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Algebra MCQ & Objective Questions

Algebra is a fundamental branch of mathematics that plays a crucial role in various school and competitive exams. Mastering algebraic concepts not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions is essential for reinforcing your understanding and identifying important questions that frequently appear in exams.

What You Will Practise Here

Basic algebraic operations and their properties
Linear equations and inequalities
Quadratic equations and their solutions
Polynomials and their applications
Functions and their graphs
Exponents and logarithms
Word problems involving algebraic expressions

Exam Relevance

Algebra is a significant topic in the CBSE curriculum and is also relevant for State Boards, NEET, and JEE exams. Students can expect questions that test their understanding of algebraic concepts through various formats, including multiple-choice questions, fill-in-the-blanks, and problem-solving scenarios. Common question patterns include solving equations, simplifying expressions, and applying algebra to real-life situations.

Common Mistakes Students Make

Misinterpreting word problems and failing to translate them into algebraic equations
Overlooking signs when solving equations, leading to incorrect answers
Confusing the properties of exponents and logarithms
Neglecting to check their solutions, resulting in errors
Rushing through calculations without verifying each step

FAQs

Question: What are some effective ways to prepare for Algebra MCQs?
Answer: Regular practice with a variety of MCQs, reviewing key concepts, and understanding common mistakes can greatly enhance your preparation.

Question: How can I improve my speed in solving Algebra objective questions?
Answer: Time yourself while practicing and focus on solving simpler problems quickly to build confidence and speed.

Don't wait any longer! Start solving practice MCQs today to test your understanding of algebra and prepare effectively for your exams. Your success in mastering algebra is just a few practice questions away!

Arithmetic Progression (AP) Exponents Functions & Graphs Geometric Progression (GP) Harmonic Progression (HP) Inequalities Linear Equations Logarithms Polynomials Quadratic Equations

Q. A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?

A. 5
B. 6
C. 4
D. 7

Solution

The last term of an AP is given by a + (n-1)d. Here, 100 = 10 + (20-1)d. Solving gives d = 5.

Correct Answer: A — 5

Q. A certain arithmetic progression has a first term of 12 and a last term of 48. If there are 10 terms in total, what is the common difference?

A. 4
B. 3
C. 5
D. 6

Solution

The common difference d can be calculated using the formula for the nth term: a + (n-1)d = last term. Here, 12 + 9d = 48, solving gives d = 4.

Correct Answer: A — 4

Q. A certain arithmetic progression has a first term of 7 and a common difference of 2. What is the sum of the first 10 terms?

A. 70
B. 75
C. 80
D. 85

Solution

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_10 = 10/2 * (2*7 + 9*2) = 5 * (14 + 18) = 5 * 32 = 160.

Correct Answer: B — 75

Q. A sequence is defined as 2, 5, 8, 11, ... What is the 15th term of this sequence?

A. 44
B. 41
C. 38
D. 45

Solution

The nth term is given by a + (n-1)d. Here, a = 2, d = 3, and n = 15. So, the 15th term = 2 + (15-1) * 3 = 2 + 42 = 44.

Correct Answer: B — 41

Q. A sequence is defined as follows: 2, 5, 8, 11, ... What is the 15th term of this sequence?

A. 44
B. 41
C. 38
D. 45

Solution

The first term a = 2 and the common difference d = 3. The 15th term = a + (15-1)d = 2 + 42 = 44.

Correct Answer: B — 41

Q. A sequence of numbers is in arithmetic progression. If the first term is 12 and the last term is 48, and there are 8 terms in total, what is the common difference?

A. 4
B. 5
C. 6
D. 3

Solution

The common difference d can be found using the formula for the nth term. The last term is given by a + (n-1)d. Here, 48 = 12 + (8-1)d, solving gives d = 4.

Correct Answer: A — 4

Q. A sequence of numbers is in arithmetic progression. If the first term is 8 and the last term is 32, and there are 6 terms, what is the common difference?

A. 4
B. 5
C. 6
D. 3

Solution

Using the formula for the last term: a + (n-1)d = last term, we have 8 + 5d = 32. Solving gives d = 4.

Correct Answer: A — 4

Q. According to the passage, what is one major consequence of ignoring social inequalities? (2023)

A. Increased economic growth.
B. Social unrest and instability.
C. Improved community relations.
D. Greater individual success.

Solution

The passage warns that neglecting social inequalities can lead to social unrest and instability, highlighting the urgency of addressing these issues.

Correct Answer: B — Social unrest and instability.

Q. According to the passage, what is the significance of the vertex in a quadratic function?

A. It represents the function's maximum or minimum value.
B. It is the point where the function crosses the y-axis.
C. It indicates the function's slope.
D. It is the point of discontinuity.

Solution

The vertex of a quadratic function is crucial as it represents the maximum or minimum point of the graph.

Correct Answer: A — It represents the function's maximum or minimum value.

Q. According to the passage, which of the following is a common misconception about inequality?

A. It is only an economic issue.
B. It affects everyone equally.
C. It can be easily solved.
D. It is a global issue.

Solution

The passage clarifies that inequality is multifaceted and not limited to economic factors.

Correct Answer: A — It is only an economic issue.

Q. According to the passage, which of the following is a common misconception about inequalities?

A. Inequalities are only a recent phenomenon.
B. Inequalities affect only certain demographics.
C. Inequalities can be easily measured.
D. Inequalities are always visible.

Solution

The passage suggests that many believe inequalities are a recent issue, which is a misconception.

Correct Answer: A — Inequalities are only a recent phenomenon.

Q. According to the passage, which of the following is a significant barrier to achieving equality?

A. Lack of awareness about inequalities.
B. Cultural differences among communities.
C. Resistance to change from those in power.
D. Insufficient funding for education.

Solution

The passage highlights resistance from those in power as a major barrier to achieving equality.

Correct Answer: C — Resistance to change from those in power.

Q. Based on the passage, which of the following actions is least likely to reduce social inequalities? (2023)

A. Implementing progressive taxation.
B. Enhancing access to quality education.
C. Promoting economic growth without regulation.
D. Increasing social welfare programs.

Solution

Promoting economic growth without regulation is least likely to address social inequalities, as it may lead to greater disparities.

Correct Answer: C — Promoting economic growth without regulation.

Q. Based on the passage, which of the following is a potential consequence of ignoring social inequalities?

A. Increased social cohesion.
B. Worsening economic conditions.
C. Greater access to education for all.
D. Enhanced community engagement.

Solution

Ignoring social inequalities can lead to worsening economic conditions, as highlighted in the passage.

Correct Answer: B — Worsening economic conditions.

Q. Based on the passage, which of the following is NOT a factor contributing to social inequalities?

A. Economic status.
B. Access to education.
C. Cultural background.
D. Personal choice.

Solution

The passage discusses systemic factors rather than individual choices as contributors to social inequalities.

Correct Answer: D — Personal choice.

Q. Based on the passage, which of the following is NOT a reason given for the persistence of inequalities?

A. Historical injustices
B. Lack of education
C. Government negligence
D. Cultural beliefs

Solution

The passage does not mention government negligence as a reason for the persistence of inequalities.

Correct Answer: C — Government negligence

Q. Based on the passage, which of the following is NOT a suggested method for addressing inequalities?

A. Implementing progressive taxation.
B. Increasing access to quality education.
C. Promoting economic growth without regulation.
D. Enhancing social welfare programs.

Solution

The passage does not support the idea of promoting unregulated economic growth as a method to address inequalities.

Correct Answer: C — Promoting economic growth without regulation.

Q. Based on the passage, which of the following is NOT a suggested solution to combat inequalities? (2023)

A. Implementing progressive taxation.
B. Enhancing access to education.
C. Promoting free market policies.
D. Increasing minimum wage.

Solution

The passage does not advocate for free market policies as a solution to inequalities.

Correct Answer: C — Promoting free market policies.

Q. Based on the passage, which of the following statements about the graph of a quadratic function is true?

A. It can have at most one x-intercept.
B. It is always increasing.
C. It is a parabola that opens upwards or downwards.
D. It has no maximum or minimum points.

Solution

A quadratic function is represented by a parabola, which can open upwards or downwards depending on the coefficient of the squared term.

Correct Answer: C — It is a parabola that opens upwards or downwards.

Q. Identify the term that does not belong in the context of harmonic progression.

A. Reciprocal
B. Arithmetic progression
C. Geometric progression
D. Sequence

Solution

Geometric progression does not relate to harmonic progression, as harmonic progression is defined through the reciprocals of an arithmetic progression.

Correct Answer: C — Geometric progression

Q. Identify the term that does not belong to the harmonic progression: 1/2, 1/3, 1/4, 1/5, 1/6.

A. 1/2
B. 1/3
C. 1/4
D. 1/5

Solution

The terms 1/2, 1/3, 1/4, and 1/5 are in harmonic progression, but 1/6 does not fit as its reciprocal does not maintain the arithmetic progression.

Correct Answer: C — 1/4

Q. If 10^(x) = 1000, what is the value of x? (2023)

A. 2
B. 3
C. 4
D. 1

Solution

Since 1000 can be expressed as 10^3, we have 10^x = 10^3, thus x = 3.

Correct Answer: B — 3

Q. If 10^(x+1) = 1000, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

1000 can be expressed as 10^3, so x + 1 = 3, leading to x = 2.

Correct Answer: B — 2

Q. If 10^(x+2) = 1000, what is the value of x? (2023)

A. 1
B. 2
C. 3
D. 0

Solution

Since 1000 can be expressed as 10^3, we have 10^(x+2) = 10^3, thus x + 2 = 3, leading to x = 1.

Correct Answer: A — 1

Q. If 2^(x+3) = 32, what is the value of x?

A. 1
B. 2
C. 3
D. 5

Solution

Since 32 can be expressed as 2^5, we have 2^(x+3) = 2^5, thus x + 3 = 5, leading to x = 2.

Correct Answer: C — 3

Q. If 4^(x-1) = 1/16, what is the value of x? (2023)

A. 0
B. 1
C. 2
D. 3

Solution

Since 1/16 can be expressed as 4^(-2), we have 4^(x-1) = 4^(-2), thus x - 1 = -2, leading to x = -1.

Correct Answer: C — 2

Q. If 4^(x-1) = 64, what is the value of x?

A. 3
B. 4
C. 5
D. 6

Solution

Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.

Correct Answer: B — 4

Q. If 7^(2x) = 49, what is the value of x? (2023)

A. 0
B. 1
C. 2
D. 3

Solution

Since 49 can be expressed as 7^2, we have 7^(2x) = 7^2, thus 2x = 2, leading to x = 1.

Correct Answer: B — 1

Q. If 7^(x) = 1/49, what is the value of x? (2023)

A. -2
B. 2
C. 0
D. -1

Solution

Since 1/49 can be expressed as 7^(-2), we have 7^x = 7^(-2), thus x = -2.

Correct Answer: A — -2

Q. If a = 2 and b = 3, what is the value of 2a + 3b?

A. 12
B. 11
C. 10
D. 9

Solution

Substituting the values gives 2(2) + 3(3) = 4 + 9 = 13.

Correct Answer: A — 12

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