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 the line 2x + 3y = 12 is transformed to slope-intercept form, what is the slope?
A.
-2/3
B.
2/3
C.
3/2
D.
-3/2
Show solution
Solution
Convert to slope-intercept form (y = mx + b).\n1. 3y = -2x + 12\n2. y = -2/3x + 4.\nThe slope is -2/3.
Correct Answer:
A
— -2/3
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Q. If the mean of a data set is 30 and the total number of observations is 10, what is the total sum of the observations?
A.
300
B.
150
C.
100
D.
50
Show solution
Solution
Total sum = Mean * Number of observations = 30 * 10 = 300.
Correct Answer:
A
— 300
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Q. If the mean of a data set is 50 and the standard deviation is 5, what is the z-score of a value 60?
Show solution
Solution
Z-score = (60 - 50) / 5 = 2.
Correct Answer:
B
— 2
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Q. If the perimeter of an equilateral triangle is 36 cm, what is the length of one side?
A.
10 cm
B.
12 cm
C.
9 cm
D.
15 cm
Show solution
Solution
Perimeter = 3 * side. Therefore, side = Perimeter / 3 = 36 / 3 = 12 cm.
Correct Answer:
B
— 12 cm
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Q. If the probability of an event is 0.2, what is the probability of the event not occurring?
A.
0.2
B.
0.5
C.
0.8
D.
1
Show solution
Solution
P(not occurring) = 1 - P(occurring) = 1 - 0.2 = 0.8
Correct Answer:
C
— 0.8
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Q. If the probability of an event occurring is 0.2, what is the probability of it not occurring?
A.
0.2
B.
0.5
C.
0.8
D.
1
Show solution
Solution
The probability of the event not occurring is 1 - 0.2 = 0.8.
Correct Answer:
C
— 0.8
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Q. If the quadratic equation x^2 - 4x - 5 = 0 is factored, what are the roots?
A.
-1, 5
B.
1, -5
C.
5, -1
D.
5, 1
Show solution
Solution
Factoring the quadratic gives (x - 5)(x + 1) = 0. Thus, the roots are x = 5 and x = -1.
Correct Answer:
A
— -1, 5
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Q. If the radius of a circle is 5 cm, what is the circumference of the circle?
A.
10π cm
B.
15π cm
C.
20π cm
D.
25π cm
Show solution
Solution
The circumference of a circle is given by the formula C = 2πr. Thus, C = 2π(5) = 10π cm.
Correct Answer:
A
— 10π cm
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Q. If the radius of a circle is 5, what is the area of the circle?
A.
25π
B.
20π
C.
30π
D.
15π
Show solution
Solution
The area of a circle is given by A = πr^2. Therefore, A = π(5^2) = 25π.
Correct Answer:
A
— 25π
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Q. If the radius of a circle is 7 cm, what is the area of the circle?
A.
154 cm²
B.
49 cm²
C.
28 cm²
D.
44 cm²
Show solution
Solution
The area of a circle is given by the formula A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
Correct Answer:
A
— 154 cm²
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Q. If the radius of a circle is 7 cm, what is the circumference of the circle?
A.
14π cm
B.
21π cm
C.
28π cm
D.
49π cm
Show solution
Solution
The circumference of a circle is calculated using the formula 2πr. Therefore, circumference = 2π × 7 cm = 14π cm.
Correct Answer:
B
— 21π cm
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Q. If the radius of a circle is 7 cm, what is the circumference?
A.
14π cm
B.
21π cm
C.
28π cm
D.
49π cm
Show solution
Solution
The circumference of a circle is calculated using the formula 2πr. Thus, the circumference is 2π × 7 cm = 14π cm.
Correct Answer:
B
— 21π cm
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Q. If the radius of a circle is doubled, by what factor does the area increase?
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Solution
Area = πr^2. If radius is doubled, new area = π(2r)^2 = 4πr^2, so area increases by a factor of 4.
Correct Answer:
D
— 4
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Q. If the radius of a circle is doubled, by what factor does the area of the circle increase?
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Solution
The area of a circle is given by A = πr². If the radius is doubled (r' = 2r), the new area A' = π(2r)² = 4πr². Thus, the area increases by a factor of 4.
Correct Answer:
C
— 4
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Q. If the radius of a circle is doubled, how does the area of the circle change?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
The area of a circle is given by A = πr². If the radius is doubled (r' = 2r), the new area A' = π(2r)² = 4πr², which is four times the original area.
Correct Answer:
D
— It quadruples
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Q. If the radius of a circle is halved, how does the area change?
A.
It remains the same
B.
It doubles
C.
It is halved
D.
It is quartered
Show solution
Solution
If the radius is halved, the area becomes π(r/2)² = π(r²/4) = (1/4) * πr², which means the area is quartered.
Correct Answer:
D
— It is quartered
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Q. If the radius of a sphere is 3 units, what is its volume?
A.
27π
B.
36π
C.
9π
D.
18π
Show solution
Solution
The volume V of a sphere is given by V = (4/3)πr³. Thus, V = (4/3)π(3)³ = (4/3)π(27) = 36π.
Correct Answer:
A
— 27π
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Q. If the radius of a sphere is doubled, how does the volume change?
A.
It doubles
B.
It triples
C.
It quadruples
D.
It increases by a factor of eight
Show solution
Solution
Volume of a sphere = (4/3)πr³. If r is doubled, the new volume = (4/3)π(2r)³ = (4/3)π(8r³) = 8 times the original volume.
Correct Answer:
D
— It increases by a factor of eight
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Q. If the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is its area?
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
72 cm²
Show solution
Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √(s(s-a)(s-b)(s-c)) = √(28(28-7)(28-24)(28-25)) = √(28*21*4*3) = 84 cm².
Correct Answer:
B
— 96 cm²
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Q. If the sides of triangle PQR are in the ratio 3:4:5, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
Show solution
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle.
Correct Answer:
D
— Right
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Q. If the sum of two numbers is 15 and one number is x, what is the other number?
A.
15 - x
B.
x + 15
C.
x - 15
D.
x/15
Show solution
Solution
Let the other number be y. Then x + y = 15. Therefore, y = 15 - x.
Correct Answer:
A
— 15 - x
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Q. If the sum of two numbers is 30 and one number is x, what is the other number?
A.
30 - x
B.
x + 30
C.
x - 30
D.
x/30
Show solution
Solution
Let the other number be y. Then x + y = 30. Therefore, y = 30 - x.
Correct Answer:
A
— 30 - x
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Q. If there are 3 apples and you buy 2 more, how many apples do you have?
Show solution
Solution
3 + 2 = 5 apples
Correct Answer:
B
— 5
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Q. If there are 4 apples and you buy 3 more, how many apples do you have in total?
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Solution
4 + 3 = 7, so you have 7 apples in total.
Correct Answer:
A
— 6
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Q. If there are 8 oranges and you buy 4 more, how many oranges do you have in total?
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Q. If triangle ABC has vertices A(1, 1), B(4, 5), and C(7, 2), what is the length of side AB?
A.
4.0
B.
5.0
C.
3.0
D.
6.0
Show solution
Solution
Using the distance formula: AB = √((4 - 1)² + (5 - 1)²) = √(9 + 16) = √25 = 5.0.
Correct Answer:
B
— 5.0
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Q. If triangle ABC has vertices A(1, 2), B(4, 6), and C(1, 6), what is the length of side AB?
A.
5.0
B.
4.0
C.
3.0
D.
6.0
Show solution
Solution
Using the distance formula: AB = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.0.
Correct Answer:
B
— 4.0
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Q. If triangle ABC has vertices A(1, 2), B(4, 6), and C(7, 2), what is the area of triangle ABC?
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Solution
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 0.5 * |1(6 - 2) + 4(2 - 2) + 7(2 - 6)| = 0.5 * |4 + 0 - 28| = 12.
Correct Answer:
B
— 10
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Q. If triangle ABC has vertices A(1, 2), B(4, 6), and C(7, 2), what is the length of side AB?
A.
5.0
B.
4.24
C.
3.0
D.
6.0
Show solution
Solution
Using the distance formula: AB = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.0.
Correct Answer:
B
— 4.24
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Q. If triangle ABC is congruent to triangle DEF, which of the following is true?
A.
AB = DE
B.
AC = DF
C.
BC = EF
D.
All of the above
Show solution
Solution
If two triangles are congruent, all corresponding sides and angles are equal.
Correct Answer:
D
— All of the above
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