Introduction to Linear Polynomials Class 9 MCQ Maths Chapter 2

Practicing Class 9 Maths MCQ and Ganita Manjari Class 9 Maths Chapter 2 Introduction to Linear Polynomials MCQ Questions Online Test with Answers daily helps in time management.

MCQ on Introduction to Linear Polynomials Class 9

Introduction to Linear Polynomials MCQ Class 9

Class 9 Maths Introduction to Linear Polynomials MCQ

Question 1.
Which of the following is a polynomial?
(a) x² + \(\frac{2}{x}\) + 3
(b) √y + 5y – 1
(c) x³ – 3x² + 7
(d) z^1/2 + 2
Answer:
(c) x³ – 3x² + 7

Explanation:
Given expression is x³ – 3x² + 7.
Here, we see that the variable x has all non-negative integer powers.
Hence, it is a polynomial.

Question 2.
The degree of the polynomial
p(x) = 5x³ – 2x² + x – 8 is
(a) 2
(b) 3
(c) 1
(d) 0
Answer:
(b) 3

Explanation:
Given expression is 5x³ – 2x² + x – 8.
Here, the highest power of the variable x is 3. Hence, the degree is 3.

Question 3.
Which of the following is a quadratic polynomial?
(a) x + 5
(b) x³ + x² + 1
(c) x² – 9
(d) 5x⁴
Answer:
(c) x² – 9

Explanation:
From the options, the expression x² – 9 has degree 2.
So, it is a quadratic polynomial.

Question 4.
Which of the following is a binomial?
(a) x² + x + 1
(b) 5x³
(c) x – 7
(d) x⁴ + 3x³ + 2x² + x
Answer:
(c) x – 7

Explanation:
From the options, the expression x – 7 contains exactly two non-zero terms.
Hence, it is a binomial.

Question 5.
A polynomial of degree 1 is called a
(a) quadratic polynomial
(b) cubic polynomial
(c) linear polynomial
(d) constant polynomial
Answer:
(c) linear polynomial

Explanation:
By definition, a polynomial of degree 1 is called a linear polynomial.

Question 6.
Which of the following is a polynomial of degree 2?
(a) 3x + 2
(b) x² – 4x + 7
(c) x³ + x
(d) 5
Answer:
(b) x² – 4x + 7

Explanation:
The highest power of x in x² – 4x + 7 is 2, so it is a polynomial of degree 2.

Question 7.
What are the coefficients of x² and x³ in the polynomial 2x⁴ – 5x³ + 4x² – x + 6 are
(a) 4, -5
(b) -5, 4
(c) 2, -5
(d) 4, 2
Answer:
(a) 4, -5

Explanation:
Coefficient of x² = 4 and coefficient of x³ = -5.

Question 8.
The slope of line 6x – y = 2 is
(a) \(\frac{1}{6}\)
(b) 1
(c) 6
(d) -6
Answer:
(c) 6

Question 9.
The y-intercept of the line \(\frac{x}{5}+\frac{y}{4}\) = 1 is
(a) -5
(b) 4
(c) -4
(d) 5
Answer:
(b) 4

Question 10.
Which of the following scenarios represents linear decay?
(a) A population doubling every year
(b) Interest compounding annually
(c) A candle burning at 2 cm/h
(d) A car accelerating at 5 m/s²
Answer:
(c) A candle burning at 2 cm/h

Explanation:
Candle burning at constant rate → Decreases uniformly.

Introduction to Linear Polynomials Class 9 Assertion and Reason Questions

Direction (Q. Nos. 1-6) In the questions given below, there are two statements marked as Assertion (A) and Reason (R). Read the statements and choose the correct option.

Question 1.
Assertion (A): \(\frac{1}{x}\) + x^-1 is not a polynomial.
Reason (R): A polynomial cannot have negative powers of variables.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.

Explanation:
We know that \(\frac{1}{x}\) + x^-1
Here, exponent of x is negative, so it is not a polynomial.
Also, polynomial does not allow negative powers.

Question 2.
Assertion (A): In the polynomial 3x² + 5x + 7, 7 is a constant term.
Reason (R): Constant term is the term independent of variable.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.

Explanation:
In the given polynomial, 7 does not contain variable x, hence it is constant.
Also, constant term is defined as the term independent of variable.

Question 3.
Assertion (A): Degree of polynomial 7x⁵ + 2x³ + 1 is 3.
Reason (R): Degree of a polynomial is the highest power of the variable.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.

Explanation:
Here, highest power of x is 5.
Hence, degree = 5 and it is true, degree of a polynomial is the highest power of the variables.

Question 4.
Assertion (A): 4x + 3 is a linear polynomial.
Reason (R): A polynomial of degree 2 is called a quadratic polynomial.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(b) Both A and R are true but R is not the correct explanation of A.

Explanation:
Highest power of x is 1, so degree = 1.
Hence, it is a linear polynomial and it is also true a polynomial of degree 2 is called a quadratic polynomial.

Question 5.
Assertion (A): The equation y = 3x + 5 represents a linear polynomial with slope 5 and y-intercept 3.
Reason (R): In the equation y = mx + c, m represents slope and c represents y-intercept.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.

Explanation:
Given, y = 3x + 5
On comparing with y = mx + c, we get m = 3 and c = 5
So, the slope and y-intercept of given linear polynomial are 3 and 5.
Hence, Assertion is false and Reason is true.

Question 6.
Assertion (A): The graph of a linear equation in . two variables is always a straight line.
Reason (R): A linear equation represents a first degree relation between variables.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(b) Both A and R are true but R is not the correct explanation of A.

Explanation:
We know that the graph of a linear equation in two variables is always a straight line and a linear equation represents a first degree relation between variables.