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 distance between the points (-1, -1) and (3, 3)?

A. 4.24
B. 5.66
C. 6.0
D. 7.0

Solution

Using the distance formula: d = √((3 - (-1))² + (3 - (-1))²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.

Correct Answer: B — 5.66

Q. What is the distance between the points (-2, -3) and (2, 1)?

A. 5.66
B. 6.32
C. 4.47
D. 5.0

Solution

Using the distance formula: d = √((2 - (-2))² + (1 - (-3))²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.

Correct Answer: A — 5.66

Q. What is the distance between the points (0, 0) and (5, 12)?

A. 12.5
B. 13.0
C. 11.0
D. 10.0

Solution

Using the distance formula: d = √((5 - 0)² + (12 - 0)²) = √(25 + 144) = √169 = 13.0.

Correct Answer: B — 13.0

Q. What is the distance between the points (0, 0) and (x, y) if the distance is 10?

A. x² + y² = 100
B. x² + y² = 10
C. x² + y² = 50
D. x² + y² = 25

Solution

Using the distance formula: d = √(x² + y²) = 10 implies x² + y² = 100.

Correct Answer: A — x² + y² = 100

Q. What is the distance between the points (1, 1) and (1, 5)?

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

Solution

Using the distance formula: d = √((1 - 1)² + (5 - 1)²) = √(0 + 16) = √16 = 4.

Correct Answer: A — 4

Q. What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?

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

Solution

Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.

Correct Answer: B — 5

Q. What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?

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

Solution

Distance = √((x2 - x1)² + (y2 - y1)²) = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. What is the distance between the points (2, 3) and (5, 7) in the coordinate plane?

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

Solution

Distance = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. What is the distance between the points (3, 4) and (3, 10) in the coordinate plane?

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

Solution

The distance formula gives d = |y2 - y1| = |10 - 4| = 6.

Correct Answer: A — 6

Q. What is the distance between the points (3, 4) and (7, 1) in the coordinate plane?

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

Solution

Distance = √((7-3)² + (1-4)²) = √(4 + 9) = √13 ≈ 3.6.

Correct Answer: A — 5

Q. What is the distance between the points (5, 5) and (5, 1)?

A. 4.0
B. 5.0
C. 3.0
D. 2.0

Solution

Using the distance formula: d = √((5 - 5)² + (1 - 5)²) = √(0 + 16) = √16 = 4.0.

Correct Answer: A — 4.0

Q. What is the distance between the points (5, 5) and (5, 10)?

A. 5.0
B. 10.0
C. 15.0
D. 0.0

Solution

Using the distance formula: d = √((5 - 5)² + (10 - 5)²) = √(0 + 25) = √25 = 5.0.

Correct Answer: A — 5.0

Q. What is the distance between the points (5, 5) and (5, 9)?

A. 4
B. 5
C. 6
D. 7

Solution

Using the distance formula: d = √((5 - 5)² + (9 - 5)²) = √(0 + 16) = √16 = 4.

Correct Answer: A — 4

Q. What is the distance from the point (1, -1) to the line 2x + 3y - 6 = 0?

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

Solution

Distance = |Ax1 + By1 + C| / √(A² + B²) = |2*1 + 3*(-1) - 6| / √(2² + 3²) = |-7| / √13 = 7/√13.

Correct Answer: A — 2

Q. What is the distance from the point (1, 2) to the line 3x + 4y - 12 = 0?

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

Solution

Distance = |Ax1 + By1 + C| / √(A² + B²) = |3(1) + 4(2) - 12| / √(3² + 4²) = |3 + 8 - 12| / 5 = | -1 | / 5 = 1/5.

Correct Answer: B — 3

Q. What is the distance from the point (2, -3) to the line 3x + 4y - 12 = 0?

A. 2.5
B. 3.0
C. 4.0
D. 5.0

Solution

Distance from point (x0, y0) to line Ax + By + C = 0 is given by |Ax0 + By0 + C| / √(A² + B²). Here, A=3, B=4, C=-12. Distance = |3*2 + 4*(-3) - 12| / √(3² + 4²) = |6 - 12 - 12| / 5 = 3.0.

Correct Answer: B — 3.0

Q. What is the distance from the point (2, 3) to the line 2x + 3y - 6 = 0?

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

Solution

Distance = |Ax1 + By1 + C| / √(A² + B²) = |2(2) + 3(3) - 6| / √(2² + 3²) = |4 + 9 - 6| / √13 = 7 / √13 ≈ 1.94, which rounds to 2.

Correct Answer: B — 2

Q. What is the distance from the point (2, 3) to the line defined by the equation 2x + 3y - 6 = 0?

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

Solution

Distance = |Ax + By + C| / √(A² + B²) = |2(2) + 3(3) - 6| / √(2² + 3²) = |4 + 9 - 6| / √13 = 7/√13.

Correct Answer: A — 1

Q. What is the distance from the point (3, 2) to the line 2x + 3y - 6 = 0?

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

Solution

Distance from point (x0, y0) to line Ax + By + C = 0 is given by |Ax0 + By0 + C| / √(A² + B²). Here, A=2, B=3, C=-6. Distance = |2*3 + 3*2 - 6| / √(2² + 3²) = |6 + 6 - 6| / √(4 + 9) = 6 / √13 ≈ 1.67, which rounds to 2.

Correct Answer: B — 2

Q. What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 6 = 0?

A. 2.0
B. 1.0
C. 3.0
D. 4.0

Solution

Distance = |Ax1 + By1 + C| / √(A² + B²) = |2*3 + 3*4 - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13 ≈ 1.0.

Correct Answer: B — 1.0

Q. What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 12 = 0?

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

Solution

Using the formula for distance from a point to a line: d = |Ax + By + C| / √(A² + B²), where A=2, B=3, C=-12. d = |2*3 + 3*4 - 12| / √(2² + 3²) = |6 + 12 - 12| / √13 = 6/√13.

Correct Answer: A — 2

Q. What is the equation of a circle with center at (0, 0) and radius 3?

A. x² + y² = 9
B. x² + y² = 3
C. x² + y² = 6
D. x² + y² = 12

Solution

The standard form is (x - h)² + (y - k)² = r². Here, h=0, k=0, r=3, so the equation is x² + y² = 3² = 9.

Correct Answer: A — x² + y² = 9

Q. What is the equation of a circle with center at (0, 0) and radius 4?

A. x² + y² = 16
B. x² + y² = 8
C. x² + y² = 4
D. x² + y² = 20

Solution

The equation of a circle is (x - h)² + (y - k)² = r². Here, h = 0, k = 0, r = 4, so x² + y² = 4² = 16.

Correct Answer: A — x² + y² = 16

Q. What is the equation of a circle with center at (0, 0) and radius 5?

A. x² + y² = 25
B. x² + y² = 5
C. x² + y² = 10
D. x² + y² = 20

Solution

The equation of a circle is (x - h)² + (y - k)² = r². Here, h=0, k=0, r=5, so x² + y² = 5² = 25.

Correct Answer: A — x² + y² = 25

Q. What is the equation of a circle with center at (1, 1) and radius 2?

A. (x - 1)² + (y - 1)² = 4
B. (x + 1)² + (y + 1)² = 4
C. (x - 1)² + (y - 1)² = 2
D. (x - 1)² + (y - 1)² = 8

Solution

The equation of a circle is (x - h)² + (y - k)² = r². Here, r = 2, so (x - 1)² + (y - 1)² = 2² = 4.

Correct Answer: A — (x - 1)² + (y - 1)² = 4

Q. What is the equation of a line parallel to y = -3x + 2 that passes through the point (1, 4)?

A. y = -3x + 7
B. y = 3x + 1
C. y = -3x + 1
D. y = 3x - 1

Solution

Parallel lines have the same slope. The slope is -3. Using point-slope form: y - 4 = -3(x - 1) gives y = -3x + 7.

Correct Answer: A — y = -3x + 7

Q. What is the equation of a line parallel to y = -3x + 4 that passes through the point (2, 1)?

A. y = -3x + 7
B. y = 3x - 5
C. y = -3x + 1
D. y = 3x + 1

Solution

The slope of the line is -3. Using point-slope form: y - 1 = -3(x - 2) gives y = -3x + 7.

Correct Answer: A — y = -3x + 7

Q. What is the equation of a line parallel to y = 3x + 2 that passes through the point (1, 1)?

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

Solution

Parallel lines have the same slope. Using point-slope form: y - 1 = 3(x - 1) gives y = 3x - 2.

Correct Answer: B — y = 3x + 1

Q. What is the equation of a line that passes through the points (1, 2) and (3, 6)?

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

Solution

Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) gives y = 2x.

Correct Answer: A — y = 2x

Q. What is the equation of a line with a slope of 2 that passes through the point (1, 3)?

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

Solution

Using point-slope form: y - y1 = m(x - x1) => y - 3 = 2(x - 1) => y = 2x + 1.

Correct Answer: B — y = 2x + 3

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