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. What is the coordinates of the point that divides the line segment joining (0, 0) and (4, 4) in the ratio 1:3?
A.
(1, 1)
B.
(2, 2)
C.
(3, 3)
D.
(1.5, 1.5)
Show solution
Solution
Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=3, P = ((1*4 + 3*0)/(1+3), (1*4 + 3*0)/(1+3)) = (1, 1).
Correct Answer:
B
— (2, 2)
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Q. What is the coordinates of the point that divides the line segment joining (2, 3) and (10, 7) in the ratio 3:1?
A.
(5, 4)
B.
(6, 5)
C.
(7, 6)
D.
(8, 5)
Show solution
Solution
Using the section formula: C = ((3*10 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (7.5, 5.25).
Correct Answer:
B
— (6, 5)
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Q. What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 3:1?
A.
(3.5, 5)
B.
(3, 4)
C.
(2.5, 4.5)
D.
(4, 5)
Show solution
Solution
Using the section formula: P = ((3*4 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (3.5, 5).
Correct Answer:
A
— (3.5, 5)
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Q. What is the coordinates of the point that divides the line segment joining (2, 3) and (4, 7) in the ratio 1:3?
A.
(3, 5)
B.
(2.5, 4)
C.
(3.5, 5.5)
D.
(3, 6)
Show solution
Solution
Using the section formula: P = ((1*4 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (3, 5).
Correct Answer:
A
— (3, 5)
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Q. What is the coordinates of the point that divides the line segment joining (3, 2) and (9, 10) in the ratio 2:1?
A.
(5, 4)
B.
(6, 6)
C.
(7, 8)
D.
(8, 9)
Show solution
Solution
Using the section formula: C = ((2*9 + 1*3)/(2+1), (2*10 + 1*2)/(2+1)) = (5, 4).
Correct Answer:
A
— (5, 4)
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Q. What is the coordinates of the point that divides the line segment joining (3, 4) and (9, 10) in the ratio 1:3?
A.
(6, 8)
B.
(5, 7)
C.
(4, 6)
D.
(7, 9)
Show solution
Solution
Using the section formula: C = ((1*9 + 3*3)/(1+3), (1*10 + 3*4)/(1+3)) = (6, 8).
Correct Answer:
A
— (6, 8)
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Q. What is the coordinates of the point that divides the line segment joining (6, 8) and (10, 12) in the ratio 1:3?
A.
(8, 10)
B.
(7, 9)
C.
(9, 11)
D.
(6.5, 8.5)
Show solution
Solution
Using the section formula: C = ((1*10 + 3*6)/(1+3), (1*12 + 3*8)/(1+3)) = (8, 10).
Correct Answer:
A
— (8, 10)
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Q. What is the coordinates of the point that divides the line segment joining (6, 8) and (2, 4) in the ratio 1:1?
A.
(4, 6)
B.
(3, 5)
C.
(5, 7)
D.
(2, 4)
Show solution
Solution
Using the section formula: P = ((1*2 + 1*6)/(1+1), (1*4 + 1*8)/(1+1)) = (4, 6).
Correct Answer:
A
— (4, 6)
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Q. What is the cosine of a 60-degree angle?
A.
0
B.
0.5
C.
0.707
D.
1
Show solution
Solution
The cosine of 60 degrees is 0.5.
Correct Answer:
B
— 0.5
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Q. What is the degree of the polynomial 3x^4 - 5x^2 + 2?
Show solution
Solution
The degree of a polynomial is the highest power of the variable. Here, the highest power is 4, so the degree is 4.
Correct Answer:
B
— 4
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Q. What is the degree of the polynomial 3x^4 - 5x^3 + 2x - 7?
Show solution
Solution
The degree of a polynomial is the highest power of the variable. Here, the highest power is 4, so the degree is 4.
Correct Answer:
C
— 4
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Q. What is the degree of the polynomial 4x^3 - 2x^2 + x - 5?
Show solution
Solution
The degree of a polynomial is the highest power of x. Here, the highest power is 3.
Correct Answer:
B
— 3
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Q. What is the degree of the polynomial 4x^3 - 2x^2 + x - 7?
Show solution
Solution
The degree of a polynomial is the highest power of x. Here, the highest power is 3.
Correct Answer:
B
— 3
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Q. What is the diameter of a circle whose circumference is 31.4 cm?
A.
10 cm
B.
5 cm
C.
15.7 cm
D.
20 cm
Show solution
Solution
Circumference = πd; 31.4 = πd; d = 31.4/π ≈ 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the diameter of a circle with a circumference of 31.4 cm?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = πd, so d = Circumference/π = 31.4/π ≈ 10 cm.
Correct Answer:
B
— 10 cm
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Q. What is the diameter of a circle with a circumference of 62.8 cm?
A.
20 cm
B.
10 cm
C.
15 cm
D.
5 cm
Show solution
Solution
Diameter = Circumference / π = 62.8 / π ≈ 20 cm.
Correct Answer:
A
— 20 cm
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Q. What is the diameter of a circle with an area of 113.04 cm²?
A.
12 cm
B.
10 cm
C.
8 cm
D.
6 cm
Show solution
Solution
Area = πr², so r² = Area/π = 113.04/π ≈ 36, thus r ≈ 6 cm, diameter = 12 cm.
Correct Answer:
B
— 10 cm
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Q. What is the diameter of a circle with an area of 50π cm²?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Area = πr², so r² = 50, thus r = √50 ≈ 7.07 cm, diameter = 2r ≈ 10 cm.
Correct Answer:
B
— 10 cm
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Q. What is the discriminant of the quadratic equation 2x^2 + 3x + 1 = 0?
Show solution
Solution
The discriminant is calculated as b^2 - 4ac. Here, a = 2, b = 3, c = 1. So, discriminant = 3^2 - 4(2)(1) = 9 - 8 = 1.
Correct Answer:
A
— 1
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Q. What is the discriminant of the quadratic equation 2x^2 + 4x + 2 = 0?
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Solution
The discriminant is given by b^2 - 4ac. Here, a = 2, b = 4, c = 2. So, the discriminant = 4^2 - 4(2)(2) = 16 - 16 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the quadratic equation 2x^2 + 4x + 2?
Show solution
Solution
Calculate the discriminant: D = b^2 - 4ac = 4^2 - 4(2)(2) = 16 - 16 = 0.
Correct Answer:
A
— 0
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Q. What is the discriminant of the quadratic equation 3x^2 + 6x + 2 = 0?
Show solution
Solution
The discriminant is given by b^2 - 4ac. Here, a = 3, b = 6, c = 2. Thus, the discriminant = 6^2 - 4*3*2 = 36 - 24 = 12.
Correct Answer:
A
— 0
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Q. What is the discriminant of the quadratic equation 3x^2 + 6x + 2?
Show solution
Solution
The discriminant is given by b^2 - 4ac. Here, a = 3, b = 6, c = 2. Thus, discriminant = 6^2 - 4(3)(2) = 36 - 24 = 12.
Correct Answer:
B
— 4
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Q. What is the discriminant of the quadratic equation x^2 - 6x + 9?
Show solution
Solution
The discriminant is given by b^2 - 4ac. Here, a = 1, b = -6, and c = 9. So, the discriminant is (-6)^2 - 4(1)(9) = 36 - 36 = 0.
Correct Answer:
A
— 0
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Q. What is the distance between the center of a circle and a point on its circumference?
A.
Diameter
B.
Radius
C.
Chord
D.
Arc
Show solution
Solution
The distance between the center of a circle and any point on its circumference is defined as the radius.
Correct Answer:
B
— Radius
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 9 cm?
A.
9 cm
B.
18 cm
C.
4.5 cm
D.
12 cm
Show solution
Solution
The distance from the center to a point on the circumference is equal to the radius, which is 9 cm.
Correct Answer:
A
— 9 cm
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Q. What is the distance between the center of a circle and a point on the circle?
A.
Diameter
B.
Circumference
C.
Radius
D.
Chord
Show solution
Solution
The distance between the center of a circle and any point on the circle is defined as the radius.
Correct Answer:
C
— Radius
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Q. What is the distance between the center of a circle at (2, 3) and a point on the circumference at (5, 7)?
Show solution
Solution
Distance = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the center of a circle at (2, 3) and a point on the circle at (5, 7)?
Show solution
Solution
Distance = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the center of a circle with radius 5 cm and a point on its circumference?
A.
0 cm
B.
5 cm
C.
10 cm
D.
2.5 cm
Show solution
Solution
The distance from the center to a point on the circumference is equal to the radius, which is 5 cm.
Correct Answer:
B
— 5 cm
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