10th Class Mathematics Polynomials Question Bank

done Case Based MCQs - Polynomials Total Questions - 30

• question_answer1)

  Directions: Q. 1 to 5

  While playing in garden, Rohit saw a Nest and asked her elder brother what is that he replied that it's a nest made by bird to live themselves. Also he told him that the shape of the nest formed is parabolic. The mathematical representation of the nest structure is shown in the graph.

  Based on the above information, answer the following questions.

  Graph of a quadratic polynomial is ___ in shape.
  A)
  straight line done clear
  B)
  parabolic done clear
  C)
  circular done clear
  D)
  None of these done clear
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• question_answer2)
  The expression of the polynomial represented by the graph is
  A)
  \[{{x}^{2}}-49\] done clear
  B)
  \[{{x}^{2}}-64\] done clear
  C)
  \[{{x}^{2}}-36\] done clear
  D)
  \[{{x}^{2}}-81\] done clear
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• question_answer3)
  Find the value of the polynomial represented by the graph when x = 8
  A)
  - 2 done clear
  B)
  - 1 done clear
  C)
  0 done clear
  D)
  1 done clear
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• question_answer4)
  The sum of zeroes of the polynomial \[{{x}^{2}}-2x-4\]is
  A)
  -1 done clear
  B)
  -2 done clear
  C)
  2 done clear
  D)
  1 done clear
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• question_answer5)
  If the sum of zeroes of polynomial \[a{{x}^{2}}+5x-3a\]is equal to their product, then find the value of a
  A)
  -5 done clear
  B)
  -3 done clear
  C)
  \[-\frac{5}{3}\] done clear
  D)
  \[\frac{5}{3}\] done clear
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• question_answer6)
   

  Directions: Q. 6 to 10

  The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial.

  A parabolic arch is an arch in the shape of a parabola.

  In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.  [CBSE Question Bank]

  Based on the above information, answer the following questions.

  In the standard form of quadratic polynomial, \[a{{x}^{2}}+bx+c,\,\]a, b and c are
  A)
  AII are real numbers done clear
  B)
  AII are rational numbers. done clear
  C)
  'o' is a non-zero real number, band care any real numbers. done clear
  D)
  All are integers. done clear
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• question_answer7)
  If the roots of the quadratic polynomial are equal, where the discriminant \[D={{b}^{2}}-4ac\], then
  A)
  \[D>0\] done clear
  B)
  \[D<0\] done clear
  C)
  \[D\,\underline{>}\,0\] done clear
  D)
  D=0 done clear
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• question_answer8)
  If \[\alpha \] and \[\frac{1}{\alpha }\]are the zeroes of the quadratic polynomial \[2{{x}^{2}}-x+8k\]then k is
  A)
  4 done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{-1}{4}\] done clear
  D)
  2 done clear
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• question_answer9)
  The graph of \[{{x}^{2}}+1=0\]
  A)
  Intersects X-axis at two distinct points. done clear
  B)
  Touches X-axis at a point. done clear
  C)
  Neither touches nor intersects X-axis. done clear
  D)
  Either touches or intersects X-axis. done clear
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• question_answer10)
  If the sum of the roots is - p and product of the roots is \[-\frac{1}{p}\], then the quadratic polynomial is
  A)
  \[k\left( -p{{x}^{2}}+\frac{x}{p}+1 \right)\] done clear
  B)
  \[k\left( p{{x}^{2}}-\frac{x}{p}-1 \right)\] done clear
  C)
  \[k\left( {{x}^{2}}+px-\frac{1}{p} \right)\] done clear
  D)
  \[k\left( {{x}^{2}}-px+\frac{1}{p} \right)\] done clear
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• question_answer11)
   

  Directions: Q. 11 to 15

  Nirahua's father gave him some money to buy papaya from the market at the rate of\[p\left( x \right)={{x}^{2}}-23x+120\]. Let \[\alpha ,\,\beta \] are the zeroes of \[p\left( x \right)\].

  Based on the above information, answer the following questions.

  Find the value of \[\alpha \] and \[\beta \], where \[\alpha <\beta \]
  A)
  -8,-16 done clear
  B)
  8,16 done clear
  C)
  8,15 done clear
  D)
  4,9 done clear
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• question_answer12)
  Find the value of \[\alpha +\beta +\alpha \beta \]
  A)
  151 done clear
  B)
  158 done clear
  C)
  143 done clear
  D)
  155 done clear
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• question_answer13)
  The value of \[p\left( 2 \right)\] is
  A)
  80 done clear
  B)
  81 done clear
  C)
  83 done clear
  D)
  78 done clear
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• question_answer14)
  If a and P are zeroes of \[{{x}^{2}}+3x-10\]then \[\frac{1}{\alpha }+\frac{1}{\beta }=\]
  A)
  3/10 done clear
  B)
  1/3 done clear
  C)
  1/4 done clear
  D)
  1/5 done clear
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• question_answer15)
  If sum of zeroes of \[q\left( x \right)=k{{x}^{2}}+2x+3k\]is equal to their product, then k =
  A)
  2/3 done clear
  B)
  1/3 done clear
  C)
  -2/3 done clear
  D)
  -1/3 done clear
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• question_answer16)
   

  Directions: Q. 16 to 20

  An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

  Based on the above information, answer the following questions.

  The shape of the poses shown is
  A)
  Spiral done clear
  B)
  Ellipse done clear
  C)
  Linear done clear
  D)
  Parabola done clear
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• question_answer17)
  The graph of parabola opens downwards, if .............
  A)
  \[a\,\underline{>}\,0\] done clear
  B)
  \[a=0\] done clear
  C)
  \[a<0\] done clear
  D)
  \[a>0\] done clear
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• question_answer18)

  In the graph, how many zeroes are there for the polynomial?

  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
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• question_answer19)

  The two zeroes in the below shown graph are

   
  A)
  2,4 done clear
  B)
  -2, 4 done clear
  C)
  -8,4 done clear
  D)
  2,-8 done clear
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• question_answer20)
  The zeroes of the quadratic polynomial \[4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}\] are
  A)
  \[\frac{2}{\sqrt{3}},\frac{\sqrt{3}}{4}\] done clear
  B)
  \[-\frac{2}{\sqrt{3}},\frac{\sqrt{3}}{4}\] done clear
  C)
  \[\frac{2}{\sqrt{3}},-\frac{\sqrt{3}}{4}\] done clear
  D)
  \[-\frac{2}{\sqrt{3}},-\frac{\sqrt{3}}{4}\] done clear
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• question_answer21)
   

  Directions: Q. 21 to 25

  Two friend, Aanchal and Amarjeet during their summer vacations went to Rishikesh. They decided to go for trekking. While trekking they observes that the trekking path is in the shape of a parabola. The mathematical representation of the track is shown in the graph.

  Based on the above information, answer the following questions.

  The zeroes of the polynomial whose graph is given are.

  A)
  4, 7 done clear
  B)
  -4, 7 done clear
  C)
  4, 3 done clear
  D)
  -7, 10 done clear
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• question_answer22)
  What will be the expression of the given polynomial p(x)
  A)
  \[{{x}^{2}}-3x-70\] done clear
  B)
  \[-{{x}^{2}}+4x+28\] done clear
  C)
  \[{{x}^{2}}-4x+28\] done clear
  D)
  \[-{{x}^{2}}+3x+28\] done clear
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• question_answer23)
  Product of zeroes of the given polynomial is
  A)
  -28 done clear
  B)
  28 done clear
  C)
  -70 done clear
  D)
  30 done clear
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• question_answer24)
  The zeroes of the polynomial \[9{{x}^{2}}-5\] are
  A)
  \[\frac{3}{\sqrt{5}},\frac{-3}{\sqrt{5}}\] done clear
  B)
  \[\frac{2}{\sqrt{5}},\frac{-2}{\sqrt{5}}\] done clear
  C)
  \[\frac{\sqrt{5}}{3},\frac{-\sqrt{5}}{3}\] done clear
  D)
  \[\frac{\sqrt{5}}{2},\frac{-\sqrt{5}}{2}\] done clear
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• question_answer25)
  If\[f\left( x \right)={{x}^{2}}-13x+1\], then \[f\left( 3 \right)\] is
  A)
  35 done clear
  B)
  -29 done clear
  C)
  36 done clear
  D)
  -36 done clear
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• question_answer26)

  Directions: Q. 26 to 30

  Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

  Based on the above information, answer the following questions.

  The shape of the path traced shown is
  A)
  Spiral done clear
  B)
  Ellipse done clear
  C)
  Linear done clear
  D)
  Parabola done clear
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• question_answer27)
  The graph of parabola opens downwards, if............ .
  A)
  \[a=0\] done clear
  B)
  \[a<0\] done clear
  C)
  \[a>0\] done clear
  D)
  \[a\underline{>}0\] done clear
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• question_answer28)

  Observe the following graph and answer.

  In the above graph, how many zeroes are there for the polynomial?

   
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3                           done clear
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• question_answer29)
  The three zeroes in the above shown graph are
  A)
  2, 3, -1 done clear
  B)
  -2, 3, 1 done clear
  C)
  -3, -1, 2 done clear
  D)
  -2, -3, -1 done clear
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• question_answer30)
  What will be the expression of the polynomial?
  A)
  \[{{x}^{3}}+2{{x}^{2}}-5x-6\] done clear
  B)
  \[{{x}^{3}}+2{{x}^{2}}-5x+6\] done clear
  C)
  \[{{x}^{3}}+2{{x}^{2}}+5x-6\] done clear
  D)
  \[{{x}^{3}}+2{{x}^{2}}+5x+6\] done clear
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