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Practice Class 8 Maths Chapter 2 Linear Equations in One Variable MCQ Questions with Answers based on NCERT syllabus. Learn solving linear equations, transposition method, variables, constants, and algebraic expressions with detailed solutions for CBSE exams.
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Chapter Information
Subject: Mathematics
Class: 8
Chapter: Linear Equations in One Variable
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Linear Equations in One Variable is a fundamental algebra chapter that helps students solve unknown quantities using mathematical operations. It forms the foundation for higher algebra and problem-solving techniques.
What You Will Learn?
✔ Variables and Constants
✔ Linear Equations
✔ Transposition Method
✔ Solving Equations
✔ Verification of Solutions
✔ Algebraic Thinking
✔ Real-Life Applications of Equations
✔ Board Exam Preparation
Why This Topic Is Important?
Linear equations are used in daily-life situations involving age calculations, shopping, budgeting, measurements, and comparisons. Understanding equations improves logical reasoning and analytical thinking.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Solve:
$$x+95=140$$
A) $$43$$
B) $$44$$
C) $$45$$
D) $$46$$
Answer:
$$45$$
Useful Formula for this Question:
If
$$x+a=b$$
then
$$x=b-a$$
Concept Behind This Question:
Students should isolate the variable using subtraction.
Step-by-Step Solution:
Given:
$$x+95=140$$
Subtract $$95$$ from both sides:
$$x=140-95$$
$$x=45$$
Therefore, the correct answer is:
$$45$$
Exam Tip:
Subtract the constant term from both sides to isolate the variable.
Q2. Solve:
$$x-67=-22$$
A) $$43$$
B) $$44$$
C) $$45$$
D) $$46$$
Answer:
$$45$$
Useful Formula for this Question:
If
$$x-a=b$$
then
$$x=b+a$$
Concept Behind This Question:
Students should apply transposition correctly.
Step-by-Step Solution:
Given:
$$x-67=-22$$
Add $$67$$ to both sides:
$$x=-22+67$$
$$x=45$$
Therefore, the correct answer is:
$$45$$
Exam Tip:
Be careful while working with negative numbers.
Q3. Solve:
$$33x=396$$
A) $$10$$
B) $$11$$
C) $$12$$
D) $$13$$
Answer:
$$12$$
Useful Formula for this Question:
If
$$ax=b$$
then
$$x=\frac{b}{a}$$
Concept Behind This Question:
Students should divide both sides by the coefficient.
Step-by-Step Solution:
Given:
$$33x=396$$
Divide both sides by $$33$$
$$x=\frac{396}{33}$$
$$x=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Always divide by the coefficient attached to the variable.
Q4. Solve:
$$\frac{x}{33}=6$$
A) $$196$$
B) $$197$$
C) $$198$$
D) $$199$$
Answer:
$$198$$
Useful Formula for this Question:
If
$$\frac{x}{a}=b$$
then
$$x=ab$$
Concept Behind This Question:
Students should eliminate fractions using multiplication.
Step-by-Step Solution:
Given:
$$\frac{x}{33}=6$$
Multiply both sides by $$33$$
$$x=6\times33$$
$$x=198$$
Therefore, the correct answer is:
$$198$$
Exam Tip:
Multiply both sides by the denominator to remove the fraction.
Q5. Solve:
$$24x+48=240$$
A) $$6$$
B) $$7$$
C) $$8$$
D) $$9$$
Answer:
$$8$$
Useful Formula for this Question:
Solve step-by-step by isolating the variable.
Concept Behind This Question:
Students should remove constants before dividing.
Step-by-Step Solution:
Given:
$$24x+48=240$$
Subtract $$48$$ from both sides:
$$24x=192$$
Divide both sides by $$24$$
$$x=8$$
Therefore, the correct answer is:
$$8$$
Exam Tip:
First remove the constant term, then divide by the coefficient.
Important Formulas & Concepts
1. Linear Equation in One Variable
$$ax+b=0,\quad a\ne0$$
2. Addition Property
If
$$a=b$$
then
$$a+c=b+c$$
3. Subtraction Property
If
$$a=b$$
then
$$a-c=b-c$$
4. Multiplication Property
If
$$a=b$$
then
$$ac=bc$$
5. Division Property
If
$$a=b,\quad c\ne0$$
then
$$\frac{a}{c}=\frac{b}{c}$$
6. Verification Rule
Substitute the obtained value into the original equation to verify the solution.
FAQs
1. What is a linear equation?
A linear equation is an equation whose highest power of the variable is 1.
2. What is a variable?
A variable is a symbol that represents an unknown quantity.
3. What is transposition?
Transposition means moving a term from one side of an equation to the other while changing its sign.
4. Why should we verify the answer?
Verification ensures that the obtained solution satisfies the original equation.
5. Where are linear equations used?
Linear equations are used in age calculations, budgeting, shopping, measurements, and many practical situations.
Common Mistakes
❌ Incorrect sign changes during transposition.
❌ Forgetting to divide by the coefficient.
❌ Arithmetic mistakes.
❌ Not checking the final answer.
❌ Solving equations in the wrong order.
Quick Revision Notes
✔ Linear equations contain variables with power 1.
✔ Use inverse operations to isolate variables.
✔ Change signs carefully during transposition.
✔ Remove constants before dividing.
✔ Verify the final answer.
✔ Practice regularly for better accuracy.
Conclusion
Linear Equations in One Variable is one of the most important chapters in Class 8 Mathematics. A strong understanding of equations helps students solve mathematical problems efficiently and prepares them for advanced algebraic concepts. Regular MCQ practice improves confidence, conceptual understanding, and examination performance.
Related links
- Class 8 Maths Chapter 2 Linear Equations in One Variable – part 10
- Class 8 Maths Chapter 2 Linear Equations in One Variable – Part 9
- Class 8 Maths Chapter 2 Linear Equations in One Variable- Part 8
- Class 8 Maths Chapter 2 Linear Equations in One Variable- Part 7
- Class 8 Maths Chapter 2 Linear Equations in One Variable- Part 6
- Class 8 Maths Chapter 2 Linear Equations in One Variable transposition method- Part 5
- Class 8 Maths Chapter 2 Linear Equations in One Variable – Part 4
- Class8 Maths Chapter2 Transposition method, variables – Part 3
- Class 8 Maths Chapter 1 Rational Numbers- Part 10
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