Geometry - General Aptitude (GA) Previous Year Questions

1

2022 · General Aptitude (GA) · Geometry · Cubes

Humanities & Social Sciences-English (XH-C2) 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

\(8r^3 \)

Open complete paper

2

2023 · General Aptitude (GA) · Geometry · Triangles

Humanities & Social Sciences-English (XH-C2) 2023

How many triangles are present in the given figure?

A

12

B

16

C

20

D

24

Open complete paper

3

2024 · General Aptitude (GA) · Geometry · Triangles

Humanities & Social Sciences-English (XH-C2) 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

Open complete paper

4

2025 · General Aptitude (GA) · Geometry · Curves

Humanities & Social Sciences-English (XH-C2) 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

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

B

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

C

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

D

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

Open complete paper

5

2026 · General Aptitude (GA) · Geometry · Circles

Humanities & Social Sciences - English (XH-C2) 2026

As shown in the figure, circle \(C_1\) with center \(O_1\) and radius \(r_1\) touches the square \(VWXY\) at points \(P\) and \(Q\) while circle \(C_2\) with center \(O_2\) and radius \(r_2\) touches the square \(VWXY\) at points \(R\) and \(S\). The two circles touch each other at \(T\).
Given \(r_1 = 1\) cm and \(\overline{VY} = \overline{VW} = 4\) cm, \(r_2 =\) ______ cm.

A

\(4 - 3\sqrt{2}\)

B

\(1 + 2\sqrt{2}\)

C

\(7 - 4\sqrt{2}\)

D

\(5 + 3\sqrt{2}\)

Open complete paper

6

2023 · General Aptitude (GA) · Geometry · Circles

Humanities & Social Sciences-English (XH-C2) 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

Open complete paper