Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 9 Mathematics 2. Polynomials to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 9 Mathematics 2. Polynomials to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 2.1. Whether you are studying for board exams or mid-term exams, 9 Mathematics Chapter 2. Polynomials solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsExercise 2.1
Q1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii)3√t + t√2
(iv) y +2/y
(v) x10 + y3 + t50
Solution:
(i) 4x2 – 3x + 7
It is polynomial in one variable. Because the power of variable is natural number.
(ii) y2 + √2
It is polynomial in one variable. Because the power of variable is natural number.
(iii)3√t + t√2
It is not a polynomial in one variable. Because the power of variable is not a natural number, it is a fractional number.
(iv) y +2/y
It is not a polynomial in one variable.
(v) x10 + y3 + t50
It is not a polynomial in one variable. while It is a polynomial in three variable.
Q2. Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x
(ii) 2 – x2 + x3 (
iii) π/2 x2 + x
(iv) √2x −1
Solution:
(i) 2 + x2 + x
Coefficient of x2 = 1
(ii) 2 – x2 + x3
Coefficient of x2 = –1
(iii) π/2 x2 + x
Coefficient of x2 = π/2
(iv) √2x −1
Coefficients of x2 = 0 [Because There is no x2 So coefficient will be 0]
Q3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
A binomial of degree 35
⇒ 2x35 + 5y
Note: Binomial means the expression of two terms. Like x + 5, 3a - 2b, 3t + 7 etc.
A monomial of degree 100
⇒ 3y100
Note: Monomial means the expression of single term, like 3x, 5t, y, 3xy etc.
Q4. Write the degree of each of the following polynomials:
(i) 5x3 + 4x2 + 7x
(ii) 4 – y2
(iii) 5t – √7
(iv) 3
Solution:
(i) 5x3 + 4x2 + 7x
Ans: The degree of polynomial = 3 [Highest power]
(ii) 4 – y2
Ans: The degree of polynomial = 2
(iii) 5t – √7
Ans: The degree of polynomial = 1
(iv) 3
Ans: The degree of polynomial = 0
[Note: There is no variable therefore degree = 0]
Q5. Classify the following as linear, quadratic and cubic polynomials:
(i) x2 + x
(ii) x – x3
(iii) y + y2 + 4
(iv) 1 + x
(v) 3t
(vi) r2
(vii) 7x2
Solution:
(i) x2 + x
Ans: Quadratic polynomial
(ii) x – x3
Ans: Cubic polynomial
(iii) y + y2 + 4
Ans: Quadratic polynomial
(iv) 1 + x
Ans : Linear polynomial
(v) 3t
Ans : Linear polynomial
(vi) r2
Ans: Quadratic polynomial
(vii) 7x2
Ans: Cubic polynomial
Exercise 2.1 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 9 Mathematics Chapter 2. Polynomials solutions help you understand the core concepts and practice effectively.
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Our Exercise 2.1 are useful for both board exams and mid-term exams. For 9 Mathematics, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 2.1 for 9 Mathematics Chapter 2. Polynomials are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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