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. What is the sum of the roots of the polynomial x^2 - 4x + 4?

A. -4
B. 4
C. 2
D. 0

Solution

The sum of the roots of a quadratic equation ax^2 + bx + c is given by -b/a. Here, -(-4)/1 = 4.

Correct Answer: B — 4

Q. What is the sum of the roots of the polynomial x^2 - 5x + 6?

A. 5
B. 6
C. 3
D. 0

Solution

The sum of the roots of a quadratic equation ax^2 + bx + c is given by -b/a. Here, -(-5)/1 = 5.

Correct Answer: A — 5

Q. What is the sum of the roots of the quadratic equation 2x^2 + 4x - 6 = 0?

A. -2
B. 2
C. -3
D. 3

Solution

Step 1: Use the formula -b/a. Here, b = 4 and a = 2. Step 2: Sum of roots = -4/2 = -2.

Correct Answer: A — -2

Q. What is the sum of the roots of the quadratic equation x^2 + 3x - 10 = 0?

A. -3
B. 3
C. 10
D. -10

Solution

The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a. Here, b = 3 and a = 1, so the sum is -3/1 = -3.

Correct Answer: A — -3

Q. What is the sum of the roots of the quadratic equation x^2 + 4x + 4 = 0?

A. -4
B. 4
C. 0
D. 2

Solution

The sum of the roots is given by -b/a = -4/1 = -4.

Correct Answer: A — -4

Q. What is the sum of the roots of the quadratic equation x^2 + 6x + 9 = 0?

A. -6
B. 6
C. 9
D. 0

Solution

Step 1: Use the formula -b/a. Here, b = 6 and a = 1. Step 2: The sum of the roots is -6/1 = -6.

Correct Answer: A — -6

Q. What is the sum of the roots of the quadratic equation x^2 - 6x + 8 = 0?

A. 6
B. 8
C. 4
D. 2

Solution

Step 1: Use the sum of roots formula -b/a. Here, b = -6, a = 1. Step 2: Sum = 6.

Correct Answer: A — 6

Q. What is the value of 7 + 5 × 2?

A. 12
B. 17
C. 10
D. 19

Solution

According to the order of operations, we first multiply 5 by 2 to get 10, then add 7 to get 17.

Correct Answer: B — 17

Q. What is the value of 9² - 4²?

A. 77
B. 81
C. 65
D. 45

Solution

9² = 81 and 4² = 16. Therefore, 81 - 16 = 65.

Correct Answer: A — 77

Q. What is the value of cos(45°)?

A. 0
B. 1/2
C. √2/2
D. √3/2

Solution

cos(45°) = √2/2.

Correct Answer: C — √2/2

Q. What is the value of k if the equation 2x^2 + kx + 3 = 0 has one solution?

A. -6
B. -4
C. 4
D. 6

Solution

For one solution, the discriminant must be zero: k^2 - 4(2)(3) = 0. Thus, k^2 = 24, so k = ±√24 = ±2√6. The integer value is -4.

Correct Answer: B — -4

Q. What is the value of k if the equation x^2 + kx + 16 = 0 has one real solution?

A. k = 8
B. k = -8
C. k = 0
D. k = 4

Solution

For one real solution, the discriminant must be zero: k^2 - 4(1)(16) = 0. Thus, k^2 = 64, so k = ±8.

Correct Answer: B — k = -8

Q. What is the value of k if the polynomial x^2 + kx + 16 has roots 4 and -4?

A. -8
B. 0
C. 8
D. 16

Solution

Using Vieta's formulas, the sum of the roots (4 + (-4)) = 0, so k = 0.

Correct Answer: A — -8

Q. What is the value of k if the polynomial x^2 + kx + 16 has roots that are both 4?

A. -8
B. -16
C. 8
D. 16

Solution

Using the fact that the sum of the roots is -k, we have 4 + 4 = -k, so k = -8.

Correct Answer: A — -8

Q. What is the value of k if the polynomial x^2 + kx + 9 has roots 3 and -3?

A. 0
B. 6
C. 9
D. 3

Solution

Using Vieta's formulas, the sum of the roots (3 + (-3)) = -k, so k = 0. The product of the roots (3 * -3) = 9, which is consistent. Thus, k = 0.

Correct Answer: B — 6

Q. What is the value of k if x^2 + kx + 16 has roots 4 and -4?

A. -8
B. 0
C. 8
D. 16

Solution

Using Vieta's formulas, the sum of the roots is -k = 4 + (-4) = 0, so k = 0.

Correct Answer: A — -8

Q. What is the value of k if x^2 - kx + 12 has roots 3 and 4?

A. 7
B. 12
C. 9
D. 8

Solution

Using the sum of roots, 3 + 4 = k, we find k = 7.

Correct Answer: A — 7

Q. What is the value of sec(θ) if cos(θ) = 0.5?

A. 0.5
B. 1
C. 2
D. √3

Solution

sec(θ) = 1/cos(θ) = 1/0.5 = 2.

Correct Answer: C — 2

Q. What is the value of sin(π/6)?

A. 0
B. 1/2
C. √3/2
D. 1

Solution

The value of sin(π/6) is 1/2.

Correct Answer: B — 1/2

Q. What is the value of x in the equation 2(x + 5) = 20?

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

Solution

Step 1: Divide both sides by 2: x + 5 = 10. Step 2: Subtract 5 from both sides: x = 5.

Correct Answer: A — x = 5

Q. What is the value of x in the equation 2(x - 3) = 8?

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

Solution

Step 1: Divide both sides by 2: x - 3 = 4. Step 2: Add 3 to both sides: x = 7.

Correct Answer: B — x = 6

Q. What is the value of x in the equation 2x^2 - 4x - 6 = 0?

A. x = 3
B. x = -1
C. x = 2
D. x = -3

Solution

Using the quadratic formula x = (-b ± √(b² - 4ac)) / 2a. Here, a = 2, b = -4, c = -6. Discriminant = (-4)² - 4(2)(-6) = 16 + 48 = 64. x = (4 ± √64) / 4 = (4 ± 8) / 4. Thus, x = 3 or x = -1.

Correct Answer: A — x = 3

Q. What is the value of x in the equation 2x^2 - 8 = 0?

A. 2
B. 4
C. 0
D. 8

Solution

First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Taking the square root gives x = ±2. The positive solution is x = 2.

Correct Answer: B — 4

Q. What is the value of x in the equation 3(x + 2) = 2(x + 5)?

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

Solution

Step 1: Distribute: 3x + 6 = 2x + 10. Step 2: Subtract 2x from both sides: x + 6 = 10. Step 3: Subtract 6 from both sides: x = 4.

Correct Answer: A — x = 1

Q. What is the value of x in the equation 3(x + 2) = 21?

A. x = 5
B. x = 7
C. x = 3
D. x = 1

Solution

Divide both sides by 3: x + 2 = 7. Then subtract 2: x = 5.

Correct Answer: A — x = 5

Q. What is the value of x in the equation 3(x - 1) = 2(x + 2)?

A. -1
B. 0
C. 1
D. 2

Solution

Step 1: Distribute: 3x - 3 = 2x + 4. Step 2: Subtract 2x from both sides: x - 3 = 4. Step 3: Add 3 to both sides: x = 7.

Correct Answer: B — 0

Q. What is the value of x in the equation 3(x - 1) = 2x + 4?

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

Solution

Step 1: Distribute: 3x - 3 = 2x + 4. Step 2: Subtract 2x from both sides: x - 3 = 4. Step 3: Add 3 to both sides: x = 7.

Correct Answer: B — x = 2

Q. What is the value of x in the equation 3(x - 2) = 12?

A. 2
B. 4
C. 6
D. 8

Solution

Divide both sides by 3: x - 2 = 4. Then add 2: x = 6.

Correct Answer: C — 6

Q. What is the value of x in the equation 3x + 2 = 11?

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

Solution

Subtract 2 from both sides: 3x = 9. Then divide by 3: x = 3.

Correct Answer: A — 3

Q. What is the value of x in the equation 3x + 4 = 10?

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

Solution

To solve 3x + 4 = 10, subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.

Correct Answer: A — x = 2

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