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. In a right triangle, if one angle is 45 degrees and the hypotenuse is 10 cm, what is the length of each leg?
A.
5√2 cm
B.
10 cm
C.
5 cm
D.
7.5 cm
Show solution
Solution
In a 45-45-90 triangle, the legs are equal and each leg = hypotenuse/√2 = 10/√2 = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In a right triangle, if one angle is 45 degrees, what are the measures of the other two angles?
A.
45, 90
B.
30, 60
C.
60, 30
D.
90, 45
Show solution
Solution
In a right triangle, the sum of the angles is 180 degrees. Therefore, the other angle must also be 45 degrees.
Correct Answer:
A
— 45, 90
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Q. In a right triangle, if one angle is 45 degrees, what is the ratio of the lengths of the legs?
A.
1:2
B.
1:1
C.
2:1
D.
√2:1
Show solution
Solution
In a 45-45-90 triangle, the legs are equal, so the ratio is 1:1.
Correct Answer:
B
— 1:1
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Q. In a right triangle, if one angle is 45 degrees, what is the ratio of the lengths of the sides opposite and adjacent to this angle?
A.
1:1
B.
1:√2
C.
√2:1
D.
2:1
Show solution
Solution
In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, hence the ratio is 1:1.
Correct Answer:
A
— 1:1
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Q. In a right triangle, if one angle is 45°, what is the ratio of the lengths of the sides opposite and adjacent to this angle?
A.
1:1
B.
1:√2
C.
√2:1
D.
2:1
Show solution
Solution
In a 45°-45°-90° triangle, the sides opposite and adjacent are equal, so the ratio is 1:1.
Correct Answer:
A
— 1:1
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Q. In a right triangle, if one angle measures 30 degrees, what is the measure of the angle opposite the shortest side?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
45 degrees
Show solution
Solution
In a right triangle, the angle opposite the shortest side is the smallest angle, which is 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a right triangle, if one leg is 3 cm and the hypotenuse is 5 cm, what is the length of the other leg?
A.
4 cm
B.
3 cm
C.
2 cm
D.
1 cm
Show solution
Solution
Using the Pythagorean theorem, a² + b² = c², we have 3² + b² = 5², which gives b² = 25 - 9 = 16, hence b = 4 cm.
Correct Answer:
A
— 4 cm
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Q. In a right triangle, if one leg is 3 cm and the other leg is 4 cm, what is the length of the hypotenuse?
A.
5 cm
B.
7 cm
C.
6 cm
D.
8 cm
Show solution
Solution
Using Pythagorean theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.
Correct Answer:
A
— 5 cm
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Q. In a right triangle, if one leg is 3 units and the hypotenuse is 5 units, what is the length of the other leg?
A.
2 units
B.
4 units
C.
6 units
D.
8 units
Show solution
Solution
Using the Pythagorean theorem, a² + b² = c², we have 3² + b² = 5², which gives b² = 25 - 9 = 16, so b = 4 units.
Correct Answer:
A
— 2 units
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Q. In a right triangle, if one leg is 3 units and the other leg is 4 units, what is the length of the hypotenuse?
A.
5 units
B.
6 units
C.
7 units
D.
8 units
Show solution
Solution
Using the Pythagorean theorem, c = √(3² + 4²) = √(9 + 16) = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. In a right triangle, if one leg is 5 cm and the other leg is 12 cm, what is the length of the hypotenuse?
A.
13 cm
B.
10 cm
C.
15 cm
D.
12 cm
Show solution
Solution
Using Pythagorean theorem: hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
Correct Answer:
A
— 13 cm
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Q. In a right triangle, if one leg is 6 and the other leg is 8, what is the length of the hypotenuse?
Show solution
Solution
Using the Pythagorean theorem: c = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10.
Correct Answer:
A
— 10
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Q. In a right triangle, if one leg is 6 cm and the hypotenuse is 10 cm, what is the length of the other leg?
A.
8 cm
B.
7 cm
C.
5 cm
D.
4 cm
Show solution
Solution
Using the Pythagorean theorem, a² + b² = c², we have 6² + b² = 10². Thus, 36 + b² = 100, leading to b² = 64, so b = 8 cm.
Correct Answer:
A
— 8 cm
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Q. In a right triangle, if one leg is 6 cm and the other leg is 8 cm, what is the area?
A.
24 cm²
B.
30 cm²
C.
48 cm²
D.
36 cm²
Show solution
Solution
Area = 1/2 * leg1 * leg2 = 1/2 * 6 * 8 = 24 cm².
Correct Answer:
A
— 24 cm²
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Q. In a right triangle, if one leg is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Using the Pythagorean theorem: hypotenuse = √(6^2 + 8^2) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In a right triangle, if one leg is 8 cm and the hypotenuse is 10 cm, what is the length of the other leg?
A.
6 cm
B.
7 cm
C.
8 cm
D.
9 cm
Show solution
Solution
Using the Pythagorean theorem: a² + b² = c². Here, 8² + b² = 10². Thus, 64 + b² = 100, so b² = 36, and b = 6 cm.
Correct Answer:
A
— 6 cm
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Q. In a right triangle, if one leg is 9 cm and the other leg is 12 cm, what is the length of the hypotenuse?
A.
15 cm
B.
13 cm
C.
10 cm
D.
14 cm
Show solution
Solution
Using Pythagorean theorem: hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.
Correct Answer:
B
— 13 cm
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Q. In a right triangle, if one leg measures 5 cm and the other leg measures 12 cm, what is the length of the hypotenuse?
A.
13 cm
B.
10 cm
C.
11 cm
D.
15 cm
Show solution
Solution
Using the Pythagorean theorem, hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
Correct Answer:
A
— 13 cm
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Q. In a right triangle, if one leg measures 6 cm and the other leg measures 8 cm, what is the length of the hypotenuse?
A.
10 cm
B.
12 cm
C.
14 cm
D.
8 cm
Show solution
Solution
Using the Pythagorean theorem, c² = a² + b². Here, c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In a right triangle, if one leg measures 6 units and the other leg measures 8 units, what is the length of the hypotenuse?
Show solution
Solution
Using the Pythagorean theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.
Correct Answer:
A
— 10
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Q. In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?
A.
3/5
B.
5/3
C.
4/5
D.
1/2
Show solution
Solution
sin(θ) = opposite/hypotenuse = 3/5
Correct Answer:
A
— 3/5
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Q. In a survey, the ages of participants are: 22, 25, 25, 30, 35. What is the mean age?
Show solution
Solution
Mean = (22 + 25 + 25 + 30 + 35) / 5 = 107 / 5 = 26.4.
Correct Answer:
B
— 26
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Q. In a survey, the number of pets owned by 6 families is: 1, 2, 2, 3, 4, 4. What is the mode?
Show solution
Solution
The mode is 2 and 4, but since we need one answer, we can choose 2 as it appears first.
Correct Answer:
B
— 2
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Q. In a transversal intersecting two parallel lines, if angle 4 is 60 degrees and angle 5 is a corresponding angle, what is the measure of angle 5?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Corresponding angles are equal, so angle 5 is also 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. In a transversal intersecting two parallel lines, if angle 5 is 150 degrees, what is the measure of angle 6, which is a same-side interior angle?
A.
30 degrees
B.
150 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Same-side interior angles are supplementary, so 180 - 150 = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a transversal intersecting two parallel lines, if angle 5 measures 120 degrees, what is the measure of the corresponding angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Corresponding angles are equal, so the corresponding angle also measures 120 degrees.
Correct Answer:
B
— 120 degrees
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Q. In a transversal intersecting two parallel lines, if angle 5 measures 75 degrees, what is the measure of the corresponding angle on the opposite side of the transversal?
A.
75 degrees
B.
105 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
Corresponding angles are equal, so the opposite angle also measures 75 degrees.
Correct Answer:
A
— 75 degrees
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Q. In a transversal intersecting two parallel lines, if angle 5 measures 85 degrees, what is the measure of the corresponding angle on the opposite side of the transversal?
A.
85 degrees
B.
95 degrees
C.
180 degrees
D.
75 degrees
Show solution
Solution
Corresponding angles are equal, so the opposite angle also measures 85 degrees.
Correct Answer:
A
— 85 degrees
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Q. In a transversal intersecting two parallel lines, if one angle measures 110°, what is the measure of the adjacent angle?
A.
70°
B.
110°
C.
90°
D.
180°
Show solution
Solution
Adjacent angles are supplementary, so the adjacent angle measures 180° - 110° = 70°.
Correct Answer:
A
— 70°
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Q. In a transversal intersecting two parallel lines, if one angle measures 30 degrees, what is the measure of the vertically opposite angle?
A.
30 degrees
B.
150 degrees
C.
90 degrees
D.
60 degrees
Show solution
Solution
Vertically opposite angles are equal. Therefore, the vertically opposite angle also measures 30 degrees.
Correct Answer:
A
— 30 degrees
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