Mathematics (School)

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Mathematics (School)

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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!

Algebra (Secondary) Arithmetic (Primary) Geometry Statistics & Probability Trigonometry

Q. In an equilateral triangle with a side length of 6 cm, what is the area?

A. 9√3 cm²
B. 12 cm²
C. 18 cm²
D. 36 cm²

Solution

Area = (√3/4) * side² = (√3/4) * 6² = 9√3 cm².

Correct Answer: A — 9√3 cm²

Q. In an equilateral triangle, if one side measures 12 cm, what is the area of the triangle?

A. 36√3 cm²
B. 24 cm²
C. 48 cm²
D. 144 cm²

Solution

The area of an equilateral triangle is given by the formula: Area = (√3/4) * side² = (√3/4) * 12² = 36√3 cm².

Correct Answer: A — 36√3 cm²

Q. In an isosceles triangle, if the equal sides are each 10 cm and the base is 12 cm, what is the height of the triangle?

A. 8 cm
B. 6 cm
C. 5 cm
D. 4 cm

Solution

Using the Pythagorean theorem, the height can be found by splitting the triangle in half: height = √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.

Correct Answer: B — 6 cm

Q. In circle O, if the radius is 5 cm, what is the circumference?

A. 10π cm
B. 15π cm
C. 20π cm
D. 25π cm

Solution

Circumference of a circle is given by C = 2πr. Therefore, C = 2π(5) = 10π cm.

Correct Answer: A — 10π cm

Q. In coordinate geometry, what is the distance between the points (1, 2) and (4, 6)?

A. 5
B. 3
C. 4
D. 7

Solution

Distance = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. In coordinate geometry, what is the distance between the points (3, 4) and (7, 1)?

A. 5
B. 4
C. 3
D. 6

Solution

Using the distance formula, d = √((x2 - x1)² + (y2 - y1)²) = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Correct Answer: A — 5

Q. In coordinate geometry, what is the midpoint of the segment connecting points (2, 3) and (4, 7)?

A. (3, 5)
B. (2, 5)
C. (4, 3)
D. (5, 7)

Solution

The midpoint M of a segment with endpoints (x1, y1) and (x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Correct Answer: A — (3, 5)

Q. In coordinate geometry, what is the slope of a line that is parallel to the line represented by the equation y = 3x + 2?

A. 3
B. 2
C. 1/3
D. 0

Solution

Parallel lines have the same slope. The slope of the given line is 3.

Correct Answer: A — 3

Q. In coordinate geometry, what is the slope of a line that is perpendicular to a line with a slope of -3?

A. 1/3
B. 3
C. -1/3
D. 0

Solution

The slope of a line perpendicular to another is the negative reciprocal. The negative reciprocal of -3 is 1/3.

Correct Answer: B — 3

Q. In coordinate geometry, what is the slope of a line that passes through the points (2, 3) and (4, 7)?

A. 2
B. 1
C. 0.5
D. 3

Solution

The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2.

Correct Answer: A — 2

Q. In coordinate geometry, what is the slope of the line passing through the points (2, 3) and (4, 7)?

A. 2
B. 1
C. 0.5
D. 3

Solution

The slope of a line is calculated using the formula (y2 - y1) / (x2 - x1). For the points (2, 3) and (4, 7), the slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.

Correct Answer: A — 2

Q. In coordinate geometry, what is the slope of the line passing through the points (1, 2) and (3, 6)?

A. 2
B. 3
C. 4
D. 1

Solution

The slope m = (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Correct Answer: A — 2

Q. In how many different ways can you arrange 3 red balls and 2 blue balls?

A. 10
B. 30
C. 60
D. 5

Solution

The number of arrangements is 5! / (3!2!) = 10.

Correct Answer: A — 10

Q. In how many ways can you choose 2 fruits from a selection of 5 different fruits?

A. 5
B. 10
C. 15
D. 20

Solution

The number of combinations of 2 fruits from 5 is C(5, 2) = 5! / (2!(5-2)!) = 10.

Correct Answer: B — 10

Q. In how many ways can you choose 3 fruits from a basket of 10 different fruits?

A. 120
B. 720
C. 10
D. 1200

Solution

The number of combinations of 10 fruits taken 3 at a time is C(10, 3) = 10! / (3!(10-3)!) = 120.

Correct Answer: A — 120

Q. In how many ways can you choose 4 toppings from a list of 10?

A. 210
B. 240
C. 300
D. 360

Solution

The number of combinations of 4 toppings from 10 is C(10, 4) = 10! / (4!(10-4)!) = 210.

Correct Answer: A — 210

Q. In similar triangles, if the ratio of the lengths of two corresponding sides is 2:3, what is the ratio of their areas?

A. 4:9
B. 2:3
C. 3:2
D. 1:1

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)^2 = 4/9.

Correct Answer: A — 4:9

Q. In similar triangles, if the ratio of the sides is 1:5, what is the ratio of their perimeters?

A. 1:5
B. 1:10
C. 1:25
D. 5:1

Solution

The ratio of the perimeters of similar triangles is the same as the ratio of their corresponding sides, which is 1:5.

Correct Answer: A — 1:5

Q. In similar triangles, if the ratio of their corresponding sides is 2:3, what is the ratio of their areas?

A. 2:3
B. 4:9
C. 3:2
D. 1:1

Solution

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2:3)² = 4:9.

Correct Answer: B — 4:9

Q. In the data set 10, 12, 10, 14, 16, what is the mode?

A. 10
B. 12
C. 14
D. 16

Solution

Mode is the number that appears most frequently. Here, 10 appears twice.

Correct Answer: A — 10

Q. In the data set 10, 20, 20, 30, 40, what is the mode?

A. 10
B. 20
C. 30
D. 40

Solution

The mode is the number that appears most frequently. Here, 20 appears twice, so the mode is 20.

Correct Answer: B — 20

Q. In the data set 2, 3, 5, 7, 7, what is the mode?

A. 2
B. 3
C. 5
D. 7

Solution

The mode is the number that appears most frequently, which is 7.

Correct Answer: D — 7

Q. In the data set 5, 5, 6, 7, 8, what is the mode?

A. 5
B. 6
C. 7
D. 8

Solution

The mode is the number that appears most frequently. Here, 5 appears twice, so the mode is 5.

Correct Answer: A — 5

Q. In the data set: 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?

A. 2
B. 3
C. 4
D. 5

Solution

The mode is 4, as it appears most frequently (three times).

Correct Answer: C — 4

Q. In the data set: 2, 3, 5, 7, 7, 8, what is the mode?

A. 2
B. 3
C. 7
D. 8

Solution

The mode is the number that appears most frequently. Here, 7 appears twice.

Correct Answer: C — 7

Q. In the data set: 7, 8, 9, 10, 10, 10, 11, what is the mode?

A. 7
B. 8
C. 10
D. 11

Solution

The mode is 10, as it appears most frequently (three times).

Correct Answer: C — 10

Q. In the figure, if angle 1 = 70 degrees and lines a and b are parallel, what is the measure of angle 2?

A. 70 degrees
B. 110 degrees
C. 180 degrees
D. 90 degrees

Solution

Angle 2 is corresponding to angle 1, so angle 2 = 70 degrees.

Correct Answer: B — 110 degrees

Q. In the figure, if angle 1 is 70 degrees, what is the measure of angle 2 if angle 1 and angle 2 are corresponding angles?

A. 70 degrees
B. 110 degrees
C. 90 degrees
D. 180 degrees

Solution

Corresponding angles are equal when two parallel lines are cut by a transversal.

Correct Answer: A — 70 degrees

Q. In the figure, if angle 1 is 70 degrees, what is the measure of angle 2 if lines are parallel?

A. 70 degrees
B. 110 degrees
C. 180 degrees
D. 90 degrees

Solution

Angle 2 is supplementary to angle 1, so 180 - 70 = 110 degrees.

Correct Answer: B — 110 degrees

Q. In triangle ABC, if AB = 12 cm, AC = 16 cm, and angle A = 60 degrees, what is the length of BC?

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Using the Law of Cosines: BC² = AB² + AC² - 2(AB)(AC)cos(A) = 12² + 16² - 2(12)(16)(0.5) = 144 + 256 - 192 = 208. Therefore, BC = √208 = 14.42 cm.

Correct Answer: C — 14 cm

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