Geometry - General Aptitude (GA) Previous Year Questions

1

2022 · General Aptitude (GA) · Geometry · Cubes

Humanities & Social Sciences-Psychology (XH-C5) 2022

A sphere of radius \( r \) cm is packed in a box of cubical shape.
What should be the minimum volume (in \( cm^3 \)) of the box that can enclose the sphere?

A

\(\frac{r^3}{8} \)

B

\(r^3 \)

C

\(2r^3 \)

D

\(8r^3 \)

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2

2023 · General Aptitude (GA) · Geometry · Circles

Humanities & Social Sciences-Psychology (XH-C5) 2023

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.
The area of the shaded region is _____ cm².

A

6π

B

18

C

20

D

9π

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3

2024 · General Aptitude (GA) · Geometry · Triangles

Humanities & Social Sciences-Psychology (XH-C5) 2024

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to

A

328

B

382

C

238

D

283

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4

2025 · General Aptitude (GA) · Geometry · Curves

Humanities & Social Sciences-Psychology (XH-C5) 2025

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after ‘Iteration \(n\)’ is:
Note: The figures shown are representative.

A

\(\left(\frac{5}{3}\right)^{\frac{n}{2}}\)

B

\(\left(\frac{5}{3}\right)^{n}\)

C

\(\left(\frac{5}{3}\right)^{2n}\)

D

\(\left(\frac{5}{3}\right)^{n(2n-1)}\)

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5

2026 · General Aptitude (GA) · Geometry · Cubes

Humanities & Social Sciences - Psychology (XH-C5) 2026

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ______

A

8

B

4

C

3

D

2

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6

2025 · General Aptitude (GA) · Geometry · Triangles

Humanities & Social Sciences-Psychology (XH-C5) 2025

A stick of length one meter is broken at two locations at distances of \( b_1 \) and \( b_2 \) from the origin (0), as shown in the figure. Note that \( 0 < b_1 < b_2 < 1 \). Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?
Note: All lengths are in meter. The figure shown is representative.

A

\(b_1 < 0.5 \)

B

\(b_2 > 0.5 \)

C

\(b_2 < b_1 + 0.5 \)

D

\(b_1 + b_2 < 1 \)

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