CBSE Class 9 Maths Ganita Manjari Part 1 Ch 02 Introduction to Linear Polynomials MCQs with Answers Set 01

Practice MCQs for Class 9 Mathematics Chapter 02 Introduction to Linear Polynomials

Review structured MCQ sets for Class 9 Mathematics Chapter 02 Introduction to Linear Polynomials. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Access Chapter 02 Introduction to Linear Polynomials Questions and Solutions

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Multiple Choice Questions

Question 1: The expression \( 9x + 7 \) is evaluated for \( x = 3 \). A student obtains 34. Which statement is correct?
(a) The student is correct.
(b) The student should get 27.
(c) The student should get 43.
(d) The expression cannot be evaluated.
Show Answer & Explanation

Answer: (a) The student is correct.

Explanation:
1. Substitute \( x = 3 \): \( 9(3) + 7 = 27 + 7 = 34 \).
2. The student's value 34 matches, so the student is correct.
3. 27 is only the value of \( 9x \); the constant 7 must also be added.

Question 2: A linear polynomial is represented by \( p(x) = ax + b \), where \( a \neq 0 \). What happens to it if \( a = 0 \)?
(a) It becomes a polynomial of degree 2.
(b) It remains of degree 1.
(c) It becomes a constant polynomial.
(d) It is no longer an expression.
Show Answer & Explanation

Answer: (c) It becomes a constant polynomial.

Explanation:
1. If \( a = 0 \), then \( p(x) = 0 \cdot x + b = b \).
2. The x-term disappears and only the constant b is left.
3. So p(x) becomes a constant polynomial, not a linear one.

Question 3: A student writes the expression \( 7x - 4 \). Which statement correctly describes it?
(a) It is a quadratic polynomial.
(b) It is a constant polynomial.
(c) It is a linear polynomial with degree 1.
(d) It is not a polynomial.
Show Answer & Explanation

Answer: (c) It is a linear polynomial with degree 1.

Explanation:
1. The highest power of x in \( 7x - 4 \) is 1.
2. A polynomial whose degree is 1 is called a linear polynomial.
3. A negative constant term (−4) is allowed in a polynomial.

Question 4: The cost of a notebook is ₹x, and the cost of a pen is ₹15. If a student buys 4 notebooks and 2 pens, the total cost is represented by:
(a) \( 4x + 15 \)
(b) \( 4x + 30 \)
(c) \( 6x + 30 \)
(d) \( 4(x + 15) \)
Show Answer & Explanation

Answer: (b) \( 4x + 30 \)

Explanation:
1. Cost of 4 notebooks = \( 4 \times x = 4x \).
2. Cost of 2 pens = \( 2 \times 15 = 30 \).
3. Total cost = \( 4x + 30 \).

Question 5: Riju wants to express the perimeter of his carrom board in terms of a linear polynomial. Which of the following polynomials can be used by him?
(a) \( 4x + 16 \)
(b) \( 4x^2 + 16 \)
(c) \( 4x^2 + 2x \)
(d) \( 4x^3 + 16x^2 \)
Show Answer & Explanation

Answer: (a) \( 4x + 16 \)

Explanation:
1. A carrom board is a square, so its perimeter is 4 × side, which is a length (power 1).
2. Only \( 4x + 16 \) has degree 1. For example, a side of \( (x + 4) \) gives \( 4(x + 4) = 4x + 16 \).
3. The other options contain \( x^2 \) or \( x^3 \), so they are not linear.

Question 6: A taxi charges ₹50 as a fixed charge and ₹12 per kilometre. Which expression represents the fare for travelling x kilometres?
(a) \( 6x + 30 \)
(b) \( 50x + 12 \)
(c) \( 62x \)
(d) \( 50 + 12x \)
Show Answer & Explanation

Answer: (d) \( 50 + 12x \)

Explanation:
1. The per-kilometre charge for x km is \( 12x \).
2. The fixed charge of ₹50 is added once, whatever the distance.
3. Fare = \( 50 + 12x \).

Question 7: Ihana puts 4 ball pens in each of the x red boxes and 5 ball pens in each of the y blue boxes, with 3 extra pens left. The number of pens Ihana has is:
(a) \( 4x + 5y \)
(b) \( 4x + 5y + 3 \)
(c) \( 5x + 4y + 3 \)
(d) \( 4x + 5y - 3 \)
Show Answer & Explanation

Answer: (b) \( 4x + 5y + 3 \)

Explanation:
1. Pens in red boxes = \( 4x \).
2. Pens in blue boxes = \( 5y \).
3. Adding the 3 extra pens: total = \( 4x + 5y + 3 \).

Question 8: A rectangular garden has length \( (x + 5) \) m and breadth 3 m. The length of wire required to fence this garden is:
(a) \( 2x + 16 \)
(b) \( 2x + 8 \)
(c) \( 3x + 5 \)
(d) \( 2x + 10 \)
Show Answer & Explanation

Answer: (a) \( 2x + 16 \)

Explanation:
1. Fencing needed = perimeter = 2(length + breadth).
2. \( 2[(x + 5) + 3] = 2(x + 8) = 2x + 16 \) m.

Question 9: Two students classify the polynomial \( p(x) = 5 - 2x \).
Student A: "Its degree is 1."
Student B: "Its coefficient of x is 5."
Who is correct?
(a) Only Student A
(b) Only Student B
(c) Both students
(d) Neither student
Show Answer & Explanation

Answer: (a) Only Student A

Explanation:
1. The highest power of x is 1, so the degree is 1. Student A is correct.
2. The term with x is \( -2x \), so the coefficient of x is −2. The number 5 is the constant term.
3. So Student B is wrong, and only Student A is correct.

Question 10: The temperature at 6 a.m. is x°C. During the day, it rises by 8°C. Which expression represents the temperature later in the day?
(a) \( 8x \)
(b) \( x - 8 \)
(c) \( x + 8 \)
(d) \( 8 - x \)
Show Answer & Explanation

Answer: (c) \( x + 8 \)

Explanation:
1. A rise means we add to the starting temperature.
2. New temperature = \( x + 8 \) °C.

Question 11: Which of the following situations can be represented by a linear polynomial in x?
(a) Area of a square of side x
(b) Cost of x pens at ₹10 each plus a fixed ₹20 charge
(c) Volume of a cube of side x
(d) Product of two numbers x and \( x + 2 \)
Show Answer & Explanation

Answer: (b) Cost of x pens at ₹10 each plus a fixed ₹20 charge

Explanation:
1. Area of a square = \( x^2 \) (degree 2).
2. Cost of pens = \( 10x + 20 \) (degree 1), which is linear.
3. Volume of a cube = \( x^3 \) (degree 3), and \( x(x + 2) = x^2 + 2x \) (degree 2).

Question 12: A student simplifies \( (5x + 8) - (2x + 3) \) as \( 3x + 11 \). What is the error?
(a) The coefficients of x cannot be subtracted.
(b) The constant terms should be subtracted as 8 − 3.
(c) The expression is not a polynomial.
(d) The x-terms should be multiplied.
Show Answer & Explanation

Answer: (b) The constant terms should be subtracted as 8 − 3.

Explanation:
1. Removing the bracket: \( 5x + 8 - 2x - 3 \).
2. x-terms: \( 5x - 2x = 3x \). Constants: \( 8 - 3 = 5 \).
3. Correct answer is \( 3x + 5 \). The student added 8 + 3 instead of subtracting.

Question 13: Observe the following table:
x: 0, 1, 2, 3
p(x): 4, 7, 10, 13
Which expression represents p(x)?
(a) \( x + 4 \)
(b) \( 2x + 4 \)
(c) \( 4x + 3 \)
(d) \( 3x + 4 \)
Show Answer & Explanation

Answer: (d) \( 3x + 4 \)

Explanation:
1. When x = 0, p(0) = 4, so the constant term is 4.
2. Each time x increases by 1, p(x) increases by 3, so the coefficient of x is 3.
3. p(x) = \( 3x + 4 \). Check: p(3) = 9 + 4 = 13 ✓.

Question 14: A shopkeeper's billing rule is represented by \( B(x) = 25x + 100 \), where x is the number of items purchased. What does the constant term 100 represent?
(a) Cost of one item
(b) Number of items
(c) Fixed charge in the bill
(d) Total cost of x items
Show Answer & Explanation

Answer: (c) Fixed charge in the bill

Explanation:
1. The term \( 25x \) changes with the number of items, so 25 is the cost per item.
2. The term 100 stays the same for any x, so it is a fixed charge added to every bill.

Question 15: Riya says, "Every polynomial containing x is a linear polynomial." Which example disproves her statement?
(a) \( 4x^2 + 2x \)
(b) \( 2x + 4 \)
(c) \( 7x - 1 \)
(d) \( 9x \)
Show Answer & Explanation

Answer: (a) \( 4x^2 + 2x \)

Explanation:
1. To disprove a claim, we need one polynomial that contains x but is not linear.
2. \( 4x^2 + 2x \) contains x but has degree 2, so it is quadratic.
3. The other three options are linear, so they support Riya instead.

Question 16: A linear polynomial \( p(x) = 2x - 6 \) is represented graphically. At which point does its graph meet the x-axis?
(a) (0, −6)
(b) (3, 0)
(c) (0, 3)
(d) (−3, 0)
Show Answer & Explanation

Answer: (b) (3, 0)

Explanation:
1. On the x-axis, the value of the polynomial (y) is 0.
2. \( 2x - 6 = 0 \Rightarrow x = 3 \).
3. So the graph meets the x-axis at (3, 0). (0, −6) is where it meets the y-axis.

Question 17: Two students simplify the expression \( 6x + 5 - (2x - 3) \). Student A gets \( 4x + 2 \), while Student B gets \( 4x + 8 \). Who is correct?
(a) Student A
(b) Student B
(c) Both
(d) Neither
Show Answer & Explanation

Answer: (b) Student B

Explanation:
1. \( 6x + 5 - (2x - 3) = 6x + 5 - 2x + 3 \).
2. The minus sign changes −3 into +3.
3. \( = 4x + 8 \). Student B is correct.

Question 18: A parking area charges ₹30 as a fixed fee and ₹10 per hour. If a vehicle stays for x hours, its parking charge is \( p(x) = 10x + 30 \). What will be the charge for 5 hours?
(a) ₹50
(b) ₹70
(c) ₹80
(d) ₹100
Show Answer & Explanation

Answer: (c) ₹80

Explanation:
1. \( p(5) = 10(5) + 30 = 50 + 30 = 80 \).
2. The charge for 5 hours is ₹80.

Assertion–Reason Questions

Question 19:
Assertion (A): A student says that \( 7 - 3x \) is a linear polynomial.
Reason (R): The highest power of the variable in a linear polynomial is 1.
(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.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. In \( 7 - 3x \), the highest power of x is 1, so it is linear. The Assertion is true.
2. The Reason gives the definition of a linear polynomial, which is true.
3. The Reason is exactly why \( 7 - 3x \) is linear, so it correctly explains the Assertion.

Question 20:
Assertion (A): The zero of the linear polynomial \( p(x) = 3x - 12 \) is −4.
Reason (R): A zero of a polynomial is the value of x for which the value of the polynomial is zero.
(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.
Show Answer & Explanation

Answer: (d) A is false, but R is true.

Explanation:
1. \( 3x - 12 = 0 \Rightarrow x = 4 \), not −4. Check: p(−4) = −12 − 12 = −24 ≠ 0. The Assertion is false.
2. The Reason is the correct definition of a zero. The Reason is true.

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Multiple Choice Questions (MCQs) for Class 9 Mathematics Chapter 02 Introduction to Linear Polynomials

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FAQs

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