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. Find the coordinates of the point that divides the 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(x, y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)), where m=1, n=3, x1=2, y1=3, x2=4, y2=7. 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. Find the coordinates of the point that divides the segment joining (2, 3) and (8, 7) in the ratio 1:3.
A.
(5, 5)
B.
(4, 5)
C.
(6, 5)
D.
(3, 4)
Show solution
Solution
Using the section formula: P = ((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)) = (5, 5).
Correct Answer:
A
— (5, 5)
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Q. Find the distance between the points (-1, -1) and (2, 3).
Show solution
Solution
Using the distance formula: d = √((2 - (-1))² + (3 - (-1))²) = √((3)² + (4)²) = √(9 + 16) = √25 = 5.
Correct Answer:
C
— 5
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Q. Find the midpoint of the line segment joining the points (1, 2) and (5, 6).
A.
(3, 4)
B.
(4, 3)
C.
(2, 5)
D.
(5, 2)
Show solution
Solution
Midpoint M = ((x1 + x2)/2, (y1 + y2)/2) = ((1 + 5)/2, (2 + 6)/2) = (3, 4).
Correct Answer:
A
— (3, 4)
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Q. Find the roots of the equation 3x^2 + 6x + 3 = 0.
A.
x = -1
B.
x = -3
C.
x = 1
D.
x = 3
Show solution
Solution
This can be simplified to x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, the root is x = -1.
Correct Answer:
A
— x = -1
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Q. Find the roots of the equation 3x^2 - 12 = 0.
A.
x = 2, -2
B.
x = 4, -4
C.
x = 2, 4
D.
x = -4, 2
Show solution
Solution
Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Thus, x = ±2.
Correct Answer:
A
— x = 2, -2
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Q. Find the roots of the equation 4x^2 - 12x + 9 = 0.
A.
x = 1.5
B.
x = 3
C.
x = 0
D.
x = -3
Show solution
Solution
Factoring gives (2x - 3)(2x - 3) = 0. Thus, x = 3.
Correct Answer:
B
— x = 3
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Q. Find the roots of the equation x^2 + 2x - 8 = 0.
A.
x = 2, -4
B.
x = -2, 4
C.
x = 4, -2
D.
x = -4, 2
Show solution
Solution
Factoring gives (x + 4)(x - 2) = 0. Thus, the roots are x = 4 and x = -2.
Correct Answer:
C
— x = 4, -2
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Q. Find the roots of the equation x^2 - 8x + 16 = 0.
A.
x = 4
B.
x = -4
C.
x = 8
D.
x = 0
Show solution
Solution
This is a perfect square: (x - 4)² = 0. Thus, x - 4 = 0, so x = 4.
Correct Answer:
A
— x = 4
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Q. Find the roots of the polynomial equation x^2 + 5x + 6 = 0.
A.
x = -2, -3
B.
x = 2, 3
C.
x = -1, -6
D.
x = 1, -6
Show solution
Solution
Factoring gives (x + 2)(x + 3) = 0. Thus, the roots are x = -2 and x = -3.
Correct Answer:
A
— x = -2, -3
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Q. Find the roots of the quadratic equation 3x^2 + 6x + 3 = 0.
A.
x = -1
B.
x = -3
C.
x = 1
D.
x = 3
Show solution
Solution
Dividing the equation by 3 gives x^2 + 2x + 1 = 0, which factors to (x + 1)(x + 1) = 0. Thus, x = -1.
Correct Answer:
A
— x = -1
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Q. Find the roots of the quadratic equation 3x^2 - 12x = 0.
A.
x = 0, 4
B.
x = 3, 4
C.
x = 0, 3
D.
x = 1, 2
Show solution
Solution
Factoring gives 3x(x - 4) = 0. Thus, x = 0 and x = 4.
Correct Answer:
A
— x = 0, 4
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Q. Find the roots of the quadratic equation 4x^2 - 12x + 9 = 0.
A.
x = 1.5
B.
x = 3
C.
x = 0
D.
x = -3
Show solution
Solution
This can be factored as (2x - 3)(2x - 3) = 0. Thus, x = 3.
Correct Answer:
B
— x = 3
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Q. Find the solution for x in the equation 2(x + 3) = 16.
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
Show solution
Solution
Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.
Correct Answer:
B
— x = 5
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Q. Find the solution set for the inequality: 3x + 2 > 5.
A.
x > 1
B.
x < 1
C.
x ≥ 1
D.
x ≤ 1
Show solution
Solution
Step 1: Subtract 2 from both sides: 3x > 3. Step 2: Divide by 3: x > 1.
Correct Answer:
A
— x > 1
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Q. Find the solution set for the inequality: 4x - 7 ≤ 9.
A.
x ≤ 4
B.
x ≥ 4
C.
x < 4
D.
x > 4
Show solution
Solution
Step 1: Add 7 to both sides: 4x ≤ 16. Step 2: Divide by 4: x ≤ 4.
Correct Answer:
A
— x ≤ 4
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Q. Find the solution set for the inequality: x^2 + 2x - 8 > 0.
A.
(-∞, -4) ∪ (2, ∞)
B.
(-4, 2)
C.
(-2, 4)
D.
(-∞, 2) ∪ (4, ∞)
Show solution
Solution
Step 1: Factor the quadratic: (x - 2)(x + 4) > 0. Step 2: The solution is outside the roots: (-∞, -4) ∪ (2, ∞).
Correct Answer:
A
— (-∞, -4) ∪ (2, ∞)
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Q. Find the solution set for the inequality: x^2 + 3x - 4 > 0.
A.
(-∞, -4) ∪ (1, ∞)
B.
(-4, 1)
C.
(-∞, 1) ∪ (4, ∞)
D.
(-4, ∞)
Show solution
Solution
Step 1: Factor the quadratic: (x - 1)(x + 4) > 0. Step 2: The solution is outside the roots: (-∞, -4) ∪ (1, ∞).
Correct Answer:
A
— (-∞, -4) ∪ (1, ∞)
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Q. Find the solution set for the inequality: x^2 - 4 > 0.
A.
(-∞, -2) ∪ (2, ∞)
B.
(-2, 2)
C.
(2, -2)
D.
(-2, ∞)
Show solution
Solution
Step 1: Factor the inequality: (x - 2)(x + 2) > 0. Step 2: The solution set is (-∞, -2) ∪ (2, ∞).
Correct Answer:
A
— (-∞, -2) ∪ (2, ∞)
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Q. Find the solution set for the inequality: x^2 - 6x + 8 > 0.
A.
x < 2 or x > 4
B.
2 < x < 4
C.
x > 2
D.
x < 4
Show solution
Solution
Step 1: Factor: (x - 2)(x - 4) > 0. Step 2: Critical points are x = 2 and x = 4. Step 3: Test intervals: valid for x < 2 or x > 4.
Correct Answer:
A
— x < 2 or x > 4
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Q. Find the solution to the inequality: -3x + 6 > 0.
A.
x < 2
B.
x > 2
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
Step 1: Subtract 6 from both sides: -3x > -6. Step 2: Divide by -3 (reverse the inequality): x < 2.
Correct Answer:
B
— x > 2
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Q. Find the solution to the inequality: 4x + 1 ≥ 2x + 5.
A.
x ≥ 2
B.
x ≤ 2
C.
x ≥ 4
D.
x ≤ 4
Show solution
Solution
Step 1: Subtract 2x from both sides: 2x + 1 ≥ 5. Step 2: Subtract 1: 2x ≥ 4. Step 3: Divide by 2: x ≥ 2.
Correct Answer:
A
— x ≥ 2
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Q. Find the solution to the inequality: 4x - 1 ≤ 3x + 2.
A.
x ≤ 3
B.
x ≤ 1
C.
x ≥ 1
D.
x ≥ 3
Show solution
Solution
Step 1: Subtract 3x from both sides: x - 1 ≤ 2. Step 2: Add 1 to both sides: x ≤ 3.
Correct Answer:
B
— x ≤ 1
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Q. Find the solution to the inequality: 4x - 7 ≤ 9.
A.
x ≤ 4
B.
x ≥ 4
C.
x ≤ 2
D.
x ≥ 2
Show solution
Solution
Step 1: Add 7 to both sides: 4x ≤ 16. Step 2: Divide by 4: x ≤ 4.
Correct Answer:
A
— x ≤ 4
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Q. Find the solution to the inequality: 4x - 7 ≥ 5.
A.
x < 3
B.
x > 3
C.
x ≤ 3
D.
x ≥ 3
Show solution
Solution
Step 1: Add 7 to both sides: 4x ≥ 12. Step 2: Divide by 4: x ≥ 3.
Correct Answer:
D
— x ≥ 3
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Q. Find the solution to the inequality: 5 - 2x > 3.
A.
x < 1
B.
x > 1
C.
x < -1
D.
x > -1
Show solution
Solution
Step 1: Subtract 5 from both sides: -2x > -2. Step 2: Divide by -2 (reverse inequality): x < 1.
Correct Answer:
A
— x < 1
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Q. Find the solution to the inequality: x^2 + 4x < 5.
A.
(-5, 1)
B.
(1, -5)
C.
(1, 5)
D.
(-5, 5)
Show solution
Solution
Step 1: Rearrange: x^2 + 4x - 5 < 0. Step 2: Factor: (x + 5)(x - 1) < 0. Step 3: Test intervals: solution is (-5, 1).
Correct Answer:
A
— (-5, 1)
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Q. Find the solution to the inequality: x^2 - 9 > 0.
A.
(-∞, -3) ∪ (3, ∞)
B.
(-3, 3)
C.
(-3, ∞)
D.
(-∞, 3)
Show solution
Solution
Step 1: Factor the inequality: (x - 3)(x + 3) > 0. Step 2: The critical points are x = -3 and x = 3. Step 3: Test intervals: The solution set is (-∞, -3) ∪ (3, ∞).
Correct Answer:
A
— (-∞, -3) ∪ (3, ∞)
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Q. Find the value of k for which the equation x^2 + kx + 9 = 0 has one real solution.
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Solution
For the equation to have one real solution, the discriminant must be zero: k^2 - 4*1*9 = 0. Thus, k^2 = 36, giving k = ±6. The correct answer is -9.
Correct Answer:
B
— -9
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Q. Find the value of x in the equation 3x^2 + 12x + 12 = 0.
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Solution
Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0. Factoring gives (x + 2)(x + 2) = 0, so x = -2.
Correct Answer:
B
— -4
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