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. A tangent to a circle is drawn from a point outside the circle. If the distance from the point to the center of the circle is 10 cm and the radius of the circle is 6 cm, what is the length of the tangent?

A. 8 cm
B. 10 cm
C. 12 cm
D. 14 cm

Solution

Using the Pythagorean theorem, the length of the tangent is √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.

Correct Answer: A — 8 cm

Q. A tangent to a circle is drawn from a point outside the circle. If the radius of the circle is 3 cm and the distance from the center to the point is 5 cm, what is the length of the tangent?

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

Solution

Length of tangent = √(d² - r²) = √(5² - 3²) = √(25 - 9) = √16 = 4 cm.

Correct Answer: A — 4 cm

Q. A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?

A. 30 km/h
B. 40 km/h
C. 50 km/h
D. 60 km/h

Solution

Let the speed of the train on the way to the destination be x km/h. The time taken to travel to the destination is 60/x hours and the time taken to return is 60/90 hours. The total time is given by: 60/x + 60/90 = 4. Solving for x gives x = 40 km/h.

Correct Answer: B — 40 km/h

Q. A train travels 60 km in 1 hour. How far will it travel in 3 hours?

A. 120 km
B. 180 km
C. 150 km
D. 200 km

Solution

If the train travels 60 km in 1 hour, in 3 hours it will travel 60 km × 3 = 180 km.

Correct Answer: B — 180 km

Q. A train travels 60 km in 1 hour. How far will it travel in t hours?

A. 60t
B. 60/t
C. t/60
D. t+60

Solution

Distance = Speed × Time. Therefore, Distance = 60 km/h × t h = 60t km.

Correct Answer: A — 60t

Q. A trapezoid has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is its area?

A. 32 cm²
B. 40 cm²
C. 24 cm²
D. 28 cm²

Solution

Area = 1/2 * (base1 + base2) * height = 1/2 * (10 + 6) * 4 = 32 cm².

Correct Answer: A — 32 cm²

Q. A tree casts a shadow of 10 meters when the angle of elevation of the sun is 30°. How tall is the tree?

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

Solution

Using tan(30°) = height/shadow, height = 10 * tan(30°) = 10 * (1/√3) = 10 m.

Correct Answer: B — 10 m

Q. A tree casts a shadow of 10 meters when the angle of elevation of the sun is 30°. What is the height of the tree?

A. 5√3
B. 10
C. 10√3
D. 15

Solution

Using tan(30°) = height/shadow, height = 10 * tan(30°) = 10 * (1/√3) = 10√3/3.

Correct Answer: A — 5√3

Q. A tree casts a shadow of 15 meters when the angle of elevation of the sun is 30 degrees. How tall is the tree?

A. 5√3 meters
B. 15 meters
C. 10 meters
D. 7.5 meters

Solution

Using the tangent function, tan(30) = height / 15. Therefore, height = 15 * tan(30) = 15 * (1/√3) = 5√3 meters.

Correct Answer: A — 5√3 meters

Q. A triangle has a base of 10 cm and a height of 6 cm. What is its area?

A. 30 cm²
B. 60 cm²
C. 20 cm²
D. 50 cm²

Solution

Area = 1/2 × base × height = 1/2 × 10 cm × 6 cm = 30 cm².

Correct Answer: A — 30 cm²

Q. A triangle has an area of 30 cm² and a base of 10 cm. What is the height?

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

Solution

Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 30) / 10 = 6 cm.

Correct Answer: A — 6 cm

Q. A triangle has an area of 48 cm² and a base of 8 cm. What is the height?

A. 12 cm
B. 6 cm
C. 8 cm
D. 10 cm

Solution

Area = 1/2 * base * height. Therefore, 48 = 1/2 * 8 * height. Solving gives height = 48 / 4 = 12 cm.

Correct Answer: B — 6 cm

Q. A triangle has an area of 50 cm² and a base of 10 cm. What is the height?

A. 5 cm
B. 10 cm
C. 8 cm
D. 12 cm

Solution

Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 50) / 10 = 10 cm.

Correct Answer: A — 5 cm

Q. A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5 cm, what is the area?

A. 12.5 cm²
B. 15 cm²
C. 10 cm²
D. 20 cm²

Solution

Area = 1/2 * base * height. Height = 5 * sin(60°) = 5 * (√3/2) = 5√3/2. Area = 1/2 * 5 * (5√3/2) = 12.5 cm².

Correct Answer: A — 12.5 cm²

Q. A triangle has angles measuring 50 degrees and 60 degrees. What is the measure of the third angle?

A. 70 degrees
B. 80 degrees
C. 90 degrees
D. 100 degrees

Solution

The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 50 - 60 = 70 degrees.

Correct Answer: B — 80 degrees

Q. A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. Is it a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angles are known

Solution

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Correct Answer: A — Yes

Q. A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. Is this triangle a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angles are known

Solution

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Correct Answer: A — Yes

Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is its area?

A. 84 cm²
B. 96 cm²
C. 70 cm²
D. 120 cm²

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

Q. A triangle has sides of lengths 9 cm, 12 cm, and 15 cm. Is it a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angles are known

Solution

Yes, because 9² + 12² = 81 + 144 = 225 = 15².

Correct Answer: A — Yes

Q. A triangle has two sides measuring 6 cm and 8 cm. If the included angle is 60 degrees, what is the area of the triangle?

A. 24 cm²
B. 18 cm²
C. 20 cm²
D. 30 cm²

Solution

Area = 1/2 * a * b * sin(C) = 1/2 * 6 * 8 * sin(60°) = 24√3/2 = 20.78 cm² (approximately 18 cm²).

Correct Answer: B — 18 cm²

Q. A triangle has two sides measuring 8 cm and 15 cm. If the angle between them is 60 degrees, what is the area of the triangle?

A. 60 cm²
B. 30 cm²
C. 40 cm²
D. 70 cm²

Solution

Area = 1/2 * a * b * sin(C) = 1/2 * 8 * 15 * sin(60°) = 60 cm².

Correct Answer: A — 60 cm²

Q. A triangle has two sides measuring 8 cm and 15 cm. If the included angle is 60 degrees, what is the area of the triangle?

A. 60 cm²
B. 30 cm²
C. 40 cm²
D. 70 cm²

Solution

Area = 1/2 * a * b * sin(C) = 1/2 * 8 * 15 * sin(60) = 60 cm².

Correct Answer: A — 60 cm²

Q. A triangle has vertices at (0, 0), (4, 0), and (0, 3). What is its area?

A. 6 cm²
B. 12 cm²
C. 8 cm²
D. 10 cm²

Solution

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6 cm².

Correct Answer: A — 6 cm²

Q. A triangle has vertices at (1, 2), (4, 6), and (1, 6). What is the area of the triangle?

A. 6 cm²
B. 8 cm²
C. 10 cm²
D. 12 cm²

Solution

Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| = 1/2 * |1(6-6) + 4(6-2) + 1(2-6)| = 1/2 * |0 + 16 - 4| = 1/2 * 12 = 6 cm².

Correct Answer: A — 6 cm²

Q. A triangle is inscribed in a circle of radius 5 cm. What is the maximum area of the triangle?

A. 12.5 cm²
B. 25 cm²
C. 20 cm²
D. 15 cm²

Solution

Maximum area = (1/2) * r^2 * sin(θ) = (1/2) * 5^2 * 1 = 25 cm².

Correct Answer: B — 25 cm²

Q. At what value of x does the function y = tan(x) have a vertical asymptote?

A. 0
B. π/4
C. π/2
D. π

Solution

The tangent function has vertical asymptotes at x = π/2 + nπ, where n is an integer. The first asymptote in [0, π] is at π/2.

Correct Answer: C — π/2

Q. Determine the solution for the inequality: 3(x - 1) < 2(x + 2).

A. x < 5
B. x > 5
C. x < 1
D. x > 1

Solution

Step 1: Expand: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

Correct Answer: A — x < 5

Q. Determine the solution set for the inequality: 2x^2 - 8 < 0.

A. (-2, 2)
B. (2, -2)
C. (-∞, -2) ∪ (2, ∞)
D. (-2, ∞)

Solution

Step 1: Factor the inequality: 2(x^2 - 4) < 0. Step 2: Roots are x = -2 and x = 2. Step 3: The solution is between the roots: (-2, 2).

Correct Answer: A — (-2, 2)

Q. Determine the solution set for the inequality: x^2 + 4x + 3 < 0.

A. (-3, -1)
B. (-1, 3)
C. (-∞, -3)
D. (-∞, -1)

Solution

Step 1: Factor the quadratic: (x + 3)(x + 1) < 0. Step 2: The critical points are x = -3 and x = -1. Step 3: Test intervals: The solution set is (-3, -1).

Correct Answer: A — (-3, -1)

Q. Determine the solution set for the inequality: x^2 - 6x + 8 ≤ 0.

A. [2, 4]
B. (2, 4)
C. [4, 2]
D. (-∞, 2) ∪ (4, ∞)

Solution

Step 1: Factor: (x - 2)(x - 4) ≤ 0. Step 2: The solution is between the roots: [2, 4].

Correct Answer: A — [2, 4]

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