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) z1/2 + 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 a constant rate → Decreases uniformly.
Question 11.
Which of the following is a linear polynomial?
(A) x2 + 3
(B) 5x3 – 2
(C) 4x – 7
(D) x2 – x + 1
Answer:
(C) 4x – 7
Question 12.
A polynomial of degree 0 is called
(A) linear polynomial
(B) quadratic polynomial
(C) cubic polynomial
(D) constant polynomial
Answer:
(D) constant polynomial
Question 13.
How many terms does the polynomial 4x3 – 2x + 7 have?
(A) 4
(B) 2
(C) 3
(D) 1
Answer:
(C) 3
Question 14.
Coefficient of x4 in the polynomial -2x4 – 3x3 + 6x2 – 2x + 7 is
(A) 6
(B) 2
(C) -2
(D) -3
Answer:
(C) -2
Question 15.
The value of 3x + 7 when x = -2 is:
(A) 1
(B) -1
(C) 13
(D) 0
Answer:
(A) 1
Question 16.
If 2x + 10 = 64, then x equals:
(A) 37
(B) 27
(C) 54
(D) 32
Answer:
(B) 27
Question 17.
When a linear polynomial is equated to a constant, we get
(A) a quadratic equation
(B) a linear equation
(C) a cubic equation
(D) an identity
Answer:
(B) a linear equation
Question 18.
If the perimeter of a square of side x is 36 cm, then what is the value of x?
(A) 4
(B) 9
(C) 36
(D) 144
Answer:
(B) 9
Question 19.
The nth term of a linear pattern 3, 7, 11, 15, … is:
(A) 3n + 1
(B) 4n – 1
(C) 2n + 1
(D) 4n + 3
Answer:
(B) 4n – 1
Question 20.
Ajay has ₹ 1000 and spends ₹ 50 daily. Amount left on the nth day =?
(A) 1000 + 5n
(B) 1000n – 50
(C) 1000 – 50n
(D) 50n – 1000
Answer:
(C) 1000 – 50n
Question 21.
Which of the following is a linear pattern?
(A) 1, 4, 9, 16, 25…
(B) 2, 4, 8, 16, 32…
(C) 5, 8, 11, 14, 17…
(D) 1, 3, 6, 10, 15…
Answer:
(C) 5, 8, 11, 14, 17…
Explanation:
The difference between consecutive terms is constant.
Question 22.
Rajesh is reading a 600-page novel, and he reads 25 pages every day. How many pages will be left after 20 days?
(A) 300
(B) 200
(C) 100
(D) 400
Answer:
(C) 100
Explanation:
Pages left after n days = 600 – 25n
Question 23.
In the sequence 2n – 1, which stage has 47 tiles?
(A) 24
(B) 48
(C) 23
(D) 25
Answer:
(A) 24
Question 24.
A quantity that decreases by a constant amount over equal intervals represents:
(A) Linear decay
(B) Quadratic growth
(C) Linear growth
(D) Quadratic decay
Answer:
(A) Linear decay
Question 25.
The value of a car depreciates by ₹ 8,000 per year. If the initial value of the car is ₹ 6,00,000, then its value after t years is:
(A) 6,00,000t – 8,000
(B) 6,00,000t + 8,000
(C) 6,00,000 – 8,000t
(D) 6,00,000 + 8,000t
Answer:
(C) 6,00,000 – 8,000t
Question 26.
Which of the following functions represents linear growth?
(A) h(t) = 5 – 0.2t
(B) P(t) = 200 + 30t
(C) V(t) = 1000 – 50t
(D) f(t) = t2 + 3
Answer:
(B) P(t) = 200 + 30t
Question 27.
In the linear equation y = ax + b, b represents:
(A) slope
(B) x-intercept
(C) value of y when x = 0
(D) value of x when y = 0
Answer:
(C) value of y when x = 0
Question 28.
The y-intercept of the line y = 9x – 5 is:
(A) 9
(B) -5
(C) -9
(D) 5
Answer:
(B) -5
Question 29.
The line y = ax always passes through:
(A) (0, 3)
(B) (3, 0)
(C) (0, 0)
(D) (1, 0)
Answer:
(C) (0, 0)
Question 30.
Lines y = 3x – 2, y = 3x, y = 3x + 5 are:
(A) All passing through origin
(B) Parallel to each other
(C) Perpendicular to each other
(D) Intersecting at one point
Answer:
(B) Parallel to each other
Question 31.
The line y = -2x + 9 cuts the y-axis at:
(A) (0, -2)
(B) (9, 0)
(C) (0, 9)
(D) (2, 0)
Answer:
(C) (0, 9)
Question 32.
The graph of y = ax + b where b changes but a stays fixed:
(A) Lines with different slopes
(B) Lines that meet at the origin
(C) Parallel lines
(D) Perpendicular lines
Answer:
(C) Parallel lines
Question 33.
Which line has a negative slope and a positive y-intercept?
(A) y = 3x – 2
(B) y = -2x + 5
(C) y = 4x + 7
(D) y = -x – 3
Answer:
(B) y = -2x + 5
Question 34.
The expression 11x6 – 4x4 + x2 – 3 is a polynomial. How many variables does it have?
(A) 6
(B) 4
(C) 2
(D) 1
Answer:
(D) 1
Question 35.
For what value of x does the linear polynomial 4x – 12 equal zero?
(A) 4
(B) 12
(C) 3
(D) -3
Answer:
(C) 3
Question 36.
The nth term of a linear pattern is 5n – 3. Which term of this pattern equals 47?
(A) 9
(B) 10
(C) 8
(D) 11
Answer:
(B) 10
Question 37.
Which of the following lines represents linear decay?
(A) y = 3x
(B) y = x + 5
(C) y = 2x – 4
(D) y = -3x + 10
Answer:
(D) y = -3x + 10
Question 38.
The graph of y = 5x passes through which of the following points?
(A) (1, 0)
(B) (0, 5)
(C) (2, 10)
(D) (5, 1)
Answer:
(C) (2, 10)
Introduction to Linear Polynomials Class 9 Assertion and Reason Questions
Direction (Q. Nos. 1-18): 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, the exponent of x is negative, so it is not a polynomial.
Also, a polynomial does not allow negative powers.
Question 2.
Assertion (A): In the polynomial 3x2 + 5x + 7, 7 is a constant term.
Reason (R): The constant term is the term independent 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:
(a) Both A and R are true, and R is the correct explanation of A.
Explanation:
In the given polynomial, 7 does not contain the variable x; hence, it is constant.
Also, the constant term is defined as the term independent of the variable.
Question 3.
Assertion (A): The degree of the polynomial 7x5 + 2x3 + 1 is 3.
Reason (R): The 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, the highest power of x is 5.
Hence, degree = 5 and it is true; the 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:
The highest power of x is 1, so degree = 1.
Hence, it is a linear polynomial, and it is also true that 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 the slope and c represents the 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 the 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.
Question 7.
Assertion (A): 5y3 + y2 + 2y – 1 is a cubic polynomial.
Reason (R): The 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:
(A) Both (A) and (R) are true, and (R) is the correct explanation of (A).
Question 8.
Assertion (A): The coefficient of y in 3y3 + y2 – 11 is 0.
Reason (R): There is no term containing y in the polynomial 3y3 + y2 – 11.
(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:
3y3 + y2 – 11 = 3y3 + y2 + 0y – 11
Question 9.
Assertion (A): 4x + 3 = 15 is a linear equation.
Reason (R): 4x + 3 is a linear polynomial equated to a constant 15.
(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).
Question 10.
Assertion (A): The polynomial 2x + 3, when evaluated at x = 4, gives output 11.
Reason (R): A polynomial acts as an input-output machine where we substitute input values to get output values.
(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).
Question 11.
Assertion (A): The difference between successive values of 200 + 50m at m = 1, 2, 3 is 100.
Reason (R): For a linear polynomial am + b, the difference between successive values is equal to the coefficient a.
(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.
Question 12.
Assertion (A): The sequence 5, 10, 15, 20, 25 is a linear pattern.
Reason (R): The difference between consecutive terms is constant 5.
(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).
Question 13.
Assertion (A): The nth term of the pattern 3, 5, 7, 9, 11,… is 2n + 1.
Reason (R): In this pattern, each term is one more than twice the term number.
(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).
Question 14.
Assertion (A): V(t) = 5000 – 200t represents linear decay.
Reason (R): The value of V decreases by a constant 200 for every unit increase in t.
(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).
Question 15.
Assertion (A): The line y = -2x + 5 represents linear growth.
Reason (R): Linear growth corresponds to a line with positive slope.
(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: The slope of the line y = -2x + 5 is -2.
Question 16.
Assertion (A): The y-intercept of the line y = 3x – 2 is -2, meaning the line cuts the y-axis 2 units below the origin.
Reason (R): The y-intercept b is the distance from the origin where the line cuts the y-axis.
(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).
Question 17.
Assertion (A): The line y = -3x represents linear decay when x ≥ 0.
Reason (R): Any line passing through the origin cannot represent linear decay.
(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:
(C) (A) is true, but (R) is false.
Explanation: A line through the origin can represent linear decay if its slope is negative.
Question 18.
Assertion (A): The expression y = 250 – 8t represents linear decay.
Reason (R): The coefficient of t is negative, so the value of y decreases as t increases.
(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).