CBSE Class 9 Maths Polynomials MCQs Set 04

Question. The value of (369)² – (368)² is
(a) 12
(b) 81
(c) 37
(d) 737
Answer: d

Question. If a³ + b³ + c³ = 3abc, then a² / bc + b² / ca + c² / ab =
(a) 0
(b) 1
(c) – 1
(d) 3
Answer: d

Question. If p(x) = x⁵¹ + 51, then value of p(–1) is
(a) 0
(b) 1
(c) 49
(d) 50
Answer: d

 Question. The coefficient of the highest power of x in the polynomial 3x³ – 4x⁴ + 5x² – 2x⁵ + 3 is
(a) 2
(b) – 4
(c) 3
(d) –2
Answer: d

 Question. (x + y)³ – (x – y)³ – 6y(x² – y² ) =
(a) y³
(b) 2y³ 
(c) 4y³ 
(d) 8y³
Answer: d

Question. The factors of x³ + 9x² + 23x + 15 are

(a) (x + 1), (x + 3), (x + 5)
(b) (x + 1), (x + 3), (x – 5)
(c) (x + 1), (x – 3), (x – 5)
(d) (x – 1), (x – 3), (x – 5)
Answer: a

Question. If p(y) = y² – y + 1, then find the value of p(0) – p(1).
(a) 1
(b) 3
(c) 0
(d) 2
Answer: c

Question. If p(x) = x¹⁶⁰ + 2x¹⁴¹ + k and p(–1) = 0, then the value of k is
(a) 1
(b) – 3
(c) 2
(d) – 2
Answer: a

Question. Factors of polynomial 12x² + 7x + 1 are
(a) (3x – 1)(4x + 1)
(b) (3x – 1)(4x – 1)
(c) (4x – 1)(3x– 1)
(d) (4x + 1)(3x + 1)
Answer: d

Question. Factorise: x²+ (a + b + c)x + ab + bc
(a) (x + a)(x + b + c)
(b) (x + a)(x + a + c)
(c) (x + b)(x + a + c)
(d) (x + b)(x + b + c)
Answer: c

 Question. If x = –2 and x²+ y² + 3xy = –5, then find y.
(a) –2
(b) 3
(c) – 4
(d) 9
Answer: b

Question. One of the zeroes of the polynomial 2x² + 7x – 4 is
(a) 2
(b) 1/2
(c) − 1/2
(d) – 2
Answer: b

Question. Simplify : x³ - 4 - x + 4x² / x² + 3x - 4
(a) 4 + x
(b) 2 + x
(c) 1 – x
(d) x + 1
Answer: d

Question. Using algebraic identity, find the value of 209 × 191.
(a) 39851
(b) 39919
(c) 39961
(d) 38951
Answer: b

Question. The degree of the polynomial (y³ – 3)(y²+ 8) is
(a) 2
(b) 3
(c) 0
(d) 5
Answer: d

Question. If a + b + c = 13 and ab + bc + ca = 84, then find the value of a² + b² + c².
(a) 1
(b) 2
(c) 3
(d) 4
Answer: a

 Question. The value of (9)³ + (– 3)³ is
(a) – 81
(b) 54
(c) 164
(d) 702
Answer: d

Assertion & Reasoning Based MCQs

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The degree of the polynomial (x² – 2)(x – 3)(x + 4) is 3.
Reason : A polynomial of degree 3 is called a cubic polynomial.
Answer: d

Question. Assertion : 3x² + x – 1 = (x + 1) (3x – 2) + 1.
Reason : To factorise ax² + bx + c, write b as sum of two numbers whose product is ac.
Answer: a

Question. Assertion : The value of (–27)³ + (–9)³ is –20412.
Reason : If a + b = 0, then a³ + b³ + c³ = 0
Answer: c

Question. Assertion : If 2x² – 32 is the volume of a cuboid, then length of cuboid can be x – 8.
Reason : Volume of a cuboid = l × b × h.
Answer: d

Question. Assertion : The expression 3x4 – 4x^3/2 + x² = 2 is not a polynomial because the term – 4x^3/2 contains a rational power of x.
Reason : The highest exponent in various terms of an algebraic expression in one variable is called its degree.
Answer: b

Question. Assertion : If x = 3/2 is a zero of polynomial 2x² + kx – 12, then k = 5.
Reason : If x = a is zero of a polynomial f(x), then f(a) = 0.
Answer: a

Question. Assertion : –7 is a constant polynomial.
Reason : Degree of a constant polynomial is zero.
Answer: a

Question. Assertion : The value of 593 × 607 is 359951.
Reason : (a + b) (a – b) = a² – b²
Answer: a
 

Fill in the blanks:

Question. If x/y + y/x = –1 , (x ≠ 0, y ≠ 0), then the value of x³ – y³  is______.
Answer: 0 

Question. Zero of the polynomial p(x) = 2x + 3 is ______. 
Answer: – 3/2 

Question. If (x – 1) is a factor of x² + x + k, then value of k is ______. 
Answer: –2 

Question. Degree of a linear polynomial is______ . 
Answer:1

Question. If x –1/x = 3 , then value of x³ – 1/ x³ s _____ .
Answer: 33

Question. Coefficient of x² in the polynomial π/4x² – 3x + 4 is ______.
Answer: π/4

True /False:

Question. Degree of the polynomial 2 – x² – 3x³ + 2x⁷ is 7. 
Answer: True 

Question. Zero of a zero polynomial is any real number.
Answer: True

Question. (x + 1) is a factor of x¹⁴⁰ + 2x¹⁴¹ + 2. 
Answer: False

Question. Zeroes of a polynomial 3(x – 2) (x + 3) are 2 and 3. 
Answer: False

Question. If p(x) = x²+ 3x + 2, then p(1) + p(2) + p(0) is 18.
Answer: False

Question. (x – 3) is a factor of 2x³ – 5x² + 2x – 18. 
Answer: False

Question. Degree of the zero polynomial is zero.
Answer: False

Case Based MCQs

Read the following passage and answer the questions.
Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x² + 12x + 5, which is the product of their individual shares.

Question. Total amount invested by both, if x = 1000 is
(a) Rs 301506
(b) Rs 370561
(c) Rs 4012005
(d) Rs 490621
Answer: c

Question. The shares of Ankur and Ranjan invested individually are
(a) Rs (2x + 1), Rs (2x + 5)
(b) Rs (2x + 3), Rs (x + 1)
(c) Rs (x + 1), Rs (x + 3)
(d) None of these
Answer: a

Question. Find the value of x, if the total amount invested is equal to 0.
(a) –1/2
(b) –5/2
(c) Both (a) and (b)
(d) None of these
Answer: c

Question. Coefficient of x² in the given polynomial is
(a) 2
(b) 3
(c) 4
(d) 12
Answer: c

Question. Name the polynomial of amounts invested by each partner.
(a) Cubic
(b) Quadratic
(c) Linear
(d) None of these
Answer: c