Geometry Study Resources for Competitive Exams

Geometry

Circles Conic Basics Lines & Angles Triangles

Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the length of the longest side? (2022)

A. 10 cm
B. 24 cm
C. 26 cm
D. Cannot be determined

Solution

The longest side of triangle GHI is GI, which measures 26 cm.

Correct Answer: C — 26 cm

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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the perimeter? (2019)

A. 50 cm
B. 60 cm
C. 70 cm
D. 80 cm

Solution

Perimeter = GH + HI + GI = 10 + 24 + 26 = 60 cm.

Correct Answer: A — 50 cm

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Q. In triangle GHI, if the lengths of sides GH, HI, and GI are in the ratio 3:4:5, what type of triangle is it? (2019)

A. Equilateral
B. Isosceles
C. Scalene
D. Right-angled

Solution

Since the sides are in the ratio 3:4:5, it follows the Pythagorean theorem, indicating it is a right-angled triangle.

Correct Answer: D — Right-angled

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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)

A. 10 cm
B. 12 cm
C. 15 cm
D. 25 cm

Solution

Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.

Correct Answer: B — 12 cm

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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of JL? (2022)

A. 10 cm
B. 12 cm
C. 15 cm
D. 25 cm

Solution

Using the Pythagorean theorem, JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12.25 cm.

Correct Answer: B — 12 cm

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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the semi-perimeter of the triangle? (2022)

A. 30 cm
B. 25 cm
C. 20 cm
D. 35 cm

Solution

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Correct Answer: A — 30 cm

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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the semi-perimeter? (2022)

A. 30 cm
B. 25 cm
C. 20 cm
D. 15 cm

Solution

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Correct Answer: A — 30 cm

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Q. In triangle JKL, if JK = 15 cm, KL = 20 cm, and JL = 25 cm, what is the type of triangle? (2023)

A. Equilateral
B. Isosceles
C. Scalene
D. Right-angled

Solution

Since 15² + 20² = 25² (225 + 400 = 625), triangle JKL is a right-angled triangle.

Correct Answer: D — Right-angled

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Q. In triangle JKL, if JK = 5 cm, KL = 12 cm, and JL = 13 cm, what is the type of triangle? (2023)

A. Equilateral
B. Isosceles
C. Scalene
D. Right-angled

Solution

Since 5² + 12² = 13² (25 + 144 = 169), triangle JKL is a right-angled triangle.

Correct Answer: D — Right-angled

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Q. In triangle MNO, if MN = 8 cm, NO = 15 cm, and MO = 17 cm, what is the type of triangle? (2023)

A. Equilateral
B. Isosceles
C. Scalene
D. Right-angled

Solution

Using the Pythagorean theorem, 8² + 15² = 64 + 225 = 289 = 17². Hence, it is a right-angled triangle.

Correct Answer: D — Right-angled

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Q. In triangle PQR, if PQ = 10 cm, PR = 24 cm, and QR = 26 cm, what is the area of the triangle? (2019)

A. 120 cm²
B. 240 cm²
C. 60 cm²
D. 80 cm²

Solution

Using Heron's formula, s = (10 + 24 + 26) / 2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = √(4800) = 120 cm².

Correct Answer: A — 120 cm²

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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the perimeter of the triangle? (2022)

A. 24 cm
B. 26 cm
C. 22 cm
D. 20 cm

Solution

Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.

Correct Answer: A — 24 cm

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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the semi-perimeter of the triangle? (2022)

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Solution

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

Correct Answer: B — 14 cm

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Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the semi-perimeter? (2022)

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Solution

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

Correct Answer: B — 14 cm

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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the length of side XY if side XZ = 10 cm? (2020)

A. 5√2 cm
B. 10 cm
C. 10√2 cm
D. 20 cm

Solution

In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.

Correct Answer: A — 5√2 cm

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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the sides opposite to these angles? (2021)

A. 1:1
B. 1:√2
C. √2:1
D. 2:1

Solution

In an isosceles triangle with angles 45-45-90, the sides opposite the equal angles are equal, hence the ratio is 1:1.

Correct Answer: A — 1:1

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Q. In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)

A. 1:1
B. 1:√2
C. √2:1
D. 2:1

Solution

In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.

Correct Answer: A — 1:1

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Q. In triangle XYZ, if XY = 12 cm, YZ = 16 cm, and XZ = 20 cm, what is the semi-perimeter? (2020)

A. 24 cm
B. 28 cm
C. 30 cm
D. 32 cm

Solution

Semi-perimeter s = (XY + YZ + XZ)/2 = (12 + 16 + 20)/2 = 24 cm.

Correct Answer: A — 24 cm

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Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, what is the length of the longest side? (2020)

A. 8 cm
B. 15 cm
C. 17 cm
D. Not determinable

Solution

The longest side in triangle XYZ is XZ, which measures 17 cm.

Correct Answer: C — 17 cm

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Q. The circumference of a circle is 31.4 cm. What is the radius of the circle? (Use π = 3.14) (2019)

A. 5 cm
B. 10 cm
C. 7 cm
D. 15 cm

Solution

Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm

Correct Answer: A — 5 cm

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Q. The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)

A. 30 cm²
B. 60 cm²
C. 24 cm²
D. 40 cm²

Solution

Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².

Correct Answer: A — 30 cm²

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Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? (2020)

A. Yes
B. No
C. Cannot be determined
D. Only if angle A is 90 degrees

Solution

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.

Correct Answer: A — Yes

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Q. The lengths of the sides of triangle GHI are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)

A. 30 cm²
B. 60 cm²
C. 65 cm²
D. 78 cm²

Solution

This is a right triangle. Area = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm².

Correct Answer: A — 30 cm²

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Q. The perimeter of an equilateral triangle is 36 cm. What is the length of each side? (2021)

A. 9 cm
B. 12 cm
C. 10 cm
D. 8 cm

Solution

In an equilateral triangle, all sides are equal. Therefore, each side = Perimeter / 3 = 36 / 3 = 12 cm.

Correct Answer: B — 12 cm

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Q. The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)

A. 50%
B. 75%
C. 100%
D. 125%

Solution

If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.

Correct Answer: C — 100%

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Q. Two circles have radii of 3 cm and 4 cm. What is the distance between their centers if they are externally tangent? (2022)

A. 7 cm
B. 1 cm
C. 12 cm
D. 5 cm

Solution

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Correct Answer: A — 7 cm

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Q. Two circles touch each other externally. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers? (2023)

A. 8 cm
B. 2 cm
C. 15 cm
D. 10 cm

Solution

Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.

Correct Answer: A — 8 cm

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Q. Two circles with radii 3 cm and 4 cm are externally tangent. What is the distance between their centers? (2022)

A. 7 cm
B. 1 cm
C. 12 cm
D. 5 cm

Solution

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Correct Answer: A — 7 cm

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Q. Two circles with radii 5 cm and 3 cm are externally tangent. What is the distance between their centers? (2023)

A. 8 cm
B. 10 cm
C. 6 cm
D. 5 cm

Solution

Distance between centers = r1 + r2 = 5 cm + 3 cm = 8 cm.

Correct Answer: A — 8 cm

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Q. Two lines are perpendicular to each other. If one line makes an angle of 30 degrees with the horizontal, what is the angle made by the other line with the horizontal? (2022)

A. 30 degrees
B. 60 degrees
C. 90 degrees
D. 120 degrees

Solution

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Correct Answer: C — 90 degrees

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Showing 91 to 120 of 166 (6 Pages)

Geometry MCQ & Objective Questions

Geometry is a crucial branch of mathematics that plays a significant role in various school and competitive exams. Mastering geometry concepts not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions helps students identify important questions and solidify their understanding, leading to better scores in their exam preparation.

What You Will Practise Here

Basic geometric shapes and their properties
Angles, lines, and their relationships
Triangles: types, congruence, and similarity
Quadrilaterals and their properties
Circles: chords, tangents, and arcs
Area and perimeter calculations
Volume and surface area of 3D shapes

Exam Relevance

Geometry is a fundamental topic in the CBSE curriculum and is also included in various State Boards. It frequently appears in competitive exams like NEET and JEE, where questions often test conceptual understanding and application of geometry principles. Students can expect to encounter problems related to geometric shapes, properties, and theorems, making it essential to practice geometry MCQ questions to familiarize themselves with common question patterns.

Common Mistakes Students Make

Confusing properties of different types of triangles
Misapplying theorems related to angles and parallel lines
Errors in calculating area and perimeter due to incorrect formulas
Overlooking the significance of diagrams in problem-solving
Neglecting to review the relationships between various geometric figures

FAQs

Question: What are some important Geometry questions for exams?
Answer: Important questions often include those related to the properties of triangles, area calculations, and theorems involving circles.

Question: How can I improve my Geometry skills for exams?
Answer: Regular practice of Geometry MCQ questions and reviewing key concepts will significantly enhance your skills.

Start solving practice MCQs today to test your understanding of geometry concepts and prepare effectively for your exams. Remember, consistent practice is the key to success!

Geometry

Geometry MCQ & Objective Questions

What You Will Practise Here

Exam Relevance

Common Mistakes Students Make

FAQs

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