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 hypotenuse of a right triangle with legs of lengths 6 cm and 8 cm?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Using the Pythagorean theorem, c² = a² + b², where a = 6 cm and b = 8 cm. Thus, c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the length of the line segment connecting the points (1, 2) and (1, 5)?
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Solution
Since the x-coordinates are the same, the distance is the difference in y-coordinates: d = |y2 - y1| = |5 - 2| = 3.
Correct Answer:
A
— 3
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Q. What is the length of the line segment connecting the points (1, 2) and (4, 6)?
A.
5.0
B.
4.0
C.
3.0
D.
6.0
Show solution
Solution
Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.0.
Correct Answer:
A
— 5.0
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Q. What is the length of the line segment connecting the points (2, 3) and (2, 7)?
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Solution
The length of a vertical line segment is the difference in the y-coordinates. Here, length = 7 - 3 = 4.
Correct Answer:
A
— 4
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Q. What is the length of the line segment joining the points (0, 0) and (5, 12)?
A.
12.5
B.
13
C.
11
D.
10
Show solution
Solution
Using the distance formula: d = √((5 - 0)² + (12 - 0)²) = √(25 + 144) = √169 = 13.
Correct Answer:
B
— 13
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Q. What is the length of the line segment joining the points (1, 1) and (4, 5)?
Show solution
Solution
Using the distance formula: d = √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.
Correct Answer:
B
— 5
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Q. What is the length of the line segment joining the points (2, 3) and (2, 7)?
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Solution
Length = |y2 - y1| = |7 - 3| = 4.
Correct Answer:
A
— 4
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Q. What is the length of the median from vertex A to side BC in triangle ABC with sides AB = 6 cm, AC = 8 cm, and BC = 10 cm?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
The length of the median can be calculated using the formula: median = 1/2 * √(2AB^2 + 2AC^2 - BC^2) = 1/2 * √(2*6^2 + 2*8^2 - 10^2) = 7 cm.
Correct Answer:
C
— 7 cm
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Q. What is the length of the radius of a circle if its area is 100π cm²?
A.
10 cm
B.
5 cm
C.
20 cm
D.
15 cm
Show solution
Solution
Using the area formula A = πr², we set 100π = πr², leading to r² = 100, thus r = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the length of the radius of a circle if its area is 36π cm²?
A.
6 cm
B.
12 cm
C.
18 cm
D.
9 cm
Show solution
Solution
Using the area formula A = πr², we have 36π = πr², thus r² = 36, and r = 6 cm.
Correct Answer:
A
— 6 cm
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Q. What is the length of the radius of a circle if its area is 50 cm²?
A.
5 cm
B.
10 cm
C.
7.07 cm
D.
8.86 cm
Show solution
Solution
Using the area formula A = πr², we have 50 = πr², thus r² = 50/π, and r ≈ 7.07 cm.
Correct Answer:
C
— 7.07 cm
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Q. What is the length of the radius of a circle if its circumference is 31.4 cm?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
The circumference C of a circle is given by C = 2πr. Thus, r = C / (2π) = 31.4 / (2π) ≈ 5 cm.
Correct Answer:
A
— 5 cm
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Q. What is the length of the radius of a circle if the area is 36π cm²?
A.
6 cm
B.
12 cm
C.
18 cm
D.
9 cm
Show solution
Solution
Using the area formula A = πr², we have 36π = πr², which simplifies to r² = 36, giving r = 6 cm.
Correct Answer:
A
— 6 cm
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Q. What is the length of the radius of a circle if the area is 50π cm²?
A.
5 cm
B.
10 cm
C.
7 cm
D.
8 cm
Show solution
Solution
The area A of a circle is given by A = πr². Therefore, r² = 50, which gives r = √50 = 5√2 cm, approximately 7.07 cm.
Correct Answer:
B
— 10 cm
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Q. What is the length of the radius of a circle if the area is 50π square units?
A.
5 units
B.
10 units
C.
25 units
D.
50 units
Show solution
Solution
Area of a circle = πr². Setting 50π = πr² gives r² = 50, so r = √50 = 5√2 ≈ 7.07 units.
Correct Answer:
B
— 10 units
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Q. What is the length of the radius of a circle if the circumference is 31.4 cm?
A.
5 cm
B.
7 cm
C.
10 cm
D.
15 cm
Show solution
Solution
The circumference C of a circle is given by C = 2πr. Thus, r = C / (2π) = 31.4 / (2π) ≈ 5 cm.
Correct Answer:
B
— 7 cm
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Q. What is the length of the side of a square if its area is 64?
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Solution
The area of a square is given by side^2. Thus, if area = 64, then side = √64 = 8.
Correct Answer:
C
— 8
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Q. What is the length of the side of a square inscribed in a circle of radius 5?
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Solution
The diagonal of the square equals the diameter of the circle. Diagonal = 2 × radius = 10. Side = diagonal/√2 = 10/√2 = 5√2.
Correct Answer:
A
— 5√2
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Q. What is the length of the side of a square with vertices at (1, 1), (1, 5), (5, 1), and (5, 5)?
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Solution
Length of side = 5 - 1 = 4.
Correct Answer:
A
— 4
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Q. What is the length of the side of a square with vertices at (1, 1), (1, 5), (5, 5), and (5, 1)?
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Solution
The length of the side is 5 - 1 = 4.
Correct Answer:
A
— 4
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Q. What is the length of the tangent from a point P outside a circle to the point of tangency T if the radius of the circle is 5 cm and the distance from P to the center O of the circle is 13 cm?
A.
12 cm
B.
10 cm
C.
8 cm
D.
6 cm
Show solution
Solution
Using the tangent-secant theorem, PT² = PO² - OT². Thus, PT² = 13² - 5² = 169 - 25 = 144, so PT = 12 cm.
Correct Answer:
A
— 12 cm
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Q. What is the maximum value of the function y = 2cos(3x)?
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Solution
The maximum value of a cosine function y = Acos(Bx) is |A|. Here, A = 2, so the maximum value is 2.
Correct Answer:
C
— 2
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Q. What is the maximum value of y = -2cos(x)?
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Solution
The maximum value occurs when cos(x) = -1, giving a maximum of -2 * -1 = 2.
Correct Answer:
C
— 2
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Q. What is the mean of the following numbers: 1, 1, 2, 3, 5?
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Solution
Mean = (1 + 1 + 2 + 3 + 5) / 5 = 12 / 5 = 2.4.
Correct Answer:
B
— 2
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Q. What is the mean of the following numbers: 12, 15, 20, 25?
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Solution
Mean = (12 + 15 + 20 + 25) / 4 = 72 / 4 = 18.
Correct Answer:
C
— 22
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Q. What is the mean of the following numbers: 15, 25, 35, 45?
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Solution
Mean = (15 + 25 + 35 + 45) / 4 = 30.
Correct Answer:
B
— 30
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Q. What is the mean of the following numbers: 5, 10, 15, 20?
A.
10
B.
12.5
C.
15
D.
17.5
Show solution
Solution
Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.
Correct Answer:
B
— 12.5
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Q. What is the mean of the numbers 1, 2, 3, 4, 5?
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Solution
Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3
Correct Answer:
B
— 3
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Q. What is the mean of the numbers: 5, 10, 15, 20, 25?
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Solution
Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.
Correct Answer:
B
— 15
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Q. What is the measure of an angle formed by a tangent and a chord drawn from the point of contact?
A.
It is equal to the angle subtended by the chord at the center.
B.
It is equal to half the angle subtended by the chord at the circumference.
C.
It is equal to the angle subtended by the tangent at the center.
D.
It is always 90 degrees.
Show solution
Solution
The angle formed by a tangent and a chord is equal to half the angle subtended by the chord at the circumference.
Correct Answer:
B
— It is equal to half the angle subtended by the chord at the circumference.
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