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. Which of the following distributions is used to model the number of successes in a fixed number of trials?
A.
Normal
B.
Binomial
C.
Poisson
D.
Exponential
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Solution
The binomial distribution models the number of successes in a fixed number of trials.
Correct Answer:
B
— Binomial
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Q. Which of the following inequalities represents the solution to 2x + 3 > 7?
A.
x > 2
B.
x < 2
C.
x > 3
D.
x < 3
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.
Correct Answer:
A
— x > 2
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Q. Which of the following inequalities represents the solution to 3x + 2 > 11?
A.
x > 3
B.
x < 3
C.
x > 4
D.
x < 4
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Solution
Subtracting 2 from both sides gives 3x > 9. Dividing by 3 results in x > 3.
Correct Answer:
C
— x > 4
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Q. Which of the following inequalities represents the solution to x + 4 > 2?
A.
x > -2
B.
x < -2
C.
x > -6
D.
x < -6
Show solution
Solution
Subtract 4 from both sides: x > -2.
Correct Answer:
A
— x > -2
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Q. Which of the following is a composite number? 2, 3, 4, 5
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Solution
4 is a composite number.
Correct Answer:
C
— 4
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Q. Which of the following is a factor of the polynomial x^2 + 4x + 4?
A.
x + 2
B.
x - 2
C.
x + 4
D.
x - 4
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Solution
The polynomial can be factored as (x + 2)(x + 2) or (x + 2)^2. Therefore, x + 2 is a factor.
Correct Answer:
A
— x + 2
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Q. Which of the following is a factor of the polynomial x^2 - 4?
A.
x - 2
B.
x + 2
C.
x^2 + 4
D.
x - 1
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Solution
The polynomial x^2 - 4 can be factored as (x - 2)(x + 2). Therefore, x - 2 is a factor.
Correct Answer:
A
— x - 2
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Q. Which of the following is a factor of the polynomial x^2 - 5x + 6?
A.
(x - 2)
B.
(x - 3)
C.
(x + 2)
D.
(x + 3)
Show solution
Solution
Step 1: Factor the polynomial: (x - 2)(x - 3). Step 2: The factors are (x - 2) and (x - 3).
Correct Answer:
A
— (x - 2)
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Q. Which of the following is a factor of the polynomial x^3 - 3x^2 - 4x + 12?
A.
x - 2
B.
x + 2
C.
x - 3
D.
x + 3
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Solution
Using synthetic division or the factor theorem, we can test x = 2. Substituting gives us 2^3 - 3(2^2) - 4(2) + 12 = 0, confirming that x - 2 is a factor.
Correct Answer:
A
— x - 2
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Q. Which of the following is a factor of the polynomial x^3 - 4x^2 + 4x?
A.
x - 2
B.
x + 2
C.
x
D.
x - 4
Show solution
Solution
We can factor out x from the polynomial: x^3 - 4x^2 + 4x = x(x^2 - 4x + 4) = x(x - 2)^2. Thus, x is a factor.
Correct Answer:
C
— x
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Q. Which of the following is a factor of x^2 - 9?
A.
(x - 3)
B.
(x + 3)
C.
(x - 3)(x + 3)
D.
(x^2 + 9)
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Solution
x^2 - 9 is a difference of squares and can be factored as (x - 3)(x + 3).
Correct Answer:
C
— (x - 3)(x + 3)
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Q. Which of the following is a polynomial?
A.
3x^2 + 2x - 1
B.
1/x + 2
C.
sqrt(x) + 3
D.
ln(x)
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Solution
A polynomial is a sum of terms with non-negative integer exponents. 3x^2 + 2x - 1 fits this definition.
Correct Answer:
A
— 3x^2 + 2x - 1
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Q. Which of the following is a prime number? 4, 5, 6, 8
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Solution
5 is a prime number.
Correct Answer:
B
— 5
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Q. Which of the following is a Pythagorean identity?
A.
sin²x + cos²x = 1
B.
tanx = sinx/cosx
C.
secx = 1/cosx
D.
cscx = 1/sinx
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Solution
The Pythagorean identity is sin²x + cos²x = 1.
Correct Answer:
A
— sin²x + cos²x = 1
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Q. Which of the following is a root of the polynomial x^2 + 3x - 10?
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Solution
Factoring gives (x + 5)(x - 2) = 0. The roots are x = -5 and x = 2, so 2 is a root.
Correct Answer:
B
— 2
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Q. Which of the following is a root of the polynomial x^2 - 4?
A.
-2
B.
0
C.
2
D.
Both -2 and 2
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Solution
Step 1: Factor the polynomial: (x - 2)(x + 2). Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Roots are x = 2 and x = -2.
Correct Answer:
D
— Both -2 and 2
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Q. Which of the following is a root of the polynomial x^2 - 7x + 10?
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Solution
The polynomial can be factored as (x - 2)(x - 5). Setting each factor to zero gives us x = 2 and x = 5, so 2 is a root.
Correct Answer:
B
— 2
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Q. Which of the following is a root of the polynomial x^3 - 6x^2 + 11x - 6?
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Solution
Using the Rational Root Theorem, we can test x = 1, 2, and 3. Testing x = 3 gives 3^3 - 6(3^2) + 11(3) - 6 = 0, so x = 3 is a root.
Correct Answer:
C
— 3
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Q. Which of the following is a solution to the equation 2x^2 - 8 = 0?
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Solution
First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Taking the square root gives x = ±2. Thus, 2 is a solution.
Correct Answer:
B
— 2
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Q. Which of the following is a solution to the equation 3x + 7 = 16?
A.
x = 3
B.
x = 2
C.
x = 1
D.
x = 0
Show solution
Solution
Step 1: Subtract 7 from both sides: 3x = 9. Step 2: Divide both sides by 3: x = 3.
Correct Answer:
B
— x = 2
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Q. Which of the following is a solution to the equation 4x + 1 = 13?
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5
Show solution
Solution
Subtract 1 from both sides: 4x = 12. Then divide by 4: x = 3.
Correct Answer:
A
— x = 2
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Q. Which of the following is a solution to the equation 4x + 1 = 17?
A.
x = 4
B.
x = 3
C.
x = 2
D.
x = 5
Show solution
Solution
Step 1: Subtract 1 from both sides: 4x = 16. Step 2: Divide by 4: x = 4.
Correct Answer:
C
— x = 2
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Q. Which of the following is a solution to the equation 4x - 7 = 5?
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
Show solution
Solution
Add 7 to both sides: 4x = 12. Then divide by 4: x = 3.
Correct Answer:
A
— x = 1
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Q. Which of the following is a solution to the equation x^2 + 2x - 8 = 0?
Show solution
Solution
Factor the equation: (x + 4)(x - 2) = 0. The solutions are x = -4 and x = 2.
Correct Answer:
A
— -4
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Q. Which of the following is a solution to the equation x^2 + 6x + 9 = 0?
A.
x = -3
B.
x = 3
C.
x = 0
D.
x = -6
Show solution
Solution
The equation can be factored as (x + 3)(x + 3) = 0. Thus, the solution is x = -3.
Correct Answer:
A
— x = -3
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Q. Which of the following is a solution to the equation x^2 - 7x + 10 = 0?
Show solution
Solution
Factoring gives (x - 5)(x - 2) = 0, so the solutions are x = 5 and x = 2.
Correct Answer:
C
— 5
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Q. Which of the following is a solution to the inequality 2x + 3 > 7?
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2. The solution includes all values greater than 2.
Correct Answer:
B
— 2
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Q. Which of the following is a solution to the inequality 3x - 4 < 5?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
Add 4 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following is a solution to the inequality 3x - 5 < 4?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
Add 5 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. Which of the following is a solution to the inequality 5x - 7 < 8?
A.
x < 3
B.
x > 3
C.
x < 2
D.
x > 2
Show solution
Solution
Add 7 to both sides: 5x < 15. Divide by 5: x < 3.
Correct Answer:
A
— x < 3
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