9th Class Mathematics blank Question Bank

done Algebra and Co-ordinate Geometry Total Questions - 40

• question_answer1)
  Which one of the following is a polynomial?
  A)
  \[\frac{{{x}^{3}}}{9}-\frac{3}{{{x}^{-\,3}}}+\sqrt{x}\] done clear
  B)
                                             \[{{x}^{3}}-\frac{3{{x}^{7/3}}}{^{3}\sqrt{x}}+\frac{{{x}^{-\,1/2}}}{{{x}^{1/2}}}\] done clear
  C)
  \[{{x}^{2}}-3\sqrt{5x}+\sqrt{2}+{{x}^{-\,1}}\] done clear
  D)
                                \[\frac{{{x}^{3/2}}}{{{x}^{1/2}}}+\frac{2{{x}^{7/5}}}{{{x}^{2/5}}}+\frac{8{{x}^{2}}}{{{x}^{-1}}}\] done clear
  E)
              None of these done clear
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• question_answer2)
  If \[A{{x}^{n}}+B{{x}^{n-2}}+C{{x}^{n-8}}+D\]is a polynomial such that \[\mathbf{A + B + C + D = 0}\] degree of the polynomial is ___________
  A)
  n                      done clear
  B)
                                             0 done clear
  C)
  1                      done clear
  D)
                                             not defined done clear
  E)
  None of these done clear
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• question_answer3)
  Which among the following statements is true?
  A)
  \[\sqrt{3}x+\frac{{{x}^{4}}}{x}+5{{x}^{2}}\] is a quadratic polynomial done clear
  B)
  Every real number is a zero of the zero polynomial. done clear
  C)
  A non-zero constant polynomial has one zero. done clear
  D)
  The degree of the polynomial, \[P(x)=\frac{\sqrt{3{{x}^{n}}}}{{{x}^{n-5}}}+\frac{\sqrt{5}{{x}^{n-2}}}{{{x}^{n-3}}}-\frac{7}{2}\frac{{{x}^{n-9}}}{{{x}^{n-15}}}+ {{x}^{4}}+ 8{{x}^{3}} + 5x + 2\]is 5 done clear
  E)
         None of these done clear
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• question_answer4)
  \[7{{8}^{3}} - 3{{3}^{3}} - 4{{5}^{3}}\] is equal to
  A)
  347490              done clear
  B)
                     247280  done clear
  C)
  387490                                                  done clear
  D)
  387280 done clear
  E)
  None of these done clear
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• question_answer5)
  One of the factors of \[(225{{x}^{2}} - 1)\text{ }+\text{ }{{(1\text{ }+ 15x)}^{2}}\] is
  A)
  \[(15x-1)\]          done clear
  B)
                                 \[(5x+1)\] done clear
  C)
   \[(5x-1)\]           done clear
  D)
                                             30x done clear
  E)
  None of these done clear
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• question_answer6)
  \[{{\mathbf{(}\sqrt{\mathbf{P}}\mathbf{-}\sqrt{\mathbf{Q}}\mathbf{)}}^{\mathbf{3}}}\mathbf{+(}\sqrt{\mathbf{Q}}\mathbf{-}\sqrt{\mathbf{R}}{{\mathbf{)}}^{\mathbf{3}}}\mathbf{+(}\sqrt{\mathbf{R}}\mathbf{-}\sqrt{\mathbf{P}}{{\mathbf{)}}^{\mathbf{3}}}\] equals to _______
  A)
  \[3(P-Q)(Q-R)(R-P)\] done clear
  B)
  \[3(\sqrt{P}-\sqrt{Q})(\sqrt{Q}-\sqrt{R})(\sqrt{R}-\sqrt{P})\] done clear
  C)
  \[\sqrt{3}(\sqrt{P}-\sqrt{Q})(\sqrt{Q}-\sqrt{R})(\sqrt{R}-\sqrt{P})\] done clear
  D)
  All the above done clear
  E)
  None of these done clear
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• question_answer7)
  Find the square root of \[4{{a}^{6}}-12{{a}^{5}}+9{{a}^{4}}+8{{a}^{3}}-12{{a}^{2}}+4\]
  A)
  \[{{a}^{3}}-3{{a}^{2}}+2\]  done clear
  B)
                                 \[2{{a}^{3}}+3{{a}^{2}}-2\] done clear
  C)
  \[2{{a}^{3}}-3{{a}^{2}}+2\] done clear
  D)
                                 \[2{{a}^{3}}+3{{a}^{2}}+2\] done clear
  E)
  None of these done clear
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• question_answer8)
  The LCM and HCF of the polynomials  \[\mathbf{p(x)=51 }{{\mathbf{x}}^{\mathbf{2}}}\mathbf{ (x+3}{{\mathbf{)}}^{\mathbf{3}}}\mathbf{ (x-2}{{\mathbf{)}}^{\mathbf{2}}}\] and \[\mathbf{q(x)=34x (x-1}{{\mathbf{)}}^{\mathbf{5}}}\mathbf{ (x-2}{{\mathbf{)}}^{\mathbf{3}}}\] are respectively.
  A)
          \[102{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}} and  17{{x}^{2}}{{(x-2)}^{2}}\] done clear
  B)
  \[204{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}} and  17x(x-2)\] done clear
  C)
  \[102{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{3}}{{(x+3)}^{3}} and  17x{{(x-2)}^{2}}\] done clear
  D)
  \[102{{x}^{2}} {{(x-1)}^{5}}{{(x-2)}^{2}}{{(x+3)}^{3}} and  17x{{(x-2)}^{2}}\] done clear
  E)
  None of these done clear
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• question_answer9)
  If  \[\frac{\mathbf{p}}{\mathbf{q}}\mathbf{+}\frac{\mathbf{q}}{\mathbf{p}}\mathbf{=-1}\], then find the  value of \[{{\mathbf{p}}^{\mathbf{3}}}\mathbf{-}{{\mathbf{q}}^{\mathbf{3}}}\] _______
  A)
  0          done clear
  B)
                                                         2pq done clear
  C)
  1          done clear
  D)
                                                         -1 done clear
  E)
  None of these done clear
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• question_answer10)
  \[\sqrt{\mathbf{(}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-x-2)(2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+5x+3)(2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-x-6)}}\]equals to ________
  A)
  \[(x-1)(x+2)(x-3)\]           done clear
  B)
                     \[(x+1)(x-2)(x-3)\] done clear
  C)
  \[(x+1)(2x+3)(x-2)\] done clear
  D)
                     \[(x-1)(x+2)(2x+3)\] done clear
  E)
  None of these done clear
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• question_answer11)
  If \[\sqrt{3{{x}^{4}}-4\sqrt{3}{{x}^{3}}-2{{x}^{2}}+4\sqrt{3}x+3}\]\[=(a{{x}^{2}}+bx+c)\] Then which one of the following is incorrect?
  A)
  a and b are of different sign done clear
  B)
                     \[{{b}^{2}}+2ac=2\] done clear
  C)
  \[2bc=4\sqrt{3}\]           done clear
  D)
                                             \[ab=-\,2\sqrt{3}\]          done clear
  E)
  None of these done clear
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• question_answer12)
  Factorize: \[{{\mathbf{p}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{3}}}\mathbf{+3pq-1}\]
  A)
   \[(p-q+1)({{p}^{2}}+{{q}^{2}}-pq)\] done clear
  B)
         \[(p+q-1)({{p}^{2}}+{{q}^{2}}+1-pq+q+p)\] done clear
  C)
  \[{{(p-1)}^{3}}(p+q)\]                                      done clear
  D)
  \[{{(p-1)}^{3}}(p-q)\] done clear
  E)
  None of these done clear
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• question_answer13)
  If \[{{\mathbf{x}}^{\mathbf{4}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x+b}\]is exactly divisible by  \[\mathbf{(x+2)}\] as well as \[\mathbf{(x-2)}\] then ______
  A)
  \[a+b=1\] done clear
  B)
                                             \[a+2b=5\]        done clear
  C)
  \[a=b+1\]         done clear
  D)
                                 All the above done clear
  E)
  None of these done clear
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• question_answer14)
  If \[\mathbf{p(x)=}{{\mathbf{x}}^{\mathbf{6}}}\mathbf{-7}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-8}\] then which of the following is /are factor(s) of p(x)?
  A)
  \[{{x}^{2}}+2x+4\] done clear
  B)
                                             \[{{x}^{2}}-x+1\] done clear
  C)
  both A and B     done clear
  D)
                                 \[(x+2)\] done clear
  E)
  None of these done clear
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• question_answer15)
  \[{{\mathbf{l}}^{\mathbf{3}}}{{\mathbf{(m-n)}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{m}}^{\mathbf{3}}}{{\mathbf{(n-l)}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{n}}^{\mathbf{3}}}{{\mathbf{(l-m)}}^{\mathbf{3}}}\]equals to _________
  A)
  \[{{(lmn)}^{3}}(l-m)(m-n)(n-l)\] done clear
  B)
                                 \[(lm+mn+nl)(3{{l}^{2}}{{m}^{2}}{{n}^{2}})\] done clear
  C)
  \[3lmn(m-n)(n-l)(l-m)\] done clear
  D)
                                 0 done clear
  E)
  None of these done clear
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• question_answer16)
  If P and Q are two polynomials of degree 5 and 4 respectively, then find the degree of\[\mathbf{P-Q}\].
  A)
  1                                                                      done clear
  B)
  5 done clear
  C)
  4                      done clear
  D)
                                             Cannot be determined done clear
  E)
  None of these done clear
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• question_answer17)
  The square root of \[{{\mathbf{(ab+ac-bc)}}^{\mathbf{2}}}\mathbf{-4abc(a-b)}\]is ________
  A)
  \[(bc+ca-ab)\]                                       done clear
  B)
  \[(ab+bc-ca)\] done clear
  C)
  \[(ab+bc+ca)\] done clear
  D)
                                             \[(ab-bc+ca)\] done clear
  E)
  None of these done clear
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• question_answer18)
  Which one among the following statements is/ are correct?
  A)
  Point \[(-\,5, 0)\]lies in the II quadrant. done clear
  B)
  A point lies on x-axis at a distance of 5 units from y-axis, Its coordinate can be \[(-\,5, 0)\] or \[(5, 0)\] done clear
  C)
  A point lies on y-axis lies on y-axis at a distance of 3 units from the x-axis. Its coordinate are \[(3, 0)\] done clear
  D)
  All the above done clear
  E)
  None of these done clear
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• question_answer19)
  The perpendicular distance of the point \[\mathbf{(6, -8)}\] from the x-axis is _______
  A)
  8 Units done clear
  B)
  6 units done clear
  C)
  10 units             done clear
  D)
                                             2 units  done clear
  E)
  None of these done clear
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• question_answer20)
  In the graph as shown, the equation of the line l is
  A)
  \[x=-\,3\] done clear
  B)
                                             \[y=-\,3\] done clear
  C)
  \[x-3=0\]           done clear
  D)
                                             \[y-3=0\] done clear
  E)
  None of these done clear
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• question_answer21)
  A line passes through the points \[\mathbf{A(-2, -2),}\]  \[\mathbf{B(-5, -5)}\]and \[\mathbf{C(-10, -10)}\]. The equation of this line will be ________
  A)
  \[x+y=0\]         done clear
  B)
                                             \[x-y=0\] done clear
  C)
  \[x= -y\]            done clear
  D)
                                             \[x= y+1\] done clear
  E)
  None of these done clear
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• question_answer22)
  The equation of a line passing through the points \[\mathbf{(-6, -4)}\] \[\mathbf{(0, 2)}\] and \[\mathbf{(-2,  0)}\] is _________
  A)
  \[y+x=2\]         done clear
  B)
                                             \[y-x=2\] done clear
  C)
  \[x-y=2\]           done clear
  D)
                                             \[x+y=-\,2\] done clear
  E)
  None of these done clear
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• question_answer23)
  The area of a square whose opposite vertices are \[\mathbf{(0, 0)}\]and \[\mathbf{(6,  6)}\]is _______
  A)
  \[36\text{ }unit{{s}^{2}}\]  done clear
  B)
                                                                                        \[30\text{ }unit{{s}^{2}}\] done clear
  C)
  \[34\text{ }unit{{s}^{2}}\]                                                        done clear
  D)
  Cannot be determined done clear
  E)
  None of these done clear
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• question_answer24)
  If a straight line \[\mathbf{ax+by=c}\] cuts x and y-axis at the points P and Q, then the area of the triangle OPQ where O is the point of intersection of coordinate axes, is _________
  A)
  \[\frac{{{a}^{2}}}{2bc}\]         done clear
  B)
                                             \[\frac{{{c}^{2}}}{2ab}\] done clear
  C)
  \[\frac{2ac}{{{b}^{2}}}\]         done clear
  D)
                                 \[\frac{2ac}{{{c}^{2}}}\] done clear
  E)
  None of these done clear
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• question_answer25)
  In a group of cows and hens m the total number of legs is 12 more than twice the total number of heads. The number cows is  __________
  A)
  2          done clear
  B)
                                             4 done clear
  C)
  6          done clear
  D)
                                                         Cannot be determined done clear
  E)
  None of these done clear
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• question_answer26)
  In a fraction, if numerator is increased by 2 and denominator is increased by 3, it becomes \[\frac{\mathbf{3}}{\mathbf{4}}\] and if numerator is decreased by 3 and denominator is decreased by 6, it becomes\[\frac{\mathbf{4}}{\mathbf{3}}\]. Find the sum of the numerator and denominator.
  A)
  12                                                         done clear
  B)
  15 done clear
  C)
  19         done clear
  D)
                                                         16 done clear
  E)
              None of these done clear
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• question_answer27)
  Any solution of the linear equation \[\mathbf{-7x+0}\mathbf{.y-14=0}\]in two variables is of the form ________
  A)
  \[(-\,2, 0)\]          done clear
  B)
                                             \[(-\,2, n)\] done clear
  C)
  \[(0, -2)\]            done clear
  D)
                                             \[(n, -2)\] done clear
  E)
  None of these done clear
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• question_answer28)
  The equation \[\mathbf{5x-3y-2=0}\]has a unique solution, if x, y are _________
  A)
  Rational numbers done clear
  B)
                                            Real numbers  done clear
  C)
  Integers  done clear
  D)
                                             Natural numbers done clear
  E)
  None of these done clear
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• question_answer29)
  The graph of \[\frac{\mathbf{5x}}{\mathbf{2}}\mathbf{=7+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{x-15}\] is a line _________
  A)
  parallel  to x-axis at a distance  of 4 units from the origin. done clear
  B)
  parallel to y-axis at a distance of 8 units from the origin. done clear
  C)
  making an intercept 4 on the y-axis. done clear
  D)
  making an intercept 4 on the y-axis done clear
  E)
  None of these done clear
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• question_answer30)
  The solution of a linear equation does not remain same when
  A)
  we add same number in both sides of the equation. done clear
  B)
  parallel to y-axis at a distance of 8 units from the origin.      done clear
  C)
  we multiply both sides of the equation by zero. done clear
  D)
  we divide both sides of the equation by same non zero number. done clear
  E)
              None of these done clear
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• question_answer31)
  \[\mathbf{x=-5}\] and \[\mathbf{y=1}\] is a solution of the linear equation _______     
  A)
  \[x-2y= 7\]                                            done clear
  B)
  \[3y-x=-\,8\] done clear
  C)
  \[6y-x=11\] done clear
  D)
                                                         \[3x=15y\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  Which among the following is not a solution of the equation \[\mathbf{-7x+2y=-}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{x-}\frac{\mathbf{3}}{\mathbf{2}}\mathbf{y+5}\]
  A)
  \[(3, 7)\] done clear
  B)
                                             \[(-\,4, -6)\] done clear
  C)
  \[(9, 18)\]           done clear
  D)
                                             \[(4, \frac{62}{7})\] done clear
  E)
  None of these done clear
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• question_answer33)
  The coordinates given in following table represents the solution of the equation _______.

  X	4	7	1	-2
  Y	5	9	1	-3

  A)
  \[3y=4x+2\] done clear
  B)
                                             \[3y+4x=1\] done clear
  C)
  \[4x-3y=1\]        done clear
  D)
                                             \[4x-8y=9\] done clear
  E)
  None of these done clear
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• question_answer34)
  If the point \[\mathbf{(-3, 8)}\] lies on the line \[\mathbf{3y-7x+a=0}\], then the value of \[\frac{\mathbf{3a}}{\mathbf{5}}\] is _________ .
  A)
  27                     done clear
  B)
                                             \[-\]27 done clear
  C)
  18                     done clear
  D)
                                             \[-\]18 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  For what value of k, the linear equation \[\mathbf{3x-ky=9}\] has equal values of x and y for its solution.
  A)
  \[\frac{9-3x}{2}\]           done clear
  B)
                                             \[\frac{3x+9}{x}, x\ne 0\] done clear
  C)
  0                      done clear
  D)
                                             \[\frac{3x-9}{x}, x\ne 0\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  The point on the graph of the linear equation \[\mathbf{6x+5y=18}\], whose ordinate is \[\mathbf{3}\frac{\mathbf{1}}{\mathbf{2}}\] times its abscissa, is _______
  A)
  \[\left( \frac{16}{19},\frac{56}{19} \right)\]          done clear
  B)
                                             \[\left( \frac{36}{19},\frac{126}{19} \right)\] done clear
  C)
  \[\left( \frac{36}{47},\frac{126}{47} \right)\]         done clear
  D)
                                             \[\left( \frac{18}{47},\frac{63}{47} \right)\] done clear
  E)
  None of these done clear
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• question_answer37)
  The point, at which the graph of the linear equation \[\mathbf{x-y=9}\]meets a line which is parallel to the y-axis, at a distance of 3 units from the origin and in the positive direction of x-axis, is _______
  A)
  \[(3, 0)\]             done clear
  B)
                                             \[(-\,3, 6)\] done clear
  C)
  \[(6, -3)\]            done clear
  D)
                                             \[(3, -6)\] done clear
  E)
  None of these done clear
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• question_answer38)
  The point on the graph of the equation \[\mathbf{3x+4y=15}\] whose abscissa is \[\frac{\mathbf{3}}{\mathbf{4}}\] times its ordinate, is  
  A)
  \[\left( \frac{12}{5},\frac{9}{5} \right)\]    done clear
  B)
                                 \[\left( \frac{9}{5},\frac{12}{5} \right)\] done clear
  C)
  \[\left( \frac{12}{5},\frac{9}{20} \right)\] done clear
  D)
                                                         \[\left( \frac{9}{20},\frac{15}{5} \right)\] done clear
  E)
  None of these done clear
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• question_answer39)

  Directions: The temperature of a liquid can be measured in kelvin units as\[\mathbf{x{}^\circ K}\] or in Fahrenheit units Units as\[\mathbf{y{}^\circ F}\], the relation between the two system of measurement of temperature is given by the linear equation\[\mathbf{y-32=}\frac{\mathbf{9}}{\mathbf{2}}\mathbf{(x-273)}\]. Based on this information, answer the following questions:

  Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is \[\mathbf{333{}^\circ K}\]
  A)
  \[-\,140{}^\circ F\]         done clear
  B)
                                             \[140{}^\circ F\] done clear
  C)
  \[158{}^\circ F\]            done clear
  D)
                                             \[-\,158{}^\circ F\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer40)

  Directions: The temperature of a liquid can be measured in kelvin units as\[\mathbf{x{}^\circ K}\] or in Fahrenheit units Units as\[\mathbf{y{}^\circ F}\], the relation between the two system of measurement of temperature is given by the linear equation\[\mathbf{y-32=}\frac{\mathbf{9}}{\mathbf{2}}\mathbf{(x-273)}\]. Based on this information, answer the following questions:

  If at a value, the temperature in Fahrenheit     equals to temperature in kelvin then this value is ________
  A)
  374.25  done clear
  B)
                                             574.25 done clear
  C)
  385                   done clear
  D)
                                             485 done clear
  E)
  None of these     done clear
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