TNPSC Group IV · Aptitude and Mental Ability Test
Dice problems — opposite faces and cube counting.
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Q1 · Dice and Cubes · MEDIUM
A standard dice is shown in two different positions. In Position 1, the top face shows 3, the front face shows 5, and the right face shows 2. In Position 2, the same dice is rotated so that the top face shows 5, the front face shows 6, and the right face shows 3. What number is on the face opposite to 2?
Q2 · Dice and Cubes · EASY
A dice is thrown twice. In the first throw, 1, 2, and 3 are visible. In the second throw, 4, 5, and 6 are visible. Which of the following pairs of numbers are definitely opposite to each other?
Q3 · Dice and Cubes · EASY
A cube is painted red on all faces and then cut into 64 smaller cubes of equal size. How many smaller cubes will have exactly two faces painted red?
Q4 · Dice and Cubes · MEDIUM
A cube is painted blue on all six faces. It is then cut into 125 identical smaller cubes. How many of the smaller cubes will have no face painted?
Q5 · Dice and Cubes · HARD
A solid cube of side 6 cm is painted on all faces and then cut into smaller cubes of side 1 cm. Among the smaller cubes, how many will have paint on exactly three faces?