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 is pivotal in the IPMAT Quantitative Aptitude section, testing students' ability to analyze spatial relationships and apply mathematical concepts to solve problems. 

Geometry questions are a scoring area and 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 easily explores key areas, solved examples, and strategies to tackle IPMAT Geometry Questions, ensuring you're well-prepared to handle any challenge in this section.

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Why IPMAT Geometry Questions Are Important?

Geometry questions in IPMAT assess your conceptual clarity and problem-solving speed.

The questions often cover 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.

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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, and z are integers that are sides 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 tangent to both the circles passing through R. P'Q' is another tangent to the circles touching them at P and Q respectively, and cutting AB at S. PQ measures 6 cm. Point S is at a distance of 5 cm and 4 cm 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 circle's radius. 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 with a radius of 6 m, a boy starts from point A on the circumference and walks along a chord AB of length of 3 m. He then walks along another chord BC of 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 the ground are 1 m apart. If a cow moves in the field in such a way that its distance from the two points is always in a 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 that: 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 circumference of a circle equals the perimeter of a triangle of equal sides and a square's perimeter. 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 examples illustrate the diversity and depth of IPMAT geometry questions.

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Additional IPMAT Geometry Questions with Answers

1. A triangle has 7 cm, 24 cm, and 25 cm sides. What type of triangle is it?

• Scalene
• Right-angled
• Isosceles
• Equilateral

Answer: B) 

2. What is the area of an equilateral triangle with a side length of 10 cm?

• 25√3 cm²
• 50√3 cm²
• 100 cm²
• 100√3 cm²

Answer: B) 

3. A circle has a radius of 14 cm. What is its circumference?

• 44 cm
• 88 cm
• 176 cm
• 28 cm

Answer: B)

4. The diagonal of a square is 10√2 cm. What is the area of the square?

• 50 cm²
• 100 cm²
• 200 cm²
• 25 cm²

Answer: B) 

5. A sector of a circle has a central angle of 90° and a radius of 14 cm. What is the area of the sector?

• 49π cm²
• 98π cm²
• 154 cm²
• 77 cm²

Answer: A) 

6. If the sum of the interior angles of a polygon is 900°, how many sides does the polygon have?

• 6
• 7
• 8
• 9

Answer: B)

7. The length and breadth of a rectangle are in the ratio 3:2. If the perimeter is 50 cm, what is its area?

• 100 cm²
• 120 cm²
• 150 cm²
• 200 cm²

Answer: A) 

8. The inradius of a right-angled triangle with legs 6 cm and 8 cm is:

• 2 cm
• 3 cm
• 4 cm
• 5 cm

Answer: A) 

9. A cone has a base radius of 7 cm and a height of 24 cm. What is its slant height?

• 25 cm
• 26 cm
• 27 cm
• 28 cm

Answer: A)

10. If the side of a cube is doubled, how many times does its volume increase?

• 2 times
• 4 times
• 6 times
• 8 times

Answer: D)

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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 understanding the wide-ranging scope of IPMAT Geometry Questions. Each topic is crucial and requires in-depth study.

Read: IPMAT Quantitative Aptitude Syllabus 2025

Strategies to Solve IPMAT Geometry Questions

Geometry problems in the IPMAT exam tend to check your skill to analyze figures, apply theorems, and utilize logical reasoning effectively.

You require a systematic preparation plan that increases accuracy and speed to perform well in this section.

Here are the major preparation strategies framed for typical situations to enable you to solve problems effectively:

1. Visualize with Accurate Diagrams

Creating accurate and well-marked diagrams is one of the best methods of solving IPMAT geometry questions.

Most problems become more straightforward when you can visualize relationships between shapes, lines, and angles.

How to use this:

• Always draw the given geometric shape neatly, even if a diagram is given in the question.
• Mark all known values, such as angles, side lengths, and points of interest.
• Use distinct markings for congruent angles or equal sides to spot patterns easily.

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

2. Understand Key Relationships and Theorems

Most IPMAT geometry questions hinge on basic theorems and principles. 

Accessing these as readily available is quite a speed-booster.

Key Theorems & Formulae:

3. Break Down Complex

Most geometry questions are about composite figures.

Rather than attempting to solve them as a whole, decompose them into simpler shapes and compute their properties separately.

How to do it:

• Find smaller known shapes inside the complex figure.
• Compute individual areas, perimeters, or angles separately.
• Add the results to obtain the final answer.

Example: For a semicircle within a rectangle, first calculate the area of the rectangle and then subtract the area of the semicircle to determine the space left.

4. Leverage Symmetry and Ratios

Identifying symmetry and proportionality in geometric shapes assists in simplifying problems and minimizing redundant calculations.

Symmetry Applications:

• In an equilateral triangle, the altitude splits it into two equal right-angled triangles.
• In regular polygons, interior angles and side lengths have a constant ratio.

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

5. Approximation for Speed

While exact values are essential, approximations can help speed up calculations when precision is not critical.

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

Knowledge of past year IPMAT geometry questions can identify typical question patterns and enhance problem-solving effectiveness. 

Practice Strategy:

• Practice old-year papers and mark down typically tested areas. 
• Practice at timed intervals to enhance speed and accuracy in test situations. 
• Go through mistakes and learn how to solve them correctly to avoid recurring errors.

Read: How to Improve Your Quantitative Aptitude Skills for IPMAT?

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Importance of Practice for IPMAT Geometry Questions

Geometry questions for the 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.

You can excel in this section with consistent practice, a clear understanding of concepts, and efficient time management.

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.

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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, tangent-secant, and 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.