Welcome To My School Study
Practice Class 10 Maths MCQ Questions with Answers based on NCERT concepts. Revise polynomial degree, zeroes of linear polynomials, HCF, LCM and solutions of equations involving parallel lines with exam-focused explanations.
Solutions
Chapter Information
Subject: Mathematics
Class: 10
Topics: Polynomials, Number System & Pair of Linear Equations
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Easy to Moderate
Based On: NCERT Concepts
Introduction
Mathematics becomes easier when fundamental concepts are clear. Topics such as polynomial degree, zeroes, HCF, LCM, and linear equations form an important foundation for solving higher-level mathematical problems.
This practice set contains five concept-based MCQs designed to help students revise these topics and prepare for school examinations.
What You Will Learn
✔ Degree of a polynomial
✔ LCM of two numbers
✔ Zeroes of a linear polynomial
✔ HCF of two numbers
✔ Solutions of equations representing parallel lines
Why This Topic Is Important?
These concepts are frequently used in mathematical calculations and provide the foundation for several topics studied in higher classes. Regular MCQ practice helps students identify concepts quickly and avoid common calculation mistakes.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. The degree of the polynomial $$5x^4+2x^2+1$$ is:
A) $$4$$
B) $$2$$
C) $$5$$
D) $$3$$
Answer
$$4$$
Concept
The degree of a polynomial is the highest power of the variable having a non-zero coefficient.
In:
$$5x^4+2x^2+1$$
the powers of $$x$$ are:
$$4,\ 2,\ 0$$
The highest power is:
$$4$$
Therefore, the degree of the polynomial is:
$$\boxed{4}$$
Exam Focus
Always identify the highest power of the variable to determine the degree of a polynomial.
Q2. What is the LCM of $$4$$ and $$6$$?
A) $$6$$
B) $$12$$
C) $$24$$
D) $$10$$
Answer
$$12$$
Concept
LCM means Least Common Multiple. It is the smallest positive number that is exactly divisible by both given numbers.
Multiples of $$4$$ include:
$$4,\ 8,\ 12,\ 16,\ldots$$
Multiples of $$6$$ include:
$$6,\ 12,\ 18,\ldots$$
The smallest common multiple is:
$$\boxed{12}$$
Exam Focus
LCM is the smallest common multiple of the given numbers.
Q3. The number of zeroes of a linear polynomial is:
A) $$0$$
B) $$1$$
C) $$2$$
D) Infinite
Answer
$$1$$
Concept
A linear polynomial has degree $$1$$. A polynomial of degree $$1$$ has exactly one zero.
For example, consider:
$$ax+b$$
where $$a\neq0$$.
Its zero is obtained by putting:
$$ax+b=0$$
Therefore, a linear polynomial has:
$$\boxed{1}$$
zero.
Exam Focus
Remember the basic relationship:
$$\text{Degree of a linear polynomial}=1$$
and therefore it has one zero.
Q4. What is the HCF of $$12$$ and $$18$$?
A) $$9$$
B) $$6$$
C) $$2$$
D) $$3$$
Answer
$$6$$
Concept
HCF means Highest Common Factor. It is the greatest number that divides both given numbers exactly.
Factors of $$12$$ are:
$$1,\ 2,\ 3,\ 4,\ 6,\ 12$$
Factors of $$18$$ are:
$$1,\ 2,\ 3,\ 6,\ 9,\ 18$$
The greatest common factor is:
$$\boxed{6}$$
Exam Focus
HCF is the greatest common factor shared by the given numbers.
Q5. Two parallel lines have:
A) Infinite solutions
B) Two solutions
C) One solution
D) No solution
Answer
No solution
Concept
When two linear equations represent distinct parallel lines, the lines never intersect.
A solution of a pair of linear equations represents the point where their graphs intersect. Since distinct parallel lines do not meet, there is no common solution.
Therefore:
$$\boxed{\text{No solution}}$$
Exam Focus
Remember:
$$\text{Intersecting lines}\rightarrow\text{One solution}$$
$$\text{Parallel lines}\rightarrow\text{No solution}$$
$$\text{Coincident lines}\rightarrow\text{Infinitely many solutions}$$
Important Formulas & Concepts
1. Degree of a Polynomial
The degree is the highest power of the variable with a non-zero coefficient.
For example:
$$5x^4+2x^2+1$$
Degree:
$$4$$
2. LCM
LCM is the smallest positive common multiple of two or more numbers.
3. HCF
HCF is the greatest common factor of two or more numbers.
4. Zero of a Linear Polynomial
A linear polynomial has exactly one zero.
5. Pair of Linear Equations
For two distinct parallel lines:
$$\text{No solution}$$
For intersecting lines:
$$\text{One solution}$$
For coincident lines:
$$\text{Infinitely many solutions}$$
Related Practice Questions
- Find the degree of:
$$7x^5+3x^2+4$$
- Find the LCM of $$8$$ and $$12$$.
- How many zeroes does a linear polynomial have?
- Find the HCF of $$24$$ and $$36$$.
- What type of solution is obtained when two distinct lines intersect?
Mini Quiz Challenge
Fill in the blanks:
- The degree of $$3x^6+2x+1$$ is ______.
- The LCM of $$5$$ and $$10$$ is ______.
- A linear polynomial has ______ zero.
- The HCF of $$8$$ and $$12$$ is ______.
- Two distinct parallel lines have ______ solution.
Exam Tips
✔ For the degree of a polynomial, look for the highest power.
✔ Do not confuse HCF with LCM.
✔ A linear polynomial has exactly one zero.
✔ Distinct parallel lines never intersect.
✔ Revise the difference between intersecting, parallel and coincident lines.
Quick Revision Notes
✔ Degree of $$5x^4+2x^2+1$$ is $$4$$.
✔ LCM of $$4$$ and $$6$$ is $$12$$.
✔ A linear polynomial has exactly one zero.
✔ HCF of $$12$$ and $$18$$ is $$6$$.
✔ Two distinct parallel lines have no solution.
Common Mistakes Students Make
❌ Choosing the coefficient instead of the highest power as the degree.
❌ Confusing HCF with LCM.
❌ Thinking that a linear polynomial can have two zeroes.
❌ Assuming that parallel lines intersect at some point.
❌ Forgetting the difference between parallel and coincident lines.
Key Takeaways
- The highest power determines the degree of a polynomial.
- LCM is the smallest common multiple.
- HCF is the greatest common factor.
- A linear polynomial has exactly one zero.
- Two distinct parallel lines have no common solution.
FAQs
1. What is the degree of $$5x^4+2x^2+1$$?
The degree is:
$$4$$
2. What is the LCM of $$4$$ and $$6$$?
The LCM is:
$$12$$
3. How many zeroes does a linear polynomial have?
A linear polynomial has exactly one zero.
4. What is the HCF of $$12$$ and $$18$$?
The HCF is:
$$6$$
5. How many solutions do two distinct parallel lines have?
They have:
$$\text{No solution}$$
Conclusion
Understanding basic polynomial concepts, HCF, LCM and the graphical interpretation of linear equations helps students build a strong mathematical foundation. Practising concept-based MCQs regularly can improve speed, accuracy and confidence during examinations.
NCERT Reference
Book: NCERT Mathematics – Class 10
Relevant Concepts: Polynomials, Real Numbers, and Pair of Linear Equations in Two Variables
Based On: NCERT concepts and Class 10 Mathematics curriculum.
Related links
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-14
- Class 10 Science Chapter 1 Chemical Reactions and Equations
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-13
- Class 10 Social Science Chapter 1 The Rise of Nationalism
- Class 10 Science Chapter 1 Chemical Reactions and Equations
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-12
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-11
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-10
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-9
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-8
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-7
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables part-6
Latest Post
- Class 9 Maths Chapter 4 Linear Equations in Two Variables
- Class 7 Maths Chapter 4 Simple Equations
- Class 8 Maths Chapter 4 Practical Geometry
- Class 10 Maths Chapter 4 Quadratic Equations
- Class 9 Science Chapter 1 Matter in Our Surroundings
Join Our Other Communities
Instagram , Youtube , Facebook
