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 relationship between the lengths of two tangents drawn from an external point to a circle?
A.
They are equal
B.
One is longer than the other
C.
They are perpendicular to the radius
D.
They are parallel
Show solution
Solution
The lengths of two tangents drawn from an external point to a circle are equal.
Correct Answer:
A
— They are equal
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Q. What is the relationship between the radius and diameter of a circle?
A.
The radius is twice the diameter.
B.
The diameter is twice the radius.
C.
The radius and diameter are equal.
D.
The radius is half the diameter.
Show solution
Solution
The diameter of a circle is twice the length of the radius.
Correct Answer:
B
— The diameter is twice the radius.
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Q. What is the relationship between the radius and the tangent at the point of contact on a circle?
A.
They are equal
B.
They are perpendicular
C.
They are parallel
D.
They are collinear
Show solution
Solution
The radius drawn to the point of contact is always perpendicular to the tangent at that point.
Correct Answer:
B
— They are perpendicular
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Q. What is the relationship between the sides of a right triangle?
A.
The sum of the two shorter sides equals the longest side
B.
The longest side is equal to the sum of the other two sides
C.
The square of the longest side equals the sum of the squares of the other two sides
D.
All sides are equal
Show solution
Solution
In a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides (Pythagorean theorem).
Correct Answer:
C
— The square of the longest side equals the sum of the squares of the other two sides
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Q. What is the result of (2x + 3)(x - 1)?
A.
2x^2 + x - 3
B.
2x^2 + 5x - 3
C.
2x^2 - x + 3
D.
2x^2 - 5x - 3
Show solution
Solution
Step 1: Use the distributive property: 2x^2 - 2x + 3x - 3. Step 2: Combine like terms: 2x^2 + x - 3.
Correct Answer:
B
— 2x^2 + 5x - 3
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Q. What is the result of (3x^2 + 2x) + (4x^2 - 5x)?
A.
7x^2 - 3x
B.
7x^2 + 3x
C.
x^2 - 3x
D.
x^2 + 3x
Show solution
Solution
Step 1: Combine like terms: (3x^2 + 4x^2) + (2x - 5x) = 7x^2 - 3x.
Correct Answer:
A
— 7x^2 - 3x
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Q. What is the result of (x + 2)(x - 2)?
A.
x^2 - 4
B.
x^2 + 4
C.
2x
D.
x^2 + 2
Show solution
Solution
Step 1: Recognize this as a difference of squares: (a + b)(a - b) = a^2 - b^2. Step 2: Here, a = x and b = 2. Result is x^2 - 4.
Correct Answer:
A
— x^2 - 4
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Q. What is the result of (x + 2)(x - 3)?
A.
x^2 - x - 6
B.
x^2 + x - 6
C.
x^2 - 6
D.
x^2 + 6
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Solution
Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
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Q. What is the result of factoring the expression x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x - 5)(x - 2)
C.
(x + 10)(x - 1)
D.
(x - 10)(x + 1)
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Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor: (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. What is the result of factoring the polynomial x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x + 10)(x - 1)
C.
(x - 5)(x - 2)
D.
(x + 1)(x + 10)
Show solution
Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor: (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. What is the result of factoring the polynomial x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x + 3)(x + 3)
D.
x(x - 9)
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Solution
x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. What is the section formula for dividing a line segment in the ratio 2:3?
A.
(2x2 + 3x1)/(2 + 3), (2y2 + 3y1)/(2 + 3)
B.
(3x2 + 2x1)/(3 + 2), (3y2 + 2y1)/(3 + 2)
C.
(x1 + x2)/2, (y1 + y2)/2
D.
(x2 - x1)/(y2 - y1)
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Solution
The section formula for dividing a line segment in the ratio m:n is ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).
Correct Answer:
A
— (2x2 + 3x1)/(2 + 3), (2y2 + 3y1)/(2 + 3)
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Q. What is the section formula for dividing the line segment joining points (1, 2) and (4, 6) in the ratio 2:1?
A.
(2, 3)
B.
(3, 4)
C.
(2.5, 4)
D.
(3, 5)
Show solution
Solution
Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=2, n=1, P = ((2*4 + 1*1)/(2+1), (2*6 + 1*2)/(2+1)) = (3, 4).
Correct Answer:
B
— (3, 4)
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Q. What is the section formula for dividing the line segment joining points (2, 3) and (8, 7) in the ratio 1:3?
A.
(5, 4)
B.
(6, 5)
C.
(4, 5)
D.
(3, 4)
Show solution
Solution
Using the section formula: P(x, y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=3. P = ((1*8 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (6, 5).
Correct Answer:
B
— (6, 5)
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Q. What is the section ratio of the point (4, 5) that divides the line segment joining (2, 3) and (6, 7) internally?
A.
1:1
B.
2:1
C.
3:1
D.
1:2
Show solution
Solution
Using the section formula, the ratio is 1:1 since the coordinates are equidistant from the midpoint (4, 5).
Correct Answer:
B
— 2:1
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Q. What is the semi-perimeter of a triangle with sides 10 cm, 14 cm, and 16 cm?
A.
20 cm
B.
25 cm
C.
30 cm
D.
22 cm
Show solution
Solution
Semi-perimeter = (10 + 14 + 16) / 2 = 40 / 2 = 20 cm.
Correct Answer:
B
— 25 cm
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Q. What is the semi-perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm?
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
Show solution
Solution
Semi-perimeter = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.
Correct Answer:
B
— 14 cm
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Q. What is the semi-perimeter of a triangle with sides measuring 7 cm, 8 cm, and 9 cm?
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
Show solution
Solution
Semi-perimeter = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.
Correct Answer:
B
— 14 cm
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Q. What is the simplified form of the expression (x^2 - 1)/(x - 1)?
A.
x + 1
B.
x - 1
C.
x^2 + 1
D.
x^2 - 1
Show solution
Solution
Step 1: Factor the numerator: (x - 1)(x + 1)/(x - 1). Step 2: Cancel (x - 1): x + 1.
Correct Answer:
A
— x + 1
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Q. What is the simplified form of the expression 2(x + 3) - 4?
A.
2x + 2
B.
2x + 6
C.
2x + 10
D.
2x - 4
Show solution
Solution
Step 1: Distribute: 2x + 6 - 4. Step 2: Combine like terms: 2x + 2.
Correct Answer:
B
— 2x + 6
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Q. What is the simplified form of the expression 2√(8) + 3√(2)?
A.
4√(2)
B.
6√(2)
C.
8√(2)
D.
5√(2)
Show solution
Solution
Step 1: Simplify 2√(8) = 2 * 2√(2) = 4√(2). Step 2: Combine: 4√(2) + 3√(2) = 7√(2).
Correct Answer:
A
— 4√(2)
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Q. What is the simplified form of the expression 2√18 + 3√8?
A.
6√2
B.
12√2
C.
8√2
D.
10√2
Show solution
Solution
Step 1: Simplify √18 = 3√2 and √8 = 2√2. Step 2: Substitute: 2(3√2) + 3(2√2) = 6√2 + 6√2 = 12√2.
Correct Answer:
A
— 6√2
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Q. What is the simplified form of the expression 3(x + 2) - 2(x - 1)?
A.
x + 8
B.
x + 7
C.
x + 6
D.
x + 5
Show solution
Solution
Step 1: Distribute: 3x + 6 - 2x + 2. Step 2: Combine like terms: (3x - 2x) + (6 + 2) = x + 8.
Correct Answer:
B
— x + 7
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Q. What is the simplified form of the expression 3x^2 - 2x + 4x^2 - 5?
A.
7x^2 - 5
B.
x^2 - 5
C.
x^2 + 5
D.
7x^2 + 5
Show solution
Solution
Step 1: Combine like terms: (3x^2 + 4x^2) + (-2x) - 5 = 7x^2 - 5.
Correct Answer:
A
— 7x^2 - 5
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Q. What is the sine of a 30-degree angle?
A.
0
B.
0.5
C.
0.707
D.
1
Show solution
Solution
The sine of 30 degrees is 0.5.
Correct Answer:
B
— 0.5
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Q. What is the slope of a line that is perpendicular to a line with a slope of -3?
A.
1/3
B.
-1/3
C.
3
D.
-3
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Solution
The slope of a line perpendicular to another is the negative reciprocal. The negative reciprocal of -3 is 1/3.
Correct Answer:
A
— 1/3
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Q. What is the slope of the line passing through the points (1, 2) and (3, 8)?
Show solution
Solution
Slope (m) = (y2 - y1) / (x2 - x1) = (8 - 2) / (3 - 1) = 6 / 2 = 3.
Correct Answer:
B
— 4
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Q. What is the slope of the line passing through the points (1, 2) and (4, 6)?
Show solution
Solution
Slope formula: m = (y2 - y1) / (x2 - x1) = (6 - 2) / (4 - 1) = 4 / 3.
Correct Answer:
B
— 2
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Q. What is the slope of the line passing through the points (2, 3) and (5, 11)?
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Solution
The slope m of a line through two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1). Here, m = (11 - 3) / (5 - 2) = 8 / 3.
Correct Answer:
B
— 3
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Q. What is the slope of the line represented by the equation 2y - 4x = 8?
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Solution
First, rewrite the equation in slope-intercept form (y = mx + b).\n1. 2y = 4x + 8\n2. y = 2x + 4.\nThe slope (m) is 2.
Correct Answer:
A
— 2
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