x (3-2) = 5 x 3 x 1 = 15, so it is correct. Statement 2: green sits on the 5 x 3 faces and blue on the 7 x 3 faces, so a cube showing exactly green and blue must lie on an edge where those faces meet - the four vertical edges of length 3. Each such edge has 3 cubes, but its two end cubes are corners that also touch a red 7 x 5 face (three painted faces), leaving 3 - 2 = 1 qualifying cube per edge, i.e. 4 cubes in total, not 6. Statement 2 is wrong. Hence option (a); (b) and (c) accept the miscount of 6, and (d) wrongly rejects the straightforward interior count of 15.

Q7
Previous year question medium

Six squares are coloured, front and back, red (R), blue (B), yellow (Y), green (G), white (W) and orange (O), and are hinged together in a cross-shaped net as shown in the figure. If they were folded to form a cube, what would be the face opposite to the white (W) face? (Note: this is a non-verbal cube-folding item based on the given net of six coloured squares.)

  1. A R
  2. B G
  3. C B
  4. D O
Show answer and explanation

Correct answer: C - B

Folding the given net into a cube and tracking which faces end up parallel, the three pairs of opposite faces work out to be: green opposite orange (G-O), yellow opposite red (Y-R), and blue opposite white (B-W). Taking either green or yellow as the base gives the same pairing. Hence the face opposite white is blue, answer (c).

Q8
Previous year question medium

125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side?

  1. A 27
  2. B 25
  3. C 21
  4. D 18
Show answer and explanation

Correct answer: A - 27

Option (a) is correct. 125 identical cubes form a 5 x 5 x 5 block. A small cube is surrounded on every side exactly when it does not touch any outer face of the block, i.e. it lies in the inner core obtained by stripping one layer from each side. That core measures (5 - 2) x (5 - 2) x (5 - 2) = 3 x 3 x 3 = 27 cubes. Option (b) 25 is a face count, not a volume; options (c) 21 and (d) 18 correspond to no consistent counting of the hidden core.

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