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 circle, if two angles subtended by the same arc are equal, what can be concluded about those angles?
A.
They are complementary
B.
They are equal
C.
They are supplementary
D.
They are proportional
Show solution
Solution
Angles subtended by the same arc at the circumference of a circle are equal.
Correct Answer:
B
— They are equal
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Q. In a circle, if two chords AB and CD are equal in length, what can be said about their distances from the center?
A.
They are equal
B.
One is longer
C.
One is shorter
D.
Cannot be determined
Show solution
Solution
If two chords are equal in length, they are equidistant from the center of the circle.
Correct Answer:
A
— They are equal
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Q. In a circle, if two chords AB and CD intersect at point E, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if DE = 2 cm?
A.
6 cm
B.
8 cm
C.
5 cm
D.
7 cm
Show solution
Solution
Using the intersecting chords theorem: AE * EB = CE * DE, so 3 * 4 = CE * 2, CE = 6 cm.
Correct Answer:
C
— 5 cm
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Q. In a circle, if two chords AB and CD intersect at point E, and AE = 3 cm, EB = 5 cm, what is the length of CE if ED = 4 cm?
A.
2 cm
B.
3 cm
C.
4 cm
D.
5 cm
Show solution
Solution
Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 5 = CE * 4. Therefore, 15 = CE * 4, which gives CE = 15/4 = 3.75 cm.
Correct Answer:
A
— 2 cm
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Q. In a circle, if two chords AB and CD intersect at point E, which of the following is true?
A.
AE * EB = CE * ED
B.
AE + EB = CE + ED
C.
AE - EB = CE - ED
D.
AE / EB = CE / ED
Show solution
Solution
According to the intersecting chords theorem, the products of the segments of the chords are equal, hence AE * EB = CE * ED.
Correct Answer:
A
— AE * EB = CE * ED
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Q. In a circle, if two chords intersect at a point inside the circle, how do you find the measure of the angles formed?
A.
Add the angles.
B.
Subtract the angles.
C.
Multiply the angles.
D.
Average the angles.
Show solution
Solution
The measure of each angle formed is equal to the sum of the measures of the arcs intercepted by the angle.
Correct Answer:
A
— Add the angles.
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Q. In a circle, if two chords intersect at a point inside the circle, what is the relationship between the angles formed?
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are not related.
Show solution
Solution
The angles formed by two intersecting chords are equal.
Correct Answer:
B
— They are supplementary.
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Q. In a circle, if two chords intersect inside the circle, what is the relationship between the angles formed?
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are adjacent.
Show solution
Solution
The angles formed by two intersecting chords inside a circle are supplementary.
Correct Answer:
B
— They are supplementary.
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Q. In a circle, if two tangents are drawn from a point outside the circle, what is the relationship between the lengths of the tangents?
A.
They are equal
B.
They are different
C.
One is longer
D.
Depends on the circle
Show solution
Solution
The lengths of the tangents from a point outside the circle to the circle are equal.
Correct Answer:
A
— They are equal
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Q. In a circle, if two tangents are drawn from an external point to the circle, what can be said about the lengths of the tangents?
A.
They are equal
B.
They are unequal
C.
One is longer than the radius
D.
They are both zero
Show solution
Solution
The lengths of the tangents drawn from an external point to a circle are always equal.
Correct Answer:
A
— They are equal
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Q. In a class, the grades are: 88, 92, 76, 85, 90. What is the mode?
A.
76
B.
85
C.
88
D.
No mode
Show solution
Solution
There is no mode since all grades appear only once.
Correct Answer:
D
— No mode
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Q. In a class, the ratio of boys to girls is 3:2. If there are 25 students in total, how many girls are there?
Show solution
Solution
Let the number of girls be 2x and boys be 3x. The equation is 2x + 3x = 25. Solving gives 5x = 25, so x = 5. Therefore, girls = 2x = 10.
Correct Answer:
A
— 10
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Q. In a class, the scores of 10 students are: 85, 90, 75, 80, 95, 70, 80, 85, 90, 100. What is the mean score?
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Solution
Mean = (85 + 90 + 75 + 80 + 95 + 70 + 80 + 85 + 90 + 100) / 10 = 85.
Correct Answer:
A
— 85
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Q. In a coordinate plane, if line A has a slope of 2 and line B is parallel to line A, what is the slope of line B?
A.
0
B.
1
C.
2
D.
Undefined
Show solution
Solution
Parallel lines have the same slope. Therefore, if line A has a slope of 2, line B also has a slope of 2.
Correct Answer:
C
— 2
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Q. In a coordinate plane, if line A has a slope of 3 and line B is perpendicular to line A, what is the slope of line B?
A.
1/3
B.
-1/3
C.
-3
D.
3
Show solution
Solution
The slope of a line perpendicular to another is the negative reciprocal. Therefore, the slope of line B is -1/3.
Correct Answer:
B
— -1/3
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Q. In a coordinate plane, if line A has the equation y = -1/2x + 4, what is the slope of a line parallel to line A?
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Solution
Parallel lines have the same slope, so the slope of the parallel line is -1/2.
Correct Answer:
A
— -1/2
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Q. In a coordinate plane, if line A has the equation y = -3x + 4 and line B is perpendicular to line A, what is the slope of line B?
A.
1/3
B.
-1/3
C.
3
D.
-3
Show solution
Solution
The slope of line A is -3. The slope of a line perpendicular to it is the negative reciprocal, which is 1/3.
Correct Answer:
C
— 3
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Q. In a coordinate plane, if line A has the equation y = 1/2x + 2 and line B is perpendicular to line A, what is the slope of line B?
A.
2
B.
-2
C.
1/2
D.
-1/2
Show solution
Solution
The slope of line A is 1/2. The slope of a line perpendicular to it is the negative reciprocal, which is -2.
Correct Answer:
B
— -2
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Q. In a coordinate plane, if line A has the equation y = 2x + 3 and line B is parallel to line A, what is the slope of line B?
Show solution
Solution
Parallel lines have the same slope. Therefore, the slope of line B is also 2.
Correct Answer:
A
— 2
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Q. In a coordinate plane, if line L1 has a slope of 2 and line L2 is parallel to L1, what is the slope of L2?
A.
0
B.
1
C.
2
D.
Undefined
Show solution
Solution
Parallel lines have the same slope, so the slope of L2 is also 2.
Correct Answer:
C
— 2
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Q. In a coordinate plane, if line L1 has the equation y = 2x + 3 and line L2 is parallel to L1, what is the slope of line L2?
Show solution
Solution
Parallel lines have the same slope. The slope of line L1 is 2, so the slope of line L2 is also 2.
Correct Answer:
A
— 2
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Q. In a coordinate plane, if line L1 has the equation y = 2x + 3 and line L2 is parallel to L1, what is the slope of L2?
Show solution
Solution
Parallel lines have the same slope. The slope of L1 is 2, so the slope of L2 is also 2.
Correct Answer:
A
— 2
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Q. In a coordinate plane, if line y = 2x + 3 is parallel to another line, what is the slope of the parallel line?
Show solution
Solution
Parallel lines have the same slope. The slope of the line y = 2x + 3 is 2, so the slope of the parallel line is also 2.
Correct Answer:
A
— 2
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Q. In a coordinate plane, if the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the distance between points A and B?
A.
4 units
B.
5 units
C.
6 units
D.
7 units
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 units.
Correct Answer:
A
— 4 units
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Q. In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), what is the distance between these two points?
A.
4 units
B.
5 units
C.
3 units
D.
6 units
Show solution
Solution
The distance between two points with the same x-coordinate is the difference in their y-coordinates: |7 - 3| = 4 units.
Correct Answer:
A
— 4 units
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Q. In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), what is the slope of the line connecting them?
A.
0
B.
Undefined
C.
1
D.
-1
Show solution
Solution
The slope is calculated as (y2 - y1) / (x2 - x1). Here, (7 - 3) / (2 - 2) is undefined because the denominator is 0.
Correct Answer:
B
— Undefined
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Q. In a coordinate plane, if the coordinates of two points on a line are (2, 3) and (4, 7), what is the slope of the line?
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Solution
The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.
Correct Answer:
A
— 2
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Q. In a coordinate plane, what is the distance between the points (1, 2) and (4, 6)?
A.
5 units
B.
4 units
C.
3 units
D.
6 units
Show solution
Solution
Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. In a coordinate plane, what is the distance between the points (3, 4) and (7, 1)?
A.
5 units
B.
4 units
C.
3 units
D.
6 units
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 = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. In a coordinate plane, what is the equation of a circle with center at (3, -2) and radius 4?
A.
(x - 3)² + (y + 2)² = 16
B.
(x + 3)² + (y - 2)² = 16
C.
(x - 3)² + (y - 2)² = 16
D.
(x + 3)² + (y + 2)² = 16
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 - 3)² + (y + 2)² = 16
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