IPMAT Geometry Questions: Sample Questions for Practice

Overview: Triangles, circles, and mensuration dominate IPMAT Geometry Questions, with triangles alone appearing in over 30% of the section. Discover strategies, solve common question types, and master formulas to ace this crucial part of the exam.

Geometry plays a pivotal role in the IPMAT Quantitative Aptitude section, testing a student's ability to analyze spatial relationships and apply mathematical concepts to solve problems. Geometry questions are not only a scoring area but also a determinant of logical reasoning skills.

These questions demand a clear understanding of core concepts, quick thinking, and an ability to apply mathematical formulas effectively.

This guide explores key areas, solved examples, and strategies to tackle IPMAT Geometry Questions with ease, ensuring you're well-prepared to handle any challenge in this section.

Download Free Study Materials for IPMAT 2025 by SuperGrads

Why IPMAT Geometry Questions Are Important?

Geometry questions in IPMAT assess your conceptual clarity and problem-solving speed. The questions often cover a mix of basic principles and advanced applications, making it essential to prepare systematically.

Topics such as triangles, circles, quadrilaterals, and mensuration form the foundation of this section of the IPMAT Exam. A well-prepared student can leverage this section to gain an edge over competitors.

Moreover, geometry questions often integrate with other quantitative aptitude topics like algebra and trigonometry, adding layers of complexity. This makes it even more critical to understand the underlying principles thoroughly.

Prepare with Online Lectures for IPMAT 2025 by SuperGrads

Sample IPMAT Geometry Questions And Solutions

These questions are designed to challenge your understanding and analytical abilities. Below are common types with detailed sample IPMAT geometry questions with answers:

Q1. x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z.

• a) 2
• b) 3
• c)1
• d) More than one possible value of z exists

Answer: B

Q2. There is an equilateral triangle with a square inscribed inside it. One of the sides of the square lies on a side of the equilateral △. What is the ratio of the area of the square to that of the equilateral triangle?

• a) 12 : 12 + 7√3
• b) 24 : 24 + 7√3
• c) 18 : 12 + 15√3
• d) 6 : 6 + 5√3

Answer: A

Q3. Triangle ABC has angles A = 60° and B = 70°. The incenter of this triangle is at I. Find angle BIC.

• a) 90°
• b) 130°
• c) 80°
• d) 120°

Answer: D

Q4. Two circles with centres O1 and O2 touch each other externally at a point R. AB is a tangent to both the circles passing through R. P'Q' is another tangent to the circles touching them at P and Q respectively and also cutting AB at S. PQ measures 6 cm and the point S is at distance of 5 cms and 4 cms from the centres of the circles. What is the area of the triangle SO1O2?

• a) 9 cm^2
• b) 3(4+√7)/2 cm^2
• c) 27/2 cm^2
• d) (3√41)/2 cm^2

Answer: B

Q5. A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals

• a) (2 + √3)
• b) (1 + √2)
• c) (7 + 4√3)
• d) (97 + 56√3)

Answer: D

Click to Download | IPMAT Sample Paper with Solutions

Q6. The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

• a) 28
• b) 29
• c) 31
• d) 33

Answer: B

Q7. On a circular path of radius 6 m a boy starts from a point A on the circumference and walks along a chord AB of length 3 m. He then walks along another chord BC of length 2 m to reach point C. The point B lies on the minor arc AC. The distance between point C from point A is

• a) 15√+35√/2 m
• b) 8 m
• c) √13 m
• d) 6 m

Answer: A

Q8. Two points on a ground are 1 m apart. If a cow moves in the field in such a way that it's distance from the two points is always in ratio 3: 2 then

• a) the cow moves in a straight line
• b) the cow moves in a circle
• c) the cow moves in a parabola
• d) the cow moves in a hyperbola

Answer: B

Q9. Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so thatAP : PB = BQ : QC = CR : RD = DS : SA = 1 : n . Then the ratio of the area of PQRS to the area of ABCD is

• a) 1 : (1 + n)
• b) 1 : n
• c) 1 + n^2 : (1 + n)^2
• d) (1 + n ) : (1 + n^2)

Answer: C

Q10. The length of the circumfernece of a circle equals the oerimeyter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c,t, and s, respectively. Then,

• a) s > t > c
• b) c > t > s
• c) c > s > t
• d) s > c > t

Answer: C

These example illustrate the diversity and depth of IPMAT geometry questions.

Download Here | IPMAT Previous Year Question Papers PDF

Click to Attempt Free Mock Test for IPMAT Prep

Topics Covered in IPMAT Geometry Questions

The geometry section of the IPMAT exam includes a diverse range of topics, as detailed below:

Topic	Subtopics
Triangles	Types of triangles, angle bisectors, incenters, circumcenters, medians, and Pythagoras theorem
Circles	Chords, tangents, arcs, sector areas, properties of concentric and externally tangent circles
Quadrilaterals	Squares, rectangles, rhombuses, trapeziums, and parallelograms
Mensuration	Areas, perimeters, and volumes of 2D and 3D shapes
Polygons	Regular polygons, angle properties, and diagonals
Coordinate Geometry	Slopes, distances, midpoints, and equations of lines

The above table serves as a roadmap to understand the wide-ranging scope of IPMAT Geometry Questions. Each topic is crucial and requires in-depth study.

Know More | IPMAT Quantitative Aptitude Syllabus 2025

Strategies to Solve IPMAT Geometry Questions

Each type of geometry problem in IPMAT requires specific techniques. Below are the preparation strategies designed to common scenarios to help you solve problems efficiently:

1. Visualize with Accurate Diagrams

Drawing diagrams simplifies complex questions and highlights relationships between shapes, angles, and lines. Label all known values, angles, and sides to streamline problem-solving.

• Tip: For circle-based questions, mark radii, chords, and tangent points clearly.

2. Understand Key Relationships and Theorems

Memorize essential geometric relationships and theorems like the Pythagoras theorem and tangent-secant rule. These are often critical in solving IPMAT Geometry Questions.

• Example Formula: Area of a triangle = ½ x base x height

3. Break Down Complex

Shapes Divide compound shapes into simpler components. Solve for each part individually and then combine the results. Use formulas specific to basic shapes to streamline calculations.

• Example: For a semicircle inscribed in a rectangle, calculate the area of the rectangle and subtract the semicircle's area.

4. Leverage Symmetry and Ratios

Use symmetry and proportionality to reduce unnecessary calculations. Recognize fixed ratios for common shapes like equilateral triangles and regular polygons.

• Example: Height of an equilateral triangle = √3/2 ×side length.

5. Approximation for Speed

Approximate intermediate values like π ≈ 3.14 = √3 ≈ 1.73 when precision isn't critical. Refine as needed in the final step.

6. Practice with Past Questions

Solve previous IPMAT Geometry Questions to understand patterns and frequently tested topics. Familiarity with question types can improve both speed and confidence.

By combining these strategies with regular practice, you can efficiently tackle these questions, reduce errors, and maximize your score in this crucial section.

Know More | How to Improve Your Quantitative Aptitude Skills for IPMAT?

Download Free IPMAT PYPs Based on Geometry by SuperGrads

Importance of Practice for IPMAT Geometry Questions

Geometry questions for IPMAT exam demand rigorous practice to build conceptual clarity and speed. Working through practice problems daily ensures you're prepared for even the trickiest questions. Incorporate a variety of problems, including those from past exams, to develop a strong problem-solving approach.

Geometry questions are a cornerstone of the quantitative aptitude section and offer a high-scoring opportunity for well-prepared students. With consistent practice, a clear understanding of concepts, and efficient time management, you can excel in this section.

Use this detailed guide as your go-to resource for mastering important IPMAT geometry questions, ensuring that you're thoroughly prepared for any challenge that comes your way.

Prepare With | IPMAT Quantitative Aptitude Books 2025

Unlock Grandmaster’s Box for IPMAT 2025 from SuperGrads

Key Takeaways:

• Essential Topics Covered: Focus on triangles, circles, quadrilaterals, mensuration, and coordinate geometry to streamline your preparation for IPMAT Geometry Questions.
• Effective Problem-Solving Strategies: Use techniques like diagram visualization, key formulas, symmetry, and approximations to tackle questions efficiently.
• Master Theorems and Formulas: Theorems like Pythagoras and tangent-secant, along with essential area and volume formulas, are vital for solving complex problems.
• Importance of Practice: Regularly solving past IPMAT question papers helps recognize patterns and improve accuracy.
• Time Management Tips: Break down complex shapes, simplify calculations, and use approximations to save time during the exam.