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GATE 2025 CE (CE1) – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

An object is said to have an $n$-fold rotational symmetry if the object, rotated by an angle of $\frac{2\pi}{n}$, is identical to the original.

Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen?

Note: The figures shown are representative.

Four plus-shaped figures (A) to (D), each made of five squares, with a black dot at one corner of each of its four arms.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (B) Option B in the figure

Explanation

A cross has 4-fold symmetry only if its dots go into each other when it is turned through 90°. In option B the dots are at the top right corner of the top arm, the bottom right corner of the right arm, the bottom left corner of the bottom arm and the top left corner of the left arm. Turning the figure 90° clockwise carries each dot onto the next one, so the figure looks the same after every quarter turn. In A, C and D the dot on one arm does not land on a dot of the next arm after a 90° turn, so those figures change.