9th Class Mathematics Linear Equations in Two Variables Question Bank

done Linear Equations in Two Variables Total Questions - 51

• question_answer1)
  How many line(s) pass through the point\[(0,\,\,0)\]?
  A)
   Only one                      done clear
  B)
   Two                 done clear
  C)
          Infinitely many done clear
  D)
          Three               done clear
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• question_answer2)
  Which of the following is true about\[y=4x-3\]?
  A)
   It has a unique solution. done clear
  B)
   It has only two solutions. done clear
  C)
   It has infinitely many solutions. done clear
  D)
   It is a linear equation in one variable. done clear
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• question_answer3)
  If \[x=-2\] and \[y=3\] is the solution of the equation\[3x-5y=k\], find\['k'\].
  A)
   \[-21\]                           done clear
  B)
   \[-9\]                done clear
  C)
   \[-18\]               done clear
  D)
          \[19\]                done clear
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• question_answer4)
  What does an equation of the form\[ax+by+c=0\], where \[a\] and \[b\] are non-zero numbers represent?
  A)
   A straight line   done clear
  B)
          A circle done clear
  C)
   A triangle          done clear
  D)
          A quadrilateral               done clear
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• question_answer5)
  Which of the following is the equation of a line parallel to\[y\text{-}\]axis?
  A)
  \[y=-2\]             done clear
  B)
  \[y=0\]  done clear
  C)
         \[y=5\]              done clear
  D)
         \[x=-4\]             done clear
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• question_answer6)
  What is the equation of \[X\text{-}\]axis?
  A)
  \[x=0\]              done clear
  B)
  \[x=-2\] done clear
  C)
         \[y=0\]              done clear
  D)
         \[y=-2\]             done clear
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• question_answer7)
  For which condition does the equation \[px+qy+r=0\] represent a linear equation in two variables?
  A)
  \[p\ne 0,\,\,q=0\]                        done clear
  B)
  \[q\ne 0,\,\,q=0\] done clear
  C)
  \[p=0,\,\,q=0\]   done clear
  D)
         \[p\ne 0,\,\,q\ne 0\]          done clear
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• question_answer8)
  Which of the following is correct with respect to the line\[x+1=0\]?
  A)
   It is parallel to \[y\text{-}\]axis. done clear
  B)
   It passes through\[(0,\,\,-1)\]. done clear
  C)
   It is parallel to x-axis. done clear
  D)
   It passes through\[(0,\,\,0)\]. done clear
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• question_answer9)
  Which is the equation of a line passing through the origin?
  A)
   \[y=2\]             done clear
  B)
   \[x=4\] done clear
  C)
          \[y=5x\]           done clear
  D)
         \[x=-7\] done clear
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• question_answer10)
  Identify the correct statement from the following with respect to the line\[y-2=0\].
  A)
   It is parallel to X-axis. done clear
  B)
   It is parallel to Y-axis. done clear
  C)
   It passes through the origin. done clear
  D)
   It passes through\[x=2\]. done clear
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• question_answer11)
  If \[(3,\,\,4)\] is a solution of the equation\[5x-2y=k\], find the value of\[k\].
  A)
   \[7\]                             done clear
  B)
   \[6\]     done clear
  C)
   \[5\]                 done clear
  D)
          \[4\] done clear
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• question_answer12)
  If the point \[(2,\,\,-3)\] lies on the graph of the equation\[ay=7x-26\], what is the value of\['a'\]?
  A)
  \[37\]                             done clear
  B)
  \[16\]                 done clear
  C)
  \[-5\]                 done clear
  D)
         \[4\] done clear
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• question_answer13)
  The cost of a shirt of a particular brand is\[Rs.\,\,800\]. What is the linear equation when the cost of x number of shirts is\[Rs.\,\,y\]?
  A)
  \[x=800y\]                     done clear
  B)
  \[x=4\]  done clear
  C)
         \[y=5x\]            done clear
  D)
         \[x=-7\] done clear
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• question_answer14)
  Where does the point of the form \[(p,\,\,p)\forall p\ne 0\] always lie?
  A)
   \[x-\]axis done clear
  B)
   origin done clear
  C)
   on the line\[y=x\] done clear
  D)
   on the line\[x+y=0\] done clear
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• question_answer15)
  What is the solution set of\[\frac{5}{3}-\frac{2}{x}=\frac{8}{x}\]for\[x\ne 0\]?
  A)
  \[\{2\}\]                         done clear
  B)
  \[\left( \frac{18}{5} \right)\]         done clear
  C)
         \[\left( \frac{26}{5} \right)\]         done clear
  D)
         \[\{6\}\]             done clear
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• question_answer16)
  What is the solution set of\[\sqrt{x+64}-8=-2\]?
  A)
  \[\{-28\}\]                      done clear
  B)
  \[\{-124\}\]        done clear
  C)
         \[\{4\}\]             done clear
  D)
         \[\{\}\] done clear
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• question_answer17)
  What are all the roots for the equation\[3|w-14|-6=21\]?
  A)
  \[19\]                             done clear
  B)
  \[23\]                 done clear
  C)
   \[5\] and \[23\] done clear
  D)
         \[9\] and \[19\] done clear
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• question_answer18)
  What is the solution of the equation given below? \[\frac{\mathbf{3y+4}}{\mathbf{2}}\mathbf{+}\frac{\mathbf{2y-5}}{\mathbf{3}}\mathbf{=}\frac{\mathbf{31}}{\mathbf{2}}\]
  A)
  \[y=1\]  done clear
  B)
                     \[y=6\]  done clear
  C)
         \[y=7\]              done clear
  D)
         \[y=13\] done clear
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• question_answer19)
  Veena heard that it is \[{{82}^{o}}\] Fahrenheit in Ooty. She knows that\[F=\frac{9}{5}C+32\], where \[F\] represents the temperature in degrees Fahrenheit and \[C\] represents the temperature in degrees Celsius. Which is closest to the temperature in Ooty, in degrees Celsius?
  A)
  \[28\]                             done clear
  B)
  \[63\]                 done clear
  C)
  \[90\]                 done clear
  D)
         \[180\]               done clear
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• question_answer20)
  Identify the point at which the graph of the equation \[7x-9y-21=0\] cuts \[x\text{-}\]axis.
  A)
  \[(21,\,\,0)\]                    done clear
  B)
  \[(0,\,\,9)\]                 done clear
  C)
         \[(3,\,\,0)\]                      done clear
  D)
         \[(3,\,\,1)\]                      done clear
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• question_answer21)
  Which of the following equations represents a straight line passing through the points \[(1,\,\,6),\,\,(0,\,\,4)\] and\[(-2,\,\,0)\]?
  A)
  \[2x-y=-4\]                    done clear
  B)
  \[x-2y=-4\]        done clear
  C)
         \[2x+y=4\]        done clear
  D)
         \[x+2y=-4\]                   done clear
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• question_answer22)
  Identify the equation of line parallel to \[y\text{-}\]axis and \[5\text{-}\]units away from the origin.
  A)
  \[y=5\]              done clear
  B)
  \[x=-5\] done clear
  C)
  \[x=5\]  done clear
  D)
         \[y=-5\] done clear
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• question_answer23)
  Find the point at which the straight lines represented by linear equations \[x-y=2\] and\[3x-2y=7\] intersect.
  A)
  \[(1,\,\,1)\]                                  done clear
  B)
  \[(1,\,\,3)\]          done clear
  C)
         \[(2,\,\,2)\]                      done clear
  D)
         \[(3,\,\,1)\]                    done clear
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• question_answer24)
    Which of the following is true?
  A)
   The equation of the \[x\text{-}\]axis is\[y=0\]. done clear
  B)
   The graph of every linear equation in two variable is a curve. done clear
  C)
   \[y=3x+5\]has a unique solution. done clear
  D)
   The graph of the equation\[2y-5=0\] is parallel to \[y\text{-}\]axis. done clear
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• question_answer25)
  If the point \[(2p,\,\,p-3)\] lies on the graph of the equation\[3x+2y+12=0\], find the value of\[p\].
  A)
  \[\frac{-3}{4}\] done clear
  B)
  \[\frac{7}{15}\] done clear
  C)
  \[\frac{-1}{6}\] done clear
  D)
         \[\frac{6}{7}\] done clear
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• question_answer26)
  If the expressions \[y-10\] and \[24-y\] are equal, what is the value of\[y\]?
  A)
   \[34\]                            done clear
  B)
   \[14\]                done clear
  C)
   \[17\]                done clear
  D)
          \[12\]                done clear
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• question_answer27)
  How many kilograms of tea at \[50\] per kg should be mixed with \[35\,\,kg\] of tea costing \[Rs.\,\,60\] per kg so as to sell the mixture at \[Rs.\,\,57\] per kg without gaining or losing anything in the transaction?
  A)
  \[5\,\,kg\]                                   done clear
  B)
  \[7\,\,kg\]                       done clear
  C)
  \[25\,\,kg\]          done clear
  D)
         \[15\,\,kg\]          done clear
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• question_answer28)
  Vihan spent \[Rs.\,\,132\] to buy movie tickets for \[20\] children and \[4\] adults. Adult tickets cost \[Rs.\,\,3\] more than child tickets. If \[A\] is the price of an adult ticket and \[S\] is the price of a child ticket, which system of equations could be used to find the price of each adult and child ticket?
  A)
  \[\left\{ \begin{align}   & S=A+3 \\  & 4A+20S=132 \\ \end{align} \right.\]         done clear
  B)
  \[\left\{ \begin{align}   & A=S+3 \\  & 4A+20S=132 \\ \end{align} \right.\] done clear
  C)
         \[\left\{ \begin{align}   & A=S+3 \\  & 20A+4S=132 \\ \end{align} \right.\] done clear
  D)
         \[\left\{ \begin{align}   & A=S+3 \\  & A+S=132 \\ \end{align} \right.\] done clear
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• question_answer29)
  The graph of a system of linear equations is given. Based upon the graph, which is the apparent solution to the system of equations?
  A)
  \[(2,\,\,5)\]                      done clear
  B)
  \[(3,\,\,4)\]          done clear
  C)
         \[(4,\,\,3)\]                      done clear
  D)
         \[(5,\,\,2)\]          done clear
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• question_answer30)
  Find\['x'\]if\[\frac{x-2}{x+3}=\frac{x+2}{x-3},\,\,x\ne 3,\,\,x\ne -3\].
  A)
  \[3\]                              done clear
  B)
  \[0\]                  done clear
  C)
  \[1\]                  done clear
  D)
         \[-2\]                 done clear
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• question_answer31)
  Three consecutive numbers such that twice the first, \[3\] times the second and \[4\] times the third together make\[191\]. Find the least of the consecutive numbers.
  A)
  \[18\]                             done clear
  B)
  \[21\]                 done clear
  C)
  \[19\]                 done clear
  D)
         \[20\] done clear
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• question_answer32)
  Rishab rode his bike to a store \[5\,\,km\] from his house. The table given shows the distance from the store paired with the number of minutes after leaving his house.

  Minutes(x)	Kilometres from store (y)
  \[2\]	\[4.3\]
  \[3\]	\[4\]
  \[5\]	\[3.4\]
  \[8\]	\[2.5\]

  Which of following equations of line best fits for the given data?
  A)
  \[y=-0.2x+4.3\] done clear
  B)
  \[y=-0.2x+6.1\] done clear
  C)
  \[y=-0.3x+4.9\] done clear
  D)
         \[y=-0.3x+6.1\] done clear
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• question_answer33)
  A man is five times as old as his son. After \[2\] years the man will be four times as old as his son. What is the present age of the man?
  A)
  \[35\]years                     done clear
  B)
  \[30\]years         done clear
  C)
         \[6\]years           done clear
  D)
         \[31\]years done clear
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• question_answer34)
  Mega city High School earned \[Rs.\,\,5100\] on tickets sales for a play. The cost per ticket was\[Rs.\,\,12\]. If \[t\] represents the number of tickets sold to the play, which of the following equations could be used to determine the number of tickets sold for the play?
  A)
  \[12=5100\,\,t\]              done clear
  B)
  \[12t=5100\]      done clear
  C)
  \[t=5100-12\]     done clear
  D)
         \[t=5100.12\]               done clear
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• question_answer35)
  The function \[f(x)=35+15x\] represents the amount of money, in Rupees, Mr. Ramesh earns for working \[x\] hours. How much money does Mr. Ramesh earn for working \[25\] hours?
  A)
  \[Rs.\,\,75\]                    done clear
  B)
  \[Rs.\,\,375\]       done clear
  C)
  \[Rs.\,\,410\]       done clear
  D)
         \[Rs.\,\,1250\] done clear
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• question_answer36)
  Two planes start from a city and fly in opposite directions, one averaging a speed of \[40\] km/hour greater than the second. If they are \[3400\,\,km\] apart from \[5\] hours, find the sum of their average speeds.
  A)
  \[680\,\,km/h\] done clear
  B)
                     \[360\,\,km/h\]                done clear
  C)
  \[320\,\,km/h\]    done clear
  D)
         \[640\,\,km/h\] done clear
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• question_answer37)
  Which equation represents the relationship between time, \[{{t}_{1}}\] and distance\[,\]\[d\]?

  Time (hours)	Distance (km)
  2	90
  3	135
  4	180
  5	225

  A)
  \[d=t+45\]                    done clear
  B)
  \[d=45t\]           done clear
  C)
         \[t=45d\]           done clear
  D)
         \[t=\frac{45}{d}\]                      done clear
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• question_answer38)
  The angles of a pentagon are in the ratio\[2:3:3:3:4\]. Find the least angle of the pentagon.
  A)
  \[{{108}^{o}}\]                                   done clear
  B)
  \[{{72}^{o}}\] done clear
  C)
  \[{{27}^{o}}\]             done clear
  D)
         \[{{90}^{o}}\]             done clear
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• question_answer39)
  Straight lines represented by linear equations \[x+y=2\] and \[5x-3y=2\] intersect at which of the given points?
  A)
  \[(1,\,\,2)\]                                  done clear
  B)
  \[(1,\,\,1)\]                      done clear
  C)
  \[(2,\,\,1)\]                                  done clear
  D)
  \[(3,\,\,2)\]                    done clear
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• question_answer40)
  A woman sells to the first customer half her stock and half an apple, to the second customer she sells half her remaining stock and half an apple, and so on to the third, and to a fourth customer. She finds that she has now \[15\] apples left. How many apples did she have before she started selling?
  A)
  \[63\]                             done clear
  B)
  \[127\]               done clear
  C)
  \[240\]               done clear
  D)
         \[289\]               done clear
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• question_answer41)
  A student was asked to divide a number by\[17/8\]. Instead, he actually multiplied it by \[17/8\] and hence got \[225\] more than the expected answer. What was the expected answer?
  A)
  \[126\]                           done clear
  B)
  \[136\]   done clear
  C)
  \[64\]                 done clear
  D)
         \[84\]                             done clear
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• question_answer42)
  If \[a\] and \[b\] are real numbers, when does the equation \[3x-5+a=bx+1\] has a unique solution\[x\]?
  A)
   for all \[a\] and \[b\]       done clear
  B)
   no root done clear
  C)
                      if\[a\ne 6\]         done clear
  D)
          if\[b\ne 3\] done clear
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• question_answer43)
  In a class, \[\frac{3}{5}\] of the students are girls and rest are boys. If \[\frac{2}{9}\] of the girls and \[\frac{1}{4}\] of the boys are absent, what part of the total number of students are present?
  A)
  \[\frac{23}{30}\]                                    done clear
  B)
  \[\frac{23}{36}\]            done clear
  C)
  \[\frac{18}{49}\]                        done clear
  D)
         \[\frac{17}{25}\]            done clear
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• question_answer44)
  How many solutions does a linear equation in two variable have?
  A)
   \[1\]                 done clear
  B)
          Infinite  done clear
  C)
   \[2\]                 done clear
  D)
          \[0\]     done clear
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• question_answer45)
  The course of an enemy submarine as plotted on a set of rectangular axes is\[2x+3y=5\]. On the same axes the course of the destroyer is indicated by\[x-y=10\]. What is the point \[(x,\,\,y)\] at which the submarine can be destroyed?
  A)
  \[(-7,\,\,3)\]                     done clear
  B)
  \[(-3,\,\,7)\]         done clear
  C)
  \[(3,\,\,-7)\]         done clear
  D)
         \[(7,\,\,-3)\]         done clear
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• question_answer46)
  When a ball bounces, it rises to \[\frac{3}{4}\] of the height from which it fell. If the ball is dropped from a height of\[32\,\,m\], how high will it rise at the third bounce?
  A)
  \[14\frac{1}{2}m\]                     done clear
  B)
  \[13\frac{1}{2}m\]         done clear
  C)
  \[13\,\,m\]                      done clear
  D)
         \[14\,\,m\]                      done clear
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• question_answer47)
  The breadth of a rectangular room is \[2\,\,m\] less than its length\[(l)\]. If the perimeter of the room is\[14\,\,m\], find the length \[(l)\] and breadth \[(b)\] of the room.
  A)
   \[l=2.5\,\,m,\,\,b=4.5\,\,m\] done clear
  B)
   \[l=3.5\,\,m,\,\,b=3.5\,\,m\] done clear
  C)
   \[l=4.5\,\,m,\,\,b=2.5\,\,m\] done clear
  D)
   \[l=2.5\,\,m,\,\,b=5.5\,\,m\] done clear
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• question_answer48)
  The total value of a collection of coins of denominations \[Rs.\,\,1.00,\,\,50\]paise, \[25\] paise, \[10\] paise and \[5\] paise, is\[Rs.\,\,380\]. If the number of coins of each denomination is the same, find the number of one-rupee coins.
  A)
  \[160\]               done clear
  B)
         \[180\]               done clear
  C)
  \[200\]               done clear
  D)
         \[220\]               done clear
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• question_answer49)
  \[x=3\]and \[y=-1\] is a solution of which of the linear equations given?
  A)
  \[x+y=3\]                     done clear
  B)
  \[2x+y=3\]        done clear
  C)
         \[x+2y=1\]        done clear
  D)
         \[2x-y=1\]                     done clear
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• question_answer50)
  Find the equation of the line that passes through the points \[(5,\,\,15)\] and\[(10,\,\,20)\].
  A)
  \[y=x+10\]                    done clear
  B)
  \[y=x-30\]         done clear
  C)
         \[y=x+30\]        done clear
  D)
         \[y=x+15\] done clear
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• question_answer51)
  Which of the following statements best models every linear equation in two variables x and y?
  A)
   A straight line parallel to \[x\text{-}\]axis done clear
  B)
   A straight line parallel by \[y\text{-}\]axis done clear
  C)
   A straight line done clear
  D)
   A straight line that passes through the origin done clear
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