Mathematics (School) MCQ & Objective Questions
Mathematics is a crucial subject in school education, forming the foundation for various competitive exams. Mastering Mathematics (School) not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps students identify important questions and understand concepts clearly.
What You Will Practise Here
Number Systems and their properties
Algebraic Expressions and Equations
Geometry: Angles, Triangles, and Circles
Statistics and Probability concepts
Mensuration: Area, Volume, and Surface Area
Trigonometry basics and applications
Functions and Graphs
Exam Relevance
Mathematics (School) is a significant part of the curriculum for CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect a variety of question patterns, including direct application of formulas, conceptual understanding, and problem-solving scenarios. Familiarity with MCQs in this subject can greatly enhance performance in both board and competitive examinations.
Common Mistakes Students Make
Misinterpreting the question, leading to incorrect answers.
Overlooking the importance of units in measurement-related problems.
Confusing similar formulas, especially in Geometry and Algebra.
Neglecting to check calculations, resulting in simple arithmetic errors.
Failing to understand the underlying concepts, which affects problem-solving ability.
FAQs
Question: How can I improve my speed in solving Mathematics (School) MCQs?Answer: Regular practice with timed quizzes and mock tests can significantly enhance your speed and accuracy.
Question: Are there any specific topics I should focus on for competitive exams?Answer: Focus on Algebra, Geometry, and Statistics, as these areas frequently appear in competitive exams.
Start your journey towards mastering Mathematics (School) today! Solve practice MCQs to test your understanding and prepare effectively for your exams. Remember, consistent practice leads to success!
Q. What is the length of the altitude from the vertex of a triangle to the base if the base is 12 cm and the area is 36 cm²?
A.
3 cm
B.
6 cm
C.
9 cm
D.
12 cm
Show solution
Solution
Area = 1/2 * base * height. Therefore, 36 = 1/2 * 12 * height. Solving gives height = 6 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from the vertex of a triangle with a base of 10 cm and an area of 30 cm²?
A.
3 cm
B.
5 cm
C.
6 cm
D.
8 cm
Show solution
Solution
Using the area formula: Area = 1/2 * base * height, we can solve for height: 30 = 1/2 * 10 * height, so height = 30 / 5 = 6 cm.
Correct Answer:
B
— 5 cm
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Q. What is the length of the altitude from the vertex of a triangle with a base of 10 cm and an area of 40 cm²?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
Using the area formula: Area = 1/2 * base * height, we can solve for height: 40 = 1/2 * 10 * height, so height = 8 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from the vertex of a triangle with a base of 12 cm and an area of 36 cm²?
A.
4 cm
B.
6 cm
C.
3 cm
D.
5 cm
Show solution
Solution
The area of a triangle is given by Area = 1/2 * base * height. Rearranging gives height = 2 * Area / base = 2 * 36 / 12 = 6 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from the vertex of a triangle with a base of 8 cm and an area of 32 cm²?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
Using the area formula: Area = 1/2 * base * height, we can solve for height: 32 = 1/2 * 8 * height, thus height = 8 cm.
Correct Answer:
A
— 4 cm
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Q. What is the length of the altitude from the vertex opposite the base of 10 cm in an isosceles triangle with equal sides of 13 cm?
A.
12 cm
B.
10 cm
C.
9 cm
D.
8 cm
Show solution
Solution
Using Pythagorean theorem: altitude = √(13² - (10/2)²) = √(169 - 25) = √144 = 12 cm.
Correct Answer:
D
— 8 cm
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Q. What is the length of the altitude from the vertex opposite the base of a triangle with a base of 10 cm and an area of 40 cm²?
A.
8 cm
B.
6 cm
C.
4 cm
D.
10 cm
Show solution
Solution
Area = 1/2 * base * height. 40 = 1/2 * 10 * height. Height = (40 * 2) / 10 = 8 cm.
Correct Answer:
B
— 6 cm
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC if AB = 10 cm, AC = 6 cm, and angle A = 30 degrees?
A.
3 cm
B.
5 cm
C.
6 cm
D.
10 cm
Show solution
Solution
The altitude h = AC * sin(A) = 6 * sin(30°) = 6 * 0.5 = 3 cm.
Correct Answer:
B
— 5 cm
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC if the area is 30 cm² and base BC = 10 cm?
A.
6 cm
B.
5 cm
C.
3 cm
D.
4 cm
Show solution
Solution
Area = 1/2 * base * height. Therefore, 30 = 1/2 * 10 * height, which gives height = 6 cm.
Correct Answer:
B
— 5 cm
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Q. What is the length of the altitude from vertex A to side BC in triangle ABC with base BC = 12 cm and area = 36 cm²?
A.
6 cm
B.
4 cm
C.
3 cm
D.
5 cm
Show solution
Solution
Area = 1/2 * base * height. Therefore, 36 = 1/2 * 12 * height, which gives height = 6 cm.
Correct Answer:
A
— 6 cm
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Q. What is the length of the altitude from vertex A(1, 1) to the base BC of triangle ABC with B(4, 1) and C(4, 5)?
Show solution
Solution
The base BC is vertical, so the length of the altitude is the horizontal distance from A to line x = 4, which is |4 - 1| = 3.
Correct Answer:
A
— 3
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Q. What is the length of the altitude to the base of a triangle with an area of 50 cm² and a base of 10 cm?
A.
10 cm
B.
5 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Area = 1/2 * base * height. 50 = 1/2 * 10 * height. Height = (50 * 2) / 10 = 10 cm.
Correct Answer:
B
— 5 cm
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Q. What is the length of the arc of a circle with a radius of 10 cm that subtends an angle of 60 degrees at the center?
A.
10.47 cm
B.
6.28 cm
C.
17.45 cm
D.
10.00 cm
Show solution
Solution
The length of an arc is given by the formula L = (θ/360) * 2πr. Here, L = (60/360) * 2π(10) = (1/6) * 20π ≈ 10.47 cm.
Correct Answer:
A
— 10.47 cm
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Q. What is the length of the arc of a circle with a radius of 10 units that subtends an angle of 60 degrees at the center?
A.
10π/3 units
B.
5π units
C.
10π/6 units
D.
20π/3 units
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(10) = (1/6) * 20π = 10π/3 units.
Correct Answer:
A
— 10π/3 units
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Q. What is the length of the arc of a circle with a radius of 4 cm and a central angle of 90 degrees?
A.
3.14 cm
B.
6.28 cm
C.
12.56 cm
D.
1.57 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π(4) = (1/4) * 8π = 2π ≈ 6.28 cm.
Correct Answer:
A
— 3.14 cm
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Q. What is the length of the arc of a circle with a radius of 4 units and a central angle of 90 degrees?
A.
2π units
B.
4π units
C.
π units
D.
8 units
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π(4) = (1/4) * 8π = 2π units.
Correct Answer:
A
— 2π units
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Q. What is the length of the arc of a circle with a radius of 5 cm and a central angle of 60°?
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) * 2 * π * r = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. What is the length of the arc of a circle with a radius of 5 cm and a central angle of 90°?
A.
3.93 cm
B.
7.85 cm
C.
12.57 cm
D.
15.71 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π * 5 = (1/4) * 10π ≈ 7.85 cm.
Correct Answer:
B
— 7.85 cm
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Q. What is the length of the arc of a circle with a radius of 6 units that subtends an angle of 60 degrees at the center?
A.
2π units
B.
3π units
C.
4π units
D.
5π units
Show solution
Solution
The length of an arc is given by L = (θ/360) * 2πr. Here, L = (60/360) * 2π(6) = (1/6) * 12π = 2π units.
Correct Answer:
B
— 3π units
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Q. What is the length of the arc of a circle with a radius of 7 cm that subtends an angle of 60 degrees at the center?
A.
7π/3
B.
14π/3
C.
7π/6
D.
14π/6
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(7) = (1/6) * 14π = 7π/3 cm.
Correct Answer:
A
— 7π/3
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Q. What is the length of the diagonal of a rectangle with a length of 12 cm and a width of 9 cm?
A.
15 cm
B.
18 cm
C.
21 cm
D.
24 cm
Show solution
Solution
Using the Pythagorean theorem: d² = length² + width² = 12² + 9² = 144 + 81 = 225, so d = 15 cm.
Correct Answer:
A
— 15 cm
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Q. What is the length of the diagonal of a rectangle with a length of 12 cm and a width of 5 cm?
A.
13 cm
B.
14 cm
C.
15 cm
D.
16 cm
Show solution
Solution
The length of the diagonal can be calculated using the Pythagorean theorem: d = √(length² + width²). Here, d = √(12² + 5²) = √(144 + 25) = √169 = 13 cm.
Correct Answer:
A
— 13 cm
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Q. What is the length of the diagonal of a rectangle with a length of 6 cm and a width of 8 cm?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the length of the diagonal of a rectangle with a length of 6 m and a width of 8 m?
A.
10 m
B.
12 m
C.
14 m
D.
16 m
Show solution
Solution
Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 m.
Correct Answer:
A
— 10 m
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Q. What is the length of the diagonal of a rectangle with a length of 8 cm and a width of 6 cm?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
The length of the diagonal of a rectangle can be calculated using the Pythagorean theorem: diagonal = √(length² + width²) = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the length of the diagonal of a rectangle with a width of 3 cm and a height of 4 cm?
A.
5 cm
B.
7 cm
C.
6 cm
D.
8 cm
Show solution
Solution
The length of the diagonal can be found using the Pythagorean theorem: d = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.
Correct Answer:
A
— 5 cm
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Q. What is the length of the diagonal of a rectangle with a width of 6 cm and a height of 8 cm?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Diagonal = √(width² + height²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the length of the diagonal of a rectangle with a width of 6 units and a height of 8 units?
A.
10 units
B.
12 units
C.
14 units
D.
16 units
Show solution
Solution
Using the Pythagorean theorem, the diagonal d = √(width² + height²) = √(6² + 8²) = √(36 + 64) = √100 = 10 units.
Correct Answer:
A
— 10 units
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Q. What is the length of the diagonal of a rectangle with length 12 cm and width 5 cm?
A.
13 cm
B.
14 cm
C.
15 cm
D.
16 cm
Show solution
Solution
Using Pythagorean theorem: diagonal = √(length² + width²) = √(12² + 5²) = √(144 + 25) = √169 = 13 cm.
Correct Answer:
A
— 13 cm
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Q. What is the length of the diagonal of a rectangle with length 12 cm and width 9 cm?
A.
15 cm
B.
18 cm
C.
21 cm
D.
24 cm
Show solution
Solution
Using the Pythagorean theorem: d² = length² + width² = 12² + 9² = 144 + 81 = 225, so d = 15 cm.
Correct Answer:
A
— 15 cm
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