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GATE 2025 CH – 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 options A to D, each a cross made of five squares, with a black dot at one corner of the outer end of each of the 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

The cross itself has 4-fold symmetry, so the dots must repeat after every 90° turn. A turn of 90° clockwise takes a dot on the right side of the top arm to the lower side of the right arm, then to the left side of the bottom arm, then to the upper side of the left arm. In option B the dots are on the right of the top arm, the bottom of the right arm, the left of the bottom arm and the top of the left arm, so it repeats. In A, C and D at least one arm's dot is on the wrong side.