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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn degree of polynomial, zero polynomial, linear polynomial, quadratic polynomial, cubic polynomial, and polynomial identification with detailed solutions and exam tips for CBSE board exams.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
Polynomials are among the most important algebraic expressions studied in Class 10 Mathematics. They help students understand mathematical relationships, equations, and graphs. Before learning about the zeroes of polynomials, students must be comfortable identifying different types of polynomials and determining their degrees. This practice set focuses on strengthening these foundational concepts through carefully designed MCQs, detailed explanations, and useful exam tips.
What You Will Learn?
✔ Degree of a Polynomial
✔ Zero Polynomial
✔ Constant Polynomial
✔ Linear Polynomial
✔ Quadratic Polynomial
✔ Cubic Polynomial
✔ Polynomial Identification
Why This Topic Is Important?
A strong understanding of polynomial basics makes it easier to learn advanced concepts such as zeroes of polynomials, factorization, and polynomial graphs. These concepts are frequently tested in school and board examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which of the following is a linear polynomial?
A) $$4x^2+3$$
B) $$7x-5$$
C) $$x^3+1$$
D) $$9$$
Answer:
$$7x-5$$
Useful Formula for this Question:
A linear polynomial has degree:
$$1$$
Concept Behind This Question:
Polynomials are classified according to their highest power.
Solution:
The highest power of $$x$$ in:
$$7x-5$$
is:
$$1$$
Therefore, it is a linear polynomial.
Hence, the correct answer is:
$$7x-5$$
Exam Tip:
If the highest exponent is $$1$$, the polynomial is linear.
————————————————–
Q2. What is the degree of the polynomial:
$$9x^4-2x^3+7x-1$$
A) $$2$$
B) $$3$$
C) $$4$$
D) $$9$$
Answer:
$$4$$
Useful Formula for this Question:
Degree of a polynomial = Highest power of the variable.
Concept Behind This Question:
The degree is determined only by the exponent, not by the coefficient.
Solution:
The powers of $$x$$ are:
$$4,\ 3,\ 1,\ 0$$
The highest power is:
$$4$$
Therefore, the degree of the polynomial is:
$$4$$
Hence, the correct answer is:
$$4$$
Exam Tip:
Never confuse the coefficient with the degree of a polynomial.
————————————————–
Q3. Which of the following is a zero polynomial?
A) $$1$$
B) $$x$$
C) $$x+1$$
D) $$0$$
Answer:
$$0$$
Useful Formula for this Question:
A polynomial whose every coefficient is zero is called a zero polynomial.
Concept Behind This Question:
The zero polynomial is a special polynomial and is treated differently from constant polynomials.
Solution:
The expression:
$$0$$
contains only the coefficient zero.
Therefore, it is called the zero polynomial.
Hence, the correct answer is:
$$0$$
Exam Tip:
Remember that the degree of the zero polynomial is not defined.
————————————————–
Q4. Which of the following is NOT a polynomial?
A) $$5x^3-2x+1$$
B) $$x^2+7$$
C) $$\frac{3}{x}+2$$
D) $$8x-1$$
Answer:
$$\frac{3}{x}+2$$
Useful Formula for this Question:
Variables cannot appear in the denominator of a polynomial.
Concept Behind This Question:
A polynomial can only contain non-negative integer powers of variables.
Solution:
$$\frac{3}{x}=3x^{-1}$$
The exponent:
$$-1$$
is negative.
Therefore, the expression is not a polynomial.
Hence, the correct answer is:
$$\frac{3}{x}+2$$
Exam Tip:
If a variable appears in the denominator, the expression is not a polynomial.
————————————————–
Q5. Which of the following is a quadratic polynomial?
A) $$x^2-9$$
B) $$x^3-9$$
C) $$4x+5$$
D) $$12$$
Answer:
$$x^2-9$$
Useful Formula for this Question:
A quadratic polynomial has degree:
$$2$$
Concept Behind This Question:
Quadratic polynomials are among the most important polynomials because they are widely used in algebra and graph-related problems.
Solution:
The highest power of $$x$$ in:
$$x^2-9$$
is:
$$2$$
Therefore, it is a quadratic polynomial.
Hence, the correct answer is:
$$x^2-9$$
Exam Tip:
A polynomial with highest exponent $$2$$ is always quadratic.
————————————————–
Important Formulas and Concepts
Degree of Polynomial:
Highest power of the variable.
Zero Polynomial:
$$0$$
Constant Polynomial:
Degree $$0$$
Linear Polynomial:
Degree $$1$$
Quadratic Polynomial:
Degree $$2$$
Cubic Polynomial:
Degree $$3$$
————————————————–
FAQs
Q. What is a zero polynomial?
Answer:
A polynomial whose every coefficient is zero is called a zero polynomial.
Q. Is the zero polynomial a constant polynomial?
Answer:
It is a special polynomial and its degree is not defined.
Q. Can a polynomial have a variable in the denominator?
Answer:
No. Such an expression is not a polynomial.
————————————————–
Common Mistakes Students Make
❌ Treating the zero polynomial as a linear polynomial.
❌ Forgetting that the degree of the zero polynomial is not defined.
❌ Confusing coefficients with exponents.
❌ Considering expressions with variables in the denominator as polynomials.
————————————————–
Quick Revision Notes
✔ Degree = Highest exponent of the variable.
✔ Linear polynomial → Degree $$1$$
✔ Quadratic polynomial → Degree $$2$$
✔ Cubic polynomial → Degree $$3$$
✔ Variable in denominator → Not a polynomial.
✔ Degree of zero polynomial is not defined.
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students build a strong understanding of polynomial classification, degree, and identification. Mastering these basic concepts is essential before learning about the zeroes and graphs of polynomials.
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