AP 10th Class Maths 2nd Chapter Polynomials Bits

Chapter 2 Polynomials Bits for 10th Class AP Board

Multiple Choice Questions (MCQs)

Question 1.
Order of the polynomial 8x⁶ – 5x⁴ + 7x – 8 is …………………. .
A) 4
B) 5
C) 6
D) 7
Answer:
C) 6

Question 2.
4y² – 7y + 2 is …………….. polynomial.
A) linear
B) quadratic
C) cubic
D) constant
Answer:
B) quadratic

Question 3.
Zero of the ax + b is ………………. .
A) \(\frac{-b}{\mathrm{a}}\)
B) \(\frac{-a}{\mathrm{b}}\)
C) \(\frac{a}{\mathrm{b}}\)
D) \(\frac{b}{\mathrm{a}}\)
Answer:
A) \(\frac{-b}{\mathrm{a}}\)

Question 4.
Degree of the polynomial √2x² – 8x + 1 is ………………… .
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2

Question 5.
Number of zeroes that can be identified by the following figure ………………… .

A) 4
B) 3
C) 2
D) 0
Answer:
D) 0

Question 6.
Number of zeroes can be identified by the given figure is ………………. .

A) 4
B) 3
C) 1
D) 2
Answer:
D) 2

Question 7.
If y = p(x) is represented by the given graph, then the number of zeroes are ………………… .

A) 2
B) 4
C) 6
D) 5
Answer:
D) 5

Question 8.
The number of zeroes of the polynomial, whose graph is given below.

A) 1
B) 0
C) 2
D) 3
Answer:
B) 0

Question 9.
a₀xⁿ + a₁x^{n – 1} + a₂x^{n – 2} + ………. a_nxⁿ is polynomial of degree ……………….. .
A) xⁿ
B) n
C) aⁿ
D) n – 1
Answer:
B) n

Question 10.
Which of the following is a cubic polynomial in general form ?
A) ax³ + bx² + cx + d
B) ax² + bx + c
C) ax + b
D) ax⁴ + bx³ + cxⁿ + dx + e
Answer:
A) ax³ + bx² + cx + d

Question 11.
p(\(\frac{\mathbf{a}}{\mathbf{b}}\)) = 0, then p(x) = ……………….. .
A) bx – a
B) ax – b
C) ax + b
D) bx + a
Answer:
A) bx – a

Question 12.
If p(x) = 4x² + 3x – 1, then p(\(\frac{1}{2}\)) = ………………….. .
A) \(\frac{3}{2}\)
B) \(\frac{2}{3}\)
C) 1
D) 2
Answer:
A) \(\frac{3}{2}\)

Question 13.
p(x) = x³ + 5x² + 8x – 3, then p(1) =
A) 10
B) 11
C) 17
D) 12
Answer:
B) 11

Question 14.
ax + b represents ……………….. polynomial.
A) cubic
B) quadratic
C) linear
D) constant
Answer:
C) linear

Question 15.
The quadratic polynomial whose zeroes are \(\sqrt{15}\) and – \(\sqrt{15}\) is ………………… .
A) x – \(\sqrt{15}\)
B) x + \(\sqrt{15}\)
C) 15x² – 1
D) x² – 15
Answer:
D) x² – 15

Question 16.
Sum of zeroes of the polynomial 3x² – 5x + 8 is …………….. .
A) \(\frac{3}{5}\)
B) \(\frac{5}{3}\)
C) \(\frac{8}{3}\)
D) \(\frac{3}{8}\)
Answer:
B) \(\frac{5}{3}\)

Question 17.
Product of zeroes of the polynomial 5x³ – 8x² + 7x + 8 is ……………. .
A) \(\frac{8}{5}\)
B) \(\frac{5}{8}\)
C) \(\frac{-8}{5}\)
D) \(\frac{-5}{8}\)
Answer:
C) \(\frac{-8}{5}\)

Question 18.
Sum of zeroes of ax² + bx + c is ………………. .
A) \(\frac{-\mathrm{a}}{\mathrm{b}}\)
B) \(\frac{\mathrm{a}}{\mathrm{b}}\)
C) \(\frac{\mathrm{a}}{-\mathrm{b}}\)
D) \(\frac{\mathrm{b}}{\mathrm{a}}\)
Answer:
C) \(\frac{\mathrm{a}}{-\mathrm{b}}\)

Question 19.
Product of zeroes of ax² + bx + c is ……………. .
A) \(\frac{-\mathrm{a}}{\mathrm{b}}\)
B) \(\frac{\mathrm{c}}{\mathrm{a}}\)
C) \(\frac{\mathrm{a}}{-\mathrm{c}}\)
D) \(\frac{-\mathrm{b}}{\mathrm{a}}\)
Answer:
B) \(\frac{\mathrm{c}}{\mathrm{a}}\)

Question 20
If 4 is one of the zeroes of p(x) = x² + kx – 5, then the value of k = …………….. .
A) \(\frac{-11}{4}\)
B) \(\frac{11}{4}\)
C) \(\frac{-4}{11}\)
D) \(\frac{4}{11}\)
Answer:
A) \(\frac{-11}{4}\)

Question 21.
The degree of the polynomial √2x³ + 3x³ – 5x + 4 is ……………… .
A) √2
B) 3
C) 2
D) 5
Answer:
B) 3

Question 22.
The quadratic polynomial having 2, 3 as zeroes is …………………. .
A) x² + 5x + 6
B) x² + 5x – 6
C) x² – 5x + 6
D) x² – 5x – 6
Answer:
C) x² – 5x + 6

Question 23.
In a division, if divisor is x + 1, quotient is x and remainder is 4, then dividend is ……………… .
A) x(x + 1) + 4
B) x² + x
C) 4x + 4
D) 4(x + 1) + x
Answer:
A) x(x + 1) + 4

Question 24.
If one zero of the quadratic polynomial 2x² + kx – 15 is 3, then the other zero is …………….. .
A) -15
B) \(\frac{-5}{2}\)
C) \(\frac{5}{2}\)
D) 15
Answer:
B) \(\frac{-5}{2}\)

Question 25.
f(\(\frac{\mathrm{a}}{\mathrm{b}}\)) = 0, then f(x) = ……………… .
A) ax + b
B) ax – b
C) bx – a
D) bx + a
Answer:
C) bx – a

Question 26.
Number of constant terms in the polynomial x² + 7x – 7 is ……………….. .
A) 1
b) 2
C) 3
D) -7
Answer:
A) 1

Question 27.
Factors of x² + x(p + q) + pq = ……………… .
A) x.p
B) x.q
C) pq
D) A and B
Answer:
D) A and B

Question 28.
The remainder when 3x³ + x² + 2x + 5 is divided by x² + 2x + 1 is …………….. .
A) x + 10
B) x + 9
C) 9x + 10
D) 10x + 9
Answer:
C) 9x + 10

Question 29.
If the product of zeroes of 9x² + 3x + a is 7, then a = ………………. .
A) -63
B) 63
C) 36
D) -36
Answer:
B) 63

Question 30.
Zeroes of the polynomial x² – 4x + 3 are 1 and a, then a = ……………….. .
A) 1
B) 2
C) 3
D) 4
Answer:
C) 3

Question 31.
α + β = 0, α.β = √3, then the polynomial is ………………. .
A) x² – √3
B) x² + √3
C) x + √3
D) x – √3
Answer:
B) x² + √3

Question 32.
Binomial contains …………….. terms.
A) 2
B) 3
C) 1
D) 4
Answer:
A) 2

Question 33.
The quadratic polynomial, whose sum . and product of zeroes are 1 and -2 respectively is ……………. .
A) x² + 3x + 1
B) x² – 3x – 2
C) x² + 3x – 1
D) x² – x – 2
Answer:
D) x² – x – 2

Question 34.
The quadratic polynomial whose zeroes are 4 + √5 and 4 – √5 is
A) x² + 8x – 11
B) x² – 11x + 8
C) x² – 8x + 8
D) x² – 8x + 11
Answer:
D) x² – 8x + 11

Question 35.
g(x) = x³ + 4x² + 5x – 2, then g(l) = …………….. .
A) 8
B) 4
C) 6
D) 5
Answer:
A) 8

Question 36.
If p and q are zeroes of the polynomial 3x² + 11x – 4, then the value of \(\frac{\mathbf{p}}{\mathbf{q}}\) + \(\frac{\mathbf{q}}{\mathbf{p}}\) = ……………. .
A) \(\frac{12}{145}\)
B) \(\frac{-12}{145}\)
C) \(\frac{145}{2}\)
D) \(\frac{-145}{2}\)
Answer:
C) \(\frac{145}{2}\)

Question 37.
If α, β are the zeroes of the polynomial p(x) = 4x² + 3x + 7, then \(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\) p is equal
A) \(\frac{-3}{7}\)
B) \(\frac{-7}{3}\)
C) \(\frac{7}{3}\)
D) \(\frac{3}{7}\)
Answer:
A) \(\frac{-3}{7}\)

Question 38.
If one zero of the polynomial f(x) = (k² + 4) x² + 13x + 4k is reciprocal of the other, then k = ……………… .
A) 1
B) 2
C) -1
D) -2
Answer:
B) 2

Question 39.
If α and β are the zeroes of the polynomial f(x) = x² + p(x) + q, then the polynomial having \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) are its zeroes is ……………… .
A) px² + qx + 7
B) x² – px + q
C) qx² + px + 1
D) x² + qx + 5
Answer:
C) qx² + px + 1

Question 40.
If α, β are the zeroes of polynomial f(x) = x² – a(x + 1) – b, then (α + 1) (β + 1) = ……………….. .
A) b – 1
B) b
C) 1 – b
D) 1 + b
Answer:
C) 1 – b

Question 41.
If the product of zeroes of the polynomial f(x) = ax² – 6x² + 11x + 6 is 4, then a = ……………… .
A) \(\frac{2}{3}\)
B) –\(\frac{2}{3}\)
C) \(\frac{3}{2}\)
D) –\(\frac{3}{2}\)
Answer:
C) \(\frac{3}{2}\)

Question 42.
If zeroes of the polynomial f(x) = x³ – 3ax² + bx – c are in A.P, then ……………. .
A) 2a³ = ab – c
B) 2c³ = bc + a
C) b³ = bc – a
D) a³ = bc + a
Answer:
A) 2a³ = ab – c

Question 43.
If the polynomial f(x) = px³ + qx – r is divisible by the polynomial g(x) = x² + qx + b, then pq = ………………. .
A) \(\frac{1}{\mathrm{a}}\)
B) 1
C) \(\frac{1}{\mathrm{b}}\)
D) -1
Answer:
B) 1

Question 44.
If one root of the polynomial p(x) = 5x² + 13x + a is reciprocal of the other, then the value of a is ……………… .
A) -5
B) 0
C) -6
D) 5
Answer:
D) 5

Question 45.
If α, β, γ are the zeroes of the polynomial f(x) = px³ + qx² + rx + s, then \(\frac{1}{\alpha}\) + \(\frac{1}{\beta}\) + \(\frac{1}{\gamma}\) = …………… .
A) –\(\frac{\underline{q}}{\mathrm{~s}}\)
B) –\(\frac{\underline{r}}{\mathrm{~s}}\)
C) \(\frac{\underline{r}}{\mathrm{~s}}\)
D) \(\frac{\underline{q}}{\mathrm{~s}}\)
Answer:
B) –\(\frac{\underline{r}}{\mathrm{~s}}\)

Question 46.
If α, β are the zeroes of the polynomial g(x) = px² + qx + r, then \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}\) = …………… .
A) \(\frac{\mathrm{q}^2+2 \mathrm{pr}}{\mathrm{p}^2}\)
B) \(\frac{q^2-2 p r}{q^2}\)
C) \(\frac{\mathrm{q}^2-2 \mathrm{pr}}{\mathrm{r}^2}\)
D) \(\frac{p^2-2 p q}{p^2}\)
Answer:
C) \(\frac{\mathrm{q}^2-2 \mathrm{pr}}{\mathrm{r}^2}\)

Question 47.
If two of the zeroes of the cubic polynomial ax³ + bx² + cx + d are each
equal to zero, then the third zero is ……………. .
A) \(\frac{b}{a}\)
B) \(\frac{c}{d}\)
C) –\(\frac{d}{c}\)
D) –\(\frac{b}{a}\)
Answer:
D) –\(\frac{b}{a}\)

Question 48.
If two zeroes of x³ + x² – 5x – 5 are √5 and – √5, then the third zero is ………………. .
A) 5
B) -√5
C) -1
D) -2
Answer:
C) -1

Question 49.
The product of the zeroes of x³ + 4x² + x – 6 is ……………. .
A) 6
B) -6
C) 4
D) -4
Answer:
A) 6

Question 50.
What should be subtracted to the polynomial x² – 16x + 30, so the 15 is the zero of the resulting polynomial ?
A) 12
B) 15
C) -6
D) -8
Answer:
B) 15

Question 51.
The polynomial which when divided by – x² + x – 1 gives a quotient x – 2 and remainder 3, is …………….. .
A) x³ + 3x² – 3x + 5
B) -x³ + 3x² – 3x + 5
C) x³ + 5x² – 5x + 2
D) -x³ – 3x² + 5x + 5
Answer:
B) -x³ + 3x² – 3x + 5

Question 52.
The quadratic polynomial having 2, 3 as zeroes is ……………. .
A) x² – 5x – 6
B) x² + 5x + 6
C) x² – 5x + 6
D) x² + 5x – 6
Answer:
C) x² – 5x + 6

Question 53.
Which of the following has only one zero ?
A) p(x) = 2x² – 3x + 4
B) p(x) = x² – 2x + 1
C) p(x) = 2x + 3
D) p(x) = 5
Answer:
C) p(x) = 2x + 3

Question 54.
Observe the given rectangular figure, then its area in polynomial function is ……………… .

A) A(x) = x² + 7x + 30
B) A(x) = – x² + 7x + 30
C) A(x) = x² – 7x + 30
D) A(x) = – x² – 7x + 30
Answer:
B) A(x) = – x² + 7x + 30

Question 55.
The following is the graph of a polynomial. Find the zeroes of the polynomial from the given graph.

A) -2, 3
B) 1,3
C) -2, 1
D) 3, 0
Answer:
C) -2, 1

Question 56.
The coefficient of x⁷ in the polynomial 7x¹⁷ – 17x¹¹ + 27x⁵ – 7 is ……………….. .
A) -1
B) 0
C) 7
D) 17
Answer:
B) 0

Question 57.
The quadratic polynomial having \(\frac{1}{3}\) and \(\frac{1}{2}\) as its zeroes, is ……………… .
A) x² + \(\frac{5 x+1}{6}\)
B) – 6x² – 5x + 1
C) x² – \(\frac{5 x-1}{6}\)
D) 6x² – 5x – 1
Answer:
C) x² – \(\frac{5 x-1}{6}\)

Question 58.
Sum of zeroes of a polynomial x³ – 2x² + 3x – 4 is ……………… .
A) -2
B) 2
C) 1
D) 4
Answer:
B) 2

Question 59.
The number of zeros of the polynomial, whose graph is given below.

A) 0
B) 1
C) 2
D) 3
Answer:
D) 3

Question 60.
The value of x, which satisfies 2 (x – 1) – (1 – x) = 2x + 3
A) 2
B) 4
C) 6
D) 8
Answer:
C) 6

Question 61.
If the polynomial p(x) = x³ – x² + 3x + k is divided by (x – 1), the remainder ob-tained is 3, then the value of k is
A) 0
B) 1
C) 3
D) -3
Answer:
A) 0

Question 62.
In a division, if divisor is x + 1, quotient is x and remainder is 4, then dividend is
A) x² + x
B) 4(x + 1) + x
C) x(x + 1) + 4
D) 4x + 4
Answer:
C) x(x + 1) + 4

Question 63.
If α, β are the zeroes of the polynomial x² + 5x + k and α – β = 3, then the value of k.
A) 6
B) 9
C) 5
D) 4
Answer:
D) 4

Question 64.
If p(x) = x² – 4x + 5, then the value of P(1)is
A) -1
B) 0
C) 1
D) 2
Answer:
D) 2

Question 65.
From the graph, the zeroes of the polynomial are ………………. .

A) -2
B) 0
C) 2
D) All the above
Answer:
D) All the above

Question 66.
If the polynomial p(x) = x⁴ – 2x³ + x² – 1 is divided by (x +1), then the degree of quotient polynomial.
A) 1
B) 3
C) 4
D) 2
Answer:
B) 3

Question 67.
The coefficient of x3 in the polynomial 2x⁴ – 5x³ + 6x² + 5 is …………….. .
A) -5
B) 5
C) 6
D) 2
Answer:
A) -5

Question 68.
If x⁴ + 3x² + 7 is divided by x + 3, then the possible degrees of quotient and remainder are ……………….. .
A) 3, 0
B) 4, 1
C) 3, 1
D) 4, 0
Answer:
A) 3, 0

Question 69.
If the zeroes of the polynomial x² + (a + 1) x + b are 2 and – 3, then the value of a and b are ………… .
A) a = – 5, b = – 1
B) a = 5, b = – 1
C) a = – 2, b = 6
D) a = 0, b = – 6
Answer:
D) a = 0, b = – 6

Question 70.
If p(x) = 5x⁴ + 6x² + 3x – 7, then p(0) is ……………… .
A) 5
B) 3
C) 6
D) -7
Answer:
D) -7

10th Class Maths Bits