Where can I find geometry aptitude questions with solutions?

ExamPrev provides comprehensive geometry aptitude questions with detailed formulas and step-by-step solutions for competitive exam preparation including GATE, CAT, SSC, and banking exams.

What are the important geometry formulas for competitive exams?

Important geometry formulas include area and perimeter of triangles, circles, rectangles, polygons, Pythagorean theorem, angle properties, similarity and congruence theorems, and coordinate geometry formulas.

How to prepare geometry for quantitative aptitude?

Prepare geometry by learning basic formulas, practicing various types of questions, understanding theorems and properties, solving previous year papers, and working through practice problems regularly.

Which exams include geometry aptitude questions?

Geometry aptitude questions appear in GATE, CAT, SSC CGL, SSC CHSL, banking exams (IBPS, SBI), railway exams, and other competitive examinations.

Basic Mathematics

Number System LCM & HCF Percentage Ratio & Proportion Average Simple Interest

Business Mathematics

Profit & Loss Compound Interest Partnership Discount Stocks & Shares Banking

Time, Work & Motion

Time & Work Pipes & Cisterns Time, Speed & Distance Trains Boats & Streams Races

Advanced Mathematics

Algebra Geometry Mensuration Trigonometry Logarithms & Indices Coordinate Geometry

Statistics & Probability

Statistics Probability Permutation Combination Set Theory Data Interpretation

Geometry Aptitude Questions & Formulas with answer

Ques 11 GATE 2025

A stick of length one meter is broken at two locations at distances of b₁ and b₂ from the origin (0), as shown in the figure. Note that 012<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.

b₁<0.5

b₂>0.5

b₂1+0.5

b₁+b₂<1

Ques 12 GATE 2025

Spheres of unit diameter are centered at (l,m,n) where l, m, and n take every possible integer values.
The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, x is the distance to its nearest sphere and y is the distance to its next nearest sphere. The value of y/x is:

2√2

1/√2

√2

Ques 13 GATE 2025

In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2. ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as shown in the figure.
Which one of the following statements is true about the shaded area PQS?
Note: The figure shown is representative.

The shaded area is 16/9 times the area of the semicircle with the diameter PS.

The shaded area is equal to the area of the semicircle with the diameter PS.

The shaded area is 14/9 times the area of the semicircle with the diameter PS.

The shaded area is 14/25 times the area of the semicircle with the diameter PQ.

Ques 14 GATE 2025

Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?

Circle; Square; Equilateral triangle; Isosceles triangle

Isosceles triangle; Equilateral triangle; Square; Circle

Equilateral triangle; Isosceles triangle; Square; Circle

Isosceles triangle; Square; Equilateral triangle; Circle

Ques 15 GATE 2025

In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.
What is the area (in cm²) of the rectangle PLMN?
Note: The figure shown is representative.

2√2

Ques 16 GATE 2025

Three villages P, Q, and R are located in such a way that the distance PQ=13 km, QR=14 km, and RP=15 km as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.

10.5

11.0

12.0

12.5

Ques 17 GATE 2025

2√2

Ques 18 GATE 2024 SET-2

A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.
The minimum number of such cuts required is

Ques 19 GATE 2023 SET-2

Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?

Ques 20 GATE 2023

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

20/7

28/5

9/2

35/4

Ques 21 GATE 2023

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

20/7

28/5

9/2

35/4

Ques 22 GATE 2022 SET-2

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other?

Ques 23 GATE 2022

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.
What is the ratio of the areas of unshaded regions of case M to that of case N?

2:3

1:1

3:2

2:1