Algebra MCQ & Objective Questions
Algebra is a crucial branch of mathematics that forms the foundation for many concepts in higher studies and competitive exams. Mastering algebraic concepts not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions in algebra is essential for students aiming to score better in their school and competitive exams. These practice questions help identify important topics and improve understanding, making them an integral part of exam preparation.
What You Will Practise Here
Basic Algebraic Operations
Linear Equations and Inequalities
Quadratic Equations and Their Solutions
Polynomials and Factorization Techniques
Functions and Graphs
Exponents and Radicals
Word Problems Involving Algebraic Concepts
Exam Relevance
Algebra is a significant topic in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions related to algebraic expressions, equations, and functions. Common question patterns include solving equations, simplifying expressions, and applying algebraic concepts to real-life problems. Understanding these patterns is vital for effective exam preparation and achieving high scores.
Common Mistakes Students Make
Misinterpreting the signs in equations, leading to incorrect solutions.
Overlooking the importance of proper factorization techniques.
Confusing the properties of exponents and their applications.
Failing to apply algebraic concepts to word problems accurately.
FAQs
Question: What are some effective ways to prepare for algebra MCQs?Answer: Regular practice of MCQs, reviewing key concepts, and solving previous years' question papers can significantly enhance your preparation.
Question: How can I improve my speed in solving algebraic problems?Answer: Time yourself while practicing and focus on understanding shortcuts and efficient methods for solving equations.
Start your journey towards mastering algebra today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Remember, consistent practice is the key to success!
Q. What is the result of (x - 1)(x + 1) when x = 3?
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Solution
Substituting x = 3, we get (3 - 1)(3 + 1) = 2 * 4 = 8.
Correct Answer:
C
— 6
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Q. What is the result of (x - 4)(x + 4)?
A.
x² - 16
B.
x² + 16
C.
x² - 8
D.
x² + 8
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Solution
(x - 4)(x + 4) = x² - 16 using the difference of squares.
Correct Answer:
A
— x² - 16
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Q. What is the solution to the equation 3(x + 2) = 21?
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Solution
Divide both sides by 3: x + 2 = 7. Then subtract 2: x = 5.
Correct Answer:
C
— 7
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Q. What is the value of (2x + 3)(2x - 3) when x = 2?
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Solution
Substituting x = 2, we get (2*2 + 3)(2*2 - 3) = (4 + 3)(4 - 3) = 7 * 1 = 7.
Correct Answer:
C
— 9
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Q. What is the value of (3x + 2)(3x - 2) when x = 1?
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Solution
(3(1) + 2)(3(1) - 2) = (3 + 2)(3 - 2) = 5 * 1 = 5.
Correct Answer:
D
— 9
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Q. What is the value of (3x + 2)(3x - 2)?
A.
9x^2 - 4
B.
9x^2 + 4
C.
6x^2 - 4
D.
6x^2 + 4
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Solution
Using the difference of squares identity, (3x + 2)(3x - 2) = (3x)^2 - (2)^2 = 9x^2 - 4.
Correct Answer:
A
— 9x^2 - 4
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Q. What is the value of (3x + 2)²?
A.
9x² + 12x + 4
B.
9x² + 6x + 4
C.
6x² + 12x + 4
D.
3x² + 6x + 4
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Solution
(3x + 2)² = 9x² + 12x + 4.
Correct Answer:
A
— 9x² + 12x + 4
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Q. What is the value of (3x - 2)² when x = 1?
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Solution
(3x - 2)² = (3(1) - 2)² = (3 - 2)² = 1² = 1
Correct Answer:
B
— 4
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Q. What is the value of (3x - 4)²?
A.
9x² - 24x + 16
B.
9x² + 24x + 16
C.
9x² - 16
D.
9x² - 12x + 16
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Solution
(3x - 4)² = 9x² - 24x + 16 using the square of a binomial formula.
Correct Answer:
A
— 9x² - 24x + 16
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Q. What is the value of (a - 2)(a + 2)?
A.
a² - 4
B.
a² + 4
C.
a² - 2
D.
a² + 2
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Solution
(a - 2)(a + 2) = a² - 4, which is a difference of squares.
Correct Answer:
A
— a² - 4
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Q. What is the value of (x + 1)^2 - (x - 1)^2?
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Solution
Using the difference of squares identity, (a + b)^2 - (a - b)^2 = 4b, we have (x + 1)^2 - (x - 1)^2 = 4(1) = 4.
Correct Answer:
A
— 4
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Q. What is the value of (x + 2)^2?
A.
x^2 + 4
B.
x^2 + 4x + 4
C.
x^2 + 2
D.
x^2 + 2x + 2
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Solution
Using the square of a binomial identity, (a + b)^2 = a^2 + 2ab + b^2, we have (x + 2)^2 = x^2 + 2(2)x + 2^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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Q. What is the value of (x + 3)(x - 3) when x = 4?
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Solution
Substituting x = 4, we get (4 + 3)(4 - 3) = 7 * 1 = 7.
Correct Answer:
D
— 25
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Q. What is the value of (x + 3)² when x = 2?
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Solution
(2 + 3)² = 5² = 25
Correct Answer:
A
— 25
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Q. What is the value of (x + 3)²?
A.
x² + 6x + 9
B.
x² + 9
C.
x² + 3
D.
x² + 3x + 3
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Solution
(x + 3)² = x² + 2*3*x + 3² = x² + 6x + 9
Correct Answer:
A
— x² + 6x + 9
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Q. What is the value of x in the equation 3(x + 4) = 21?
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Solution
Divide both sides by 3: x + 4 = 7. Subtract 4: x = 3.
Correct Answer:
C
— 7
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Q. What is the value of x in the equation 5x + 2 = 17? (2023)
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Solution
5x + 2 = 17 => 5x = 15 => x = 3.
Correct Answer:
B
— 3
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Q. What is the value of x in the equation 7x - 4 = 3x + 12?
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Solution
Subtract 3x from both sides: 4x - 4 = 12. Add 4: 4x = 16. Divide by 4: x = 4.
Correct Answer:
B
— 3
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Q. What is the value of y in the equation 9y - 5 = 22? (2023)
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Solution
9y - 5 = 22 => 9y = 27 => y = 3.
Correct Answer:
B
— 3
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Q. Which of the following inequalities is equivalent to 3x - 5 > 1?
A.
x > 2
B.
x < 2
C.
x > 1
D.
x < 1
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Solution
Adding 5 to both sides gives 3x > 6, and dividing by 3 gives x > 2.
Correct Answer:
A
— x > 2
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Q. Which of the following inequalities is equivalent to 5 - 2x > 1?
A.
2x < 4
B.
2x > 4
C.
x < 2
D.
x > 2
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Solution
Rearranging gives 5 - 1 > 2x, thus 4 > 2x or 2x < 4.
Correct Answer:
A
— 2x < 4
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Q. Which of the following inequalities is equivalent to x/3 + 2 < 5?
A.
x < 9
B.
x > 9
C.
x < 6
D.
x > 6
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Solution
x/3 < 3 => x < 9.
Correct Answer:
A
— x < 9
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Q. Which of the following is NOT a solution to the inequality 2x - 3 ≤ 5?
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Solution
Solving gives 2x ≤ 8, thus x ≤ 4. The value 4 is not a solution.
Correct Answer:
D
— 4
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Q. Which of the following is NOT a solution to the inequality 4x - 1 < 3?
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Solution
4x < 4 => x < 1. Therefore, 2 is not a solution.
Correct Answer:
C
— 2
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Q. Which of the following is the correct factorization of x^2 + 10x + 21?
A.
(x + 3)(x + 7)
B.
(x + 1)(x + 21)
C.
(x + 2)(x + 10)
D.
(x + 5)(x + 5)
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Solution
To factor x^2 + 10x + 21, we look for two numbers that multiply to 21 and add to 10, which are 3 and 7. Thus, it factors to (x + 3)(x + 7).
Correct Answer:
A
— (x + 3)(x + 7)
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Q. Which of the following is the correct factorization of x² + 10x + 25?
A.
(x + 5)²
B.
(x + 10)(x + 5)
C.
(x - 5)(x + 5)
D.
(x + 25)(x + 1)
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Solution
x² + 10x + 25 = (x + 5)².
Correct Answer:
A
— (x + 5)²
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Q. Which of the following is the correct factorization of x² + 6x + 9?
A.
(x + 3)²
B.
(x + 2)(x + 4)
C.
(x + 1)(x + 8)
D.
(x + 3)(x + 3)
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Solution
x² + 6x + 9 is a perfect square trinomial, which factors to (x + 3)².
Correct Answer:
A
— (x + 3)²
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Q. Which of the following is the correct factorization of x² - 16?
A.
(x - 4)(x + 4)
B.
(x - 8)(x + 2)
C.
(x + 8)(x - 2)
D.
(x - 2)(x + 2)
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Solution
x² - 16 = (x - 4)(x + 4) (Difference of squares)
Correct Answer:
A
— (x - 4)(x + 4)
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Q. Which of the following is the correct factorization of x² - 9x + 20?
A.
(x - 4)(x - 5)
B.
(x + 4)(x + 5)
C.
(x - 2)(x - 10)
D.
(x - 5)(x + 4)
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Solution
x² - 9x + 20 = (x - 4)(x - 5) by finding two numbers that multiply to 20 and add to -9.
Correct Answer:
A
— (x - 4)(x - 5)
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Q. Which of the following is the expanded form of (2x + 5)(3x - 4)?
A.
6x^2 + 7x - 20
B.
6x^2 - 8x + 15
C.
6x^2 + 15x - 8
D.
6x^2 + 10x - 20
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Solution
Expanding using the distributive property: (2x)(3x) + (2x)(-4) + (5)(3x) + (5)(-4) = 6x^2 - 8x + 15.
Correct Answer:
A
— 6x^2 + 7x - 20
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