Delhi Police PC · Reasoning Ability
3-D figure manipulation and rotation.
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Q1 · Spatial Visualization · EASY
A cube is painted red on all six faces. It is then cut into 27 smaller identical cubes by making two cuts along each edge. How many of the smaller cubes will have exactly two faces painted red?
Q2 · Spatial Visualization · MEDIUM
If a paper is folded in a particular manner as shown by the figures (imagine a square paper folded twice to form a smaller square), and a hole is punched in the folded paper, which of the following patterns will the paper show when unfolded? The folded paper has 4 layers. A single circular hole is punched through all layers at a position that is off-center but not at the corner.
Q3 · Spatial Visualization · MEDIUM
A solid cube of side 6 cm is painted on all faces and then cut into smaller cubes of side 1 cm each. How many of these smaller cubes will have paint on exactly one face?
Q4 · Spatial Visualization · HARD
A rectangular sheet of dimensions 22 cm × 15 cm is rolled along its length to form a cylinder. Another identical sheet is rolled along its breadth to form another cylinder. What is the ratio of the volumes of the two cylinders thus formed? (Use π = 22/7)
Q5 · Spatial Visualization · MEDIUM
A piece of paper is folded once and punched with two holes. How will it appear when unfolded? If the paper is folded vertically in half and two holes are punched on the right side near the fold, how many holes will appear when unfolded?