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. If sin(θ) = 0.6, what is the value of cos(θ) using the Pythagorean identity?
A.
0.8
B.
0.6
C.
0.4
D.
0.2
Show solution
Solution
cos(θ) = √(1 - sin²(θ)) = √(1 - 0.36) = √0.64 = 0.8
Correct Answer:
A
— 0.8
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Q. If sin(θ) = 0.6, what is θ in degrees (to the nearest degree)?
Show solution
Solution
θ = arcsin(0.6) ≈ 36.87°, rounded to 37°
Correct Answer:
D
— 70
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Q. If sin(θ) = 0.8, what is the value of θ in degrees?
A.
30
B.
45
C.
53.13
D.
60
Show solution
Solution
θ = sin⁻¹(0.8) ≈ 53.13°
Correct Answer:
C
— 53.13
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Q. If tan(x) = 1, what is the value of x in the interval [0°, 360°)?
A.
45°
B.
135°
C.
225°
D.
315°
Show solution
Solution
tan(x) = 1 at x = 45° and 225°; in the interval [0°, 360°), the first solution is 45°.
Correct Answer:
A
— 45°
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Q. If tan(θ) = 3/4, what is sin(θ)?
A.
3/5
B.
4/5
C.
5/5
D.
1
Show solution
Solution
Using the identity tan(θ) = sin(θ)/cos(θ), we find sin(θ) = 3/5.
Correct Answer:
A
— 3/5
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Q. If the ages of a group of friends are: 22, 24, 26, 28, 30, what is the mean age?
Show solution
Solution
Mean = (22 + 24 + 26 + 28 + 30) / 5 = 130 / 5 = 26.
Correct Answer:
B
— 26
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Q. If the angle of elevation from a point on the ground to the top of a hill is 30 degrees and the distance from the point to the base of the hill is 20 meters, what is the height of the hill?
A.
10√3 meters
B.
20 meters
C.
15 meters
D.
5√3 meters
Show solution
Solution
Using tan(30) = height / 20, height = 20 * tan(30) = 20 * (1/√3) = 20/√3 = 10√3 meters.
Correct Answer:
A
— 10√3 meters
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Q. If the angle of elevation to the top of a tower from a point 40 meters away is 30 degrees, what is the height of the tower?
A.
20√3 meters
B.
40 meters
C.
30 meters
D.
10√3 meters
Show solution
Solution
Using tan(30°) = height/40, height = 40 * (1/√3) = 40/√3 = 20√3 meters.
Correct Answer:
A
— 20√3 meters
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Q. If the angle subtended by an arc at the center of a circle is 60 degrees, what is the angle subtended at any point on the circumference?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The angle subtended at the circumference is half of that at the center. Therefore, it is 60 degrees / 2 = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. If the angles of a triangle are 30°, 60°, and 90°, and the shortest side is 5 cm, what is the length of the longest side?
A.
10 cm
B.
5√3 cm
C.
5 cm
D.
15 cm
Show solution
Solution
In a 30-60-90 triangle, the longest side (hypotenuse) is twice the shortest side: 2 * 5 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. If the area of a circle is 50.24 cm², what is the radius?
A.
4 cm
B.
5 cm
C.
6 cm
D.
7 cm
Show solution
Solution
Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 4 cm.
Correct Answer:
B
— 5 cm
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Q. If the area of a sector of a circle is 20π square units and the radius is 10 units, what is the angle of the sector in radians?
A.
1 radian
B.
2 radians
C.
3 radians
D.
4 radians
Show solution
Solution
The area of a sector is given by (θ/2) * r². Thus, 20π = (θ/2) * 10². Solving gives θ = 4 radians.
Correct Answer:
B
— 2 radians
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Q. If the area of a triangle is 36 cm² and the base is 12 cm, what is the height?
A.
6 cm
B.
8 cm
C.
4 cm
D.
10 cm
Show solution
Solution
Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 36) / 12 = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If the area of triangle XYZ is 24 cm² and the base is 8 cm, what is the height of the triangle?
A.
6 cm
B.
8 cm
C.
4 cm
D.
3 cm
Show solution
Solution
Area = 1/2 * base * height. Thus, 24 = 1/2 * 8 * height. Therefore, height = 24 / 4 = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If the base of a triangle is doubled and the height remains the same, how does the area change?
A.
It doubles
B.
It triples
C.
It remains the same
D.
It halves
Show solution
Solution
Area = 1/2 * base * height; if base is doubled, area = 1/2 * (2 * base) * height = 2 * (1/2 * base * height).
Correct Answer:
A
— It doubles
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Q. If the center of a circle is at (2, 3) and the radius is 5, what is the equation of the circle?
A.
(x - 2)² + (y - 3)² = 25
B.
(x + 2)² + (y + 3)² = 25
C.
(x - 2)² + (y + 3)² = 5
D.
(x + 2)² + (y - 3)² = 25
Show solution
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 2)² + (y - 3)² = 25
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Q. If the coordinates of a triangle's vertices are (0, 0), (4, 0), and (0, 3), what is the area of the triangle?
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Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. If the coordinates of point A are (2, 3) and point B are (2, 7), what is the slope of line AB?
A.
0
B.
Undefined
C.
1
D.
2
Show solution
Solution
The slope is calculated as (y2 - y1) / (x2 - x1). Here, it is (7 - 3) / (2 - 2), which is undefined since the denominator is 0.
Correct Answer:
B
— Undefined
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Q. If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between points A and B?
A.
5 units
B.
4 units
C.
3 units
D.
6 units
Show solution
Solution
Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. If the coordinates of point A are (2, 3) and point B are (5, 7), what is the slope of line AB?
A.
4/3
B.
3/4
C.
1/2
D.
2/3
Show solution
Solution
Slope = (y2 - y1) / (x2 - x1) = (7 - 3) / (5 - 2) = 4/3.
Correct Answer:
A
— 4/3
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Q. If the coordinates of point A are (x, y) and point B are (x+4, y+3), what is the distance AB?
A.
√34
B.
√25
C.
√29
D.
√20
Show solution
Solution
Using the distance formula: d = √((x+4 - x)² + (y+3 - y)²) = √(4² + 3²) = √(16 + 9) = √25 = 5.
Correct Answer:
A
— √34
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Q. If the coordinates of point D are (5, 5) and it is the midpoint of line segment joining points E(3, 1) and F(x, y), what are the coordinates of F?
A.
(7, 9)
B.
(9, 7)
C.
(8, 6)
D.
(6, 8)
Show solution
Solution
Using the midpoint formula: D = ((x1 + x2)/2, (y1 + y2)/2). Solving gives F(7, 9).
Correct Answer:
B
— (9, 7)
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Q. If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the distance between points A and B?
Show solution
Solution
The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Here, distance = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = 4.
Correct Answer:
A
— 4
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Q. If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the slope of the line segment AB?
A.
0
B.
Undefined
C.
1
D.
4
Show solution
Solution
The slope is undefined because the x-coordinates are the same, indicating a vertical line.
Correct Answer:
B
— Undefined
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Q. If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the length of line segment AB?
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Solution
The length of line segment AB is the difference in the y-coordinates: |7 - 3| = 4.
Correct Answer:
A
— 4
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Q. If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is the distance AB?
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Solution
Distance AB = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. If the coordinates of points A and B are (2, 3) and (5, 7) respectively, what is the length of segment AB?
Show solution
Solution
Length AB = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
B
— 5
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Q. If the coordinates of points A(1, 2) and B(1, 5) are given, what is the slope of line AB?
A.
0
B.
Undefined
C.
3
D.
1
Show solution
Solution
The slope is calculated as (y2 - y1) / (x2 - x1). Here, it is (5 - 2) / (1 - 1), which is undefined.
Correct Answer:
B
— Undefined
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Q. If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance AB?
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Solution
Distance AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer:
B
— 5
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Q. If the coordinates of points A(1, 2) and B(4, 6) are given, what is the distance between points A and B?
Show solution
Solution
The distance between two points (x1, y1) and (x2, y2) is given by the formula: √((x2 - x1)² + (y2 - y1)²). Thus, distance = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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