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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 one of the most important chapters in Class 8 Mathematics. It helps students learn how to solve equations systematically and develop strong algebraic reasoning skills.
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 many real-life situations involving age, money, distance, measurements, and business calculations. Understanding equations builds a strong foundation for future mathematics.
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:
$$x+71=116$$
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:
$$x+71=116$$
Subtract $$71$$ from both sides:
$$x=116-71$$
$$x=45$$
Therefore, the correct answer is:
$$45$$
Exam Tip:
Subtract the constant term from both sides.
Q2. Solve:
$$x-52=-7$$
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:
$$x-52=-7$$
Add $$52$$ to both sides:
$$x=-7+52$$
$$x=45$$
Therefore, the correct answer is:
$$45$$
Exam Tip:
Be careful while adding positive and negative numbers.
Q3. Solve:
$$27x=324$$
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:
$$27x=324$$
Divide both sides by $$27$$
$$x=\frac{324}{27}$$
$$x=12$$
Therefore, the correct answer is:
$$12$$
Exam Tip:
Always divide by the coefficient attached to the variable.
Q4. Solve:
$$\frac{x}{27}=6$$
A) $$160$$
B) $$161$$
C) $$162$$
D) $$163$$
Answer:
$$162$$
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:
$$\frac{x}{27}=6$$
Multiply both sides by $$27$$
$$x=6\times27$$
$$x=162$$
Therefore, the correct answer is:
$$162$$
Exam Tip:
Multiply both sides by the denominator to remove the fraction.
Q5. Solve:
$$20x+40=200$$
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:
$$20x+40=200$$
Subtract $$40$$ from both sides:
$$20x=160$$
Divide both sides by $$20$$
$$x=8$$
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 representing 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 is verification important?
Verification ensures that the obtained solution satisfies the original equation.
5. Are linear equations useful in daily life?
Yes, they are used in age calculations, shopping, budgeting, measurements, and many real-world situations.
Common Mistakes
❌ Incorrect sign changes during transposition.
❌ Forgetting to divide by the coefficient.
❌ Arithmetic calculation mistakes.
❌ Not verifying the answer.
❌ Solving operations 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.
✔ Regular practice improves speed and accuracy.
Conclusion
Linear Equations in One Variable is a crucial chapter in Class 8 Mathematics. Understanding equations helps students solve mathematical problems efficiently and prepares them for higher 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 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 2 Linear Equations in One Variable MCQ – Part 2
- Class8 Maths Chapter2 Linear Equations in One Variable MCQ – Part 1
- Class 8 Maths Chapter 1 Rational Numbers- Part 10
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