10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank

done Pair of Linear Equations In Two Variables Total Questions - 63

• question_answer1)
  Which of the following is a linear equation?
  A)
   \[x-2y=7\]                          done clear
  B)
   \[{{x}^{3}}-1=0\] done clear
  C)
   \[x+\frac{6}{x}=12\]      done clear
  D)
          \[\frac{x}{2}+\frac{3}{x}=14\] done clear
  View Solution play_arrow

• question_answer2)
  Which of the following is a solution of\[\text{2p}+\text{3q}=\text{5}\]?
  A)
   \[\text{p}=-\text{1},\text{q}=\text{1}\]               done clear
  B)
          \[\text{p }=\text{ 1},\text{ q }=\text{ }-\text{1}\] done clear
  C)
   \[\text{p}=\text{1},\text{q}=\text{1}\]                done clear
  D)
          \[~\text{p}=-\text{1},\text{q}=-\text{1}\] done clear
  View Solution play_arrow

• question_answer3)
  Which of the following is the other name for a pair of linear equations in two variables?
  A)
   Consistent equations done clear
  B)
   Simultaneous equations done clear
  C)
   Inconsistent equations done clear
  D)
   Dependent equations done clear
  View Solution play_arrow

• question_answer4)
  What is the condition that a system of simultaneous equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]must satisfy to have exactly one solution?
  A)
   \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\]              done clear
  B)
          \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] done clear
  C)
   \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]                done clear
  D)
          \[\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] done clear
  View Solution play_arrow

• question_answer5)
  How many solutions do the equations satisfying \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\]have?
  A)
   One                                      done clear
  B)
   Two done clear
  C)
   Three                   done clear
  D)
          Infinitely many done clear
  View Solution play_arrow

• question_answer6)
  What is a system of simultaneous equations called if it has no solution?
  A)
   Consistent system done clear
  B)
   independent system done clear
  C)
   Inconsistent system done clear
  D)
   Dependent system                done clear
  View Solution play_arrow

• question_answer7)
  How many solutions does the system of equations \[\text{p}+\text{2q}=\text{4}\]and\[\text{2p}+\text{4q}-\text{12}=0\] have?
  A)
   0                             done clear
  B)
          1     done clear
  C)
   2                             done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer8)
  What is a system of simultaneous equations called if its graph has intersecting lines?
  A)
   Inconsistent system done clear
  B)
   Consistent system done clear
  C)
   Dependent system done clear
  D)
   Independent system done clear
  View Solution play_arrow

• question_answer9)
  HI What is the nature of the graphs of a dependent system?
  A)
   Parallel lines done clear
  B)
   Perpendicular lines done clear
  C)
   Intersecting lines done clear
  D)
   Coincident lines done clear
  View Solution play_arrow

• question_answer10)
  What is the nature of the graphs of a system of linear equations with exactly one solution?
  A)
   Parallel lines done clear
  B)
   Perpendicular lines done clear
  C)
   Coincident lines done clear
  D)
   Intersecting lines done clear
  View Solution play_arrow

• question_answer11)
  What is the number of solutions of the pair of linear equations\[\text{4p}-\text{6q}+\text{18}=0\]and\[\text{2p}-\text{3q}+\text{9}=0\]?
  A)
   0                                             done clear
  B)
   1 done clear
  C)
   2                             done clear
  D)
          Infinitely many done clear
  View Solution play_arrow

• question_answer12)
  Which of the following is a consistent system of simultaneous equations?
  A)
   \[\text{m}+\text{3n}=\text{6}\] \[\text{2m}+\text{6n}=\text{12}\] done clear
  B)
                         \[\text{a }+\text{ 3b }=\text{ 6}\]\[\text{2a}-\text{3b}=\text{12}\] done clear
  C)
   \[\text{x}-\text{4y}=\text{6}\]\[\text{2x}-\text{8y}=\text{12}\]                              done clear
  D)
   \[l-\text{2m}=\text{6}\]\[3l-6m=12\] done clear
  View Solution play_arrow

• question_answer13)
  Find the unique solution of the system of simultaneous equations\[\text{2x}-\text{y}=\text{2}\] and\[\text{4x}-\text{y}=\text{4}\].
  A)
   \[\text{x}=0,\text{y}=\text{1}\]    done clear
  B)
          \[\text{x}=0,\text{y}=0\] done clear
  C)
   \[\text{x}=\text{1},\text{y}=0\]    done clear
  D)
          \[~\text{x}=\text{1},\text{y}=\text{1}\] done clear
  View Solution play_arrow

• question_answer14)
  The sum of a two-digit number and the number obtained by reversing its digits is 154. If the digits differ by 4, find the number.
  A)
   95                          done clear
  B)
          73   done clear
  C)
   84                          done clear
  D)
          62 done clear
  View Solution play_arrow

• question_answer15)
  Choose the dependent system from the following.
  A)
   \[\text{m}+\text{n}=\text{7}\]\[\text{3m}+\text{3n}=\text{21}\] done clear
  B)
                          \[\text{3x}-\text{2y}=\text{5}\]\[\text{2x}-\text{3y}=\text{7}\] done clear
  C)
   \[\text{3x}-\text{3y}=\text{18}\]\[\text{x}-\text{y}=\text{1}0\] done clear
  D)
    \[\text{2x}+\text{y}=\text{6}\]\[\text{4x}-\text{2y}=\text{4}\] done clear
  View Solution play_arrow

• question_answer16)
  Five years ago, a father's age was seven times his son's age. Five years from now, the father's age will be thrice the son's age. What are the respective present ages of father and son?
  A)
   40 years, 10 years done clear
  B)
   10 years, 40 years done clear
  C)
   25 years, 5 years done clear
  D)
   30 years, 8 years done clear
  View Solution play_arrow

• question_answer17)
  Rajesh buys 7 books and 6 pens for Rs.3800 and Amar buys 3 books and 5 pens of the same kind for Rs.1750. What are the respective costs of a book and a pen?
  A)
   Rs.350, Rs.50                     done clear
  B)
   Rs.500, Rs.75 done clear
  C)
   Rs.250, Rs.100   done clear
  D)
          Rs.500, Rs.50 done clear
  View Solution play_arrow

• question_answer18)
  The system of simultaneous equations \[\text{3m}+\text{n}=\text{1and(2k}-\text{1)m}+(\text{k}-\text{1})\text{n}=\text{2k}+\text{1}\], is inconsistent. What is the value of 'k'?
  A)
   3                                             done clear
  B)
   1 done clear
  C)
   2                             done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer19)
  What type of a system of equations is the pair of linear equations 2x - 3y = 8 and 4x - 6y = 9?
  A)
   Consistent system done clear
  B)
   Inconsistent system done clear
  C)
   Dependent system done clear
  D)
   Independent system done clear
  View Solution play_arrow

• question_answer20)
  If the pair of linear equations\[\text{2x}+\text{ky}-\text{3}=0\]and\[\text{6x}+\frac{2}{3}\text{y}+\text{7}=0\]has a unique solution, which of the following is true?
  A)
   \[k=\frac{2}{3}\]                              done clear
  B)
   \[k\ne \frac{2}{3}\] done clear
  C)
   \[k=\frac{2}{9}\]              done clear
  D)
          \[k\ne \frac{2}{9}\] done clear
  View Solution play_arrow

• question_answer21)
  If the length of a rectangle is increased by 2 m and breadth is reduced by 2 m, its area decreases by 28 sq. m. If the length is reduced by 1 m and the breadth is increased by 2 m, the area increases by 33 sq m. Find the actual measurements of the rectangle.
  A)
   \[l=\text{13m},\text{b}=\text{11 m}\] done clear
  B)
   \[l=\text{ 23 m},\text{ b }=\text{ 11 m}\] done clear
  C)
   \[l=\text{23m},\text{b}=\text{2}0\text{m}\] done clear
  D)
   \[l=\text{12 m},\text{ b }=\text{ 1}0\text{ m}\] done clear
  View Solution play_arrow

• question_answer22)
  The side of a square is 4m more than the side of another square. The sum of their areas is 208 sq. m. What is the side of the larger square?
  A)
   12m                      done clear
  B)
          8m done clear
  C)
   9m                         done clear
  D)
          5m done clear
  View Solution play_arrow

• question_answer23)
  Two numbers are in the ratio 2:7. If 6 is added to each of the numbers, the ratio becomes 1:3. Find the numbers.
  A)
   14, 49                   done clear
  B)
          16, 56 done clear
  C)
   18, 63                   done clear
  D)
          24, 84 done clear
  View Solution play_arrow

• question_answer24)
  If the pair of equations \[3x+5y=k\] and\[9x+12y=6\]has infinitely many solutions, which of the following is true?
  A)
   k = 2                      done clear
  B)
          k = 6 done clear
  C)
   \[k\ne 6\]           done clear
  D)
          k = 3 done clear
  View Solution play_arrow

• question_answer25)
  If the pair of linear equations\[3x+5y=3\] and \[6x+ky=6\] do not have any solution, which of the following is true?
  A)
   k = 5                      done clear
  B)
          k = 10 done clear
  C)
   \[k\ne 10\]        done clear
  D)
          \[k\ne 5\] done clear
  View Solution play_arrow

• question_answer26)
  When is the pair of linear equations \[7x-3y=4;3x\frac{k}{7}y=4\] consistent?
  A)
   k = 9                      done clear
  B)
          \[~\text{k}=-\text{9}\] done clear
  C)
   \[~\text{k}\ne -\text{9}\]           done clear
  D)
          \[~\text{k}\ne 7\] done clear
  View Solution play_arrow

• question_answer27)
  When does the pair of linear equations \[7x+ky=k;14x+2y=k+1\]have infinitely many solutions?
  A)
   k = 1                      done clear
  B)
          \[k\ne 1\] done clear
  C)
   k = 2                      done clear
  D)
          k = 4 done clear
  View Solution play_arrow

• question_answer28)
  The pair of linear equations \[x+y=3\]; \[2x+5y=12\]has a unique solution \[x={{x}_{1}},\] \[y={{y}_{1}}\]Find the value of\[{{x}_{1}}\].
  A)
   1                                             done clear
  B)
   2 done clear
  C)
   -1                           done clear
  D)
          -2 done clear
  View Solution play_arrow

• question_answer29)
  Which of the following solutions does the pair of linear equations\[x+2y=5\]; \[3x+12y=10\]have?
  A)
   A unique solution done clear
  B)
   No solution done clear
  C)
   More than two solutions done clear
  D)
   Infinitely many solutions done clear
  View Solution play_arrow

• question_answer30)
  If the sum of the ages (in years) of a father and his son is 65 and twice the difference of their ages (in years) is 50, what is the age of the father?
  A)
   45 years                              done clear
  B)
   40 years done clear
  C)
   50 years              done clear
  D)
          55 years done clear
  View Solution play_arrow

• question_answer31)
  Three chairs and two tables cost Rs.1850.Five chairs and three tables cost Rs.2850. Find the total cost of one chair and one table.
  A)
   Rs.800                                  done clear
  B)
   Rs.850 done clear
  C)
   Rs.900                  done clear
  D)
          Rs.950 done clear
  View Solution play_arrow

• question_answer32)
  If \[\text{a}+\text{b}=\text{5}\]and\[\text{3a}+\text{2b}=\text{2}0\], find\[\text{3a}+\text{b}\].
  A)
   25                                          done clear
  B)
   20 done clear
  C)
   15                          done clear
  D)
          10 done clear
  View Solution play_arrow

• question_answer33)
  Which of the respective values of 'x' and 'y' satisfy the following equations I and II?

  (I) \[3x+y=19\]

  (II) \[x-y=9\]

  A)
   7, 2                                        done clear
  B)
   7, -2 done clear
  C)
   -7, 2                      done clear
  D)
          -7, -2 done clear
  View Solution play_arrow

• question_answer34)
  If\[3x-5y=5\]and\[\frac{x}{x+y}=\frac{5}{7}\], what is the value of\[x-y\]?
  A)
   9                                             done clear
  B)
   6 done clear
  C)
   4                             done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer35)
  If \[\text{12a}+\text{3b}=\text{1}\]and\[\text{7b}-\text{2a}=\text{9}\], find the average (arithmetic mean) of 'a' and 'b'.
  A)
   2.5                                         done clear
  B)
   1 done clear
  C)
   0.1                         done clear
  D)
          0.5 done clear
  View Solution play_arrow

• question_answer36)
  If\[4x+6y=32\]and\[4x-2y=4\], find the value of 8y.
  A)
   24                          done clear
  B)
          28 done clear
  C)
   36                          done clear
  D)
          42 done clear
  View Solution play_arrow

• question_answer37)
  For the equations\[(p+2)\left( q-\frac{1}{2} \right)=pq-5\] and\[(p-2)\left( q-\frac{1}{2} \right)=pq-5\], find the solution set (p, q).
  A)
   \[\left( -10,-\frac{1}{2} \right)\]                                done clear
  B)
   \[\left( -10,\frac{1}{2} \right)\] done clear
  C)
   \[\left( 10,-\frac{1}{2} \right)\] done clear
  D)
          \[\left( 10,\frac{1}{2} \right)\] done clear
  View Solution play_arrow

• question_answer38)
  Identify the solution of\[\frac{2}{3}x-\frac{3}{4}y=1\]and\[8x-9y=16\].
  A)
   \[\text{x}=\text{6},\text{y}=\text{4}\] done clear
  B)
   Infinitely many solutions done clear
  C)
   \[\text{x}=\text{4},\text{y}=\text{6}\] done clear
  D)
   No solution done clear
  View Solution play_arrow

• question_answer39)
  Find the values of 'x' and y for \[x-y=0.9\];\[\frac{11}{x+y}=2\]
  A)
   3.2, 5.6                 done clear
  B)
          3.2, 2.3 done clear
  C)
   5.6, 2.3                 done clear
  D)
          4.5, 6.4 done clear
  View Solution play_arrow

• question_answer40)
  What is the solution of the equations,\[\frac{3x-y+1}{3}=\frac{2x+y+2}{5}=\frac{3x+2y+1}{6}?\]
  A)
   \[\text{x}=-\text{1},\text{y}=-\text{1}\] done clear
  B)
   \[~\text{x}=\text{1},\text{ y}=\text{1}\] done clear
  C)
   \[\text{x}=\text{1},\text{ y}=\text{2}\] done clear
  D)
   \[\text{x}=\text{2},\text{y}=\text{1}\] done clear
  View Solution play_arrow

• question_answer41)
  The course of an enemy submarine as plotted on a set of rectangular axes gives the equation \[2x+3y=5\]. On the same axes. the course of a destroyer is indicated by the equation \[x-y=10\]. Find the point \[(x,y)\]at which the submarine can be destroyed.
  A)
   (-7, 3)                   done clear
  B)
          (7, -3) done clear
  C)
   (-3, 7)                   done clear
  D)
          (3, -7) done clear
  View Solution play_arrow

• question_answer42)
  Find the solution of the equations\[8x-9y=6xy\]\[10x+6y=19xy\].
  A)
   \[x=\frac{3}{2},y=\frac{3}{2}\]                  done clear
  B)
   \[x=\frac{2}{3},y=\frac{3}{2}\] done clear
  C)
   \[x=\frac{3}{2},y=\frac{2}{3}\]  done clear
  D)
          \[x=3,y=2\] done clear
  View Solution play_arrow

• question_answer43)
  Find the values of 'x' and y, for the equations \[\frac{{{a}^{2}}}{x}-\frac{{{b}^{2}}}{y}=0;\frac{{{a}^{2}}b}{x}+\frac{{{b}^{2}}a}{y}=a+b\] where \[x,y\ne 0\].
  A)
   \[x={{a}^{2}},y={{b}^{2}}\]         done clear
  B)
   \[x={{b}^{2}},y={{a}^{2}}\] done clear
  C)
   \[x=\frac{b}{a},y=\frac{a}{b}\]  done clear
  D)
          \[x=\frac{1}{b},y=\frac{1}{a}\] done clear
  View Solution play_arrow

• question_answer44)
  If \[x+\frac{1}{y}=5\]and \[2x+\frac{3}{y}=13\], what is the value of \[(2x-3y)\]?
  A)
   1                             done clear
  B)
          2    done clear
  C)
   3                             done clear
  D)
          5 done clear
  View Solution play_arrow

• question_answer45)
  Which of the following is the solution of the system of equations \[\frac{4}{x}+5y=7\]and \[\frac{3}{x}+4y=5\]?
  A)
   \[x=-\frac{1}{3},y=-1\]  done clear
  B)
   \[x=\frac{1}{3},y=-1\] done clear
  C)
   \[x=-\frac{1}{3},y=1\] done clear
  D)
          \[x=\frac{1}{3},y=1\] done clear
  View Solution play_arrow

• question_answer46)
  The solution of\[2x+3y=2\]and\[3x+2y=2\]can be represented by a point. In which of the following parts of the coordinate plane does the point lie?
  A)
   First quadrant done clear
  B)
   Second quadrant done clear
  C)
   Third quadrant done clear
  D)
   Fourth quadrant done clear
  View Solution play_arrow

• question_answer47)
  cm Find 'x' and 'y' for the equations\[\frac{x}{3}+\frac{y}{4}=4\]and\[\frac{5x}{3}+\frac{y}{4}=8\].
  A)
   \[\text{x}=\text{8},\text{y}=\text{6}\]                 done clear
  B)
   \[\text{x}=\text{3},\text{y}=\text{4}\] done clear
  C)
   \[\text{x}=\text{6},\text{y}=\text{8}\]   done clear
  D)
          \[~\text{x}=\text{4},\text{y}-\text{6}\] done clear
  View Solution play_arrow

• question_answer48)
  How many solutions does the system of equations,\[3x-4y=5\]and\[12x-16y=20\]have?
  A)
   More than two solutions done clear
  B)
   Exactly two solutions done clear
  C)
   Exactly one solution done clear
  D)
   No solution done clear
  View Solution play_arrow

• question_answer49)
  Find the number of solutions of the equations \[x+\frac{1}{y}=2\]and\[2xy-3y=-2\].
  A)
   0                                             done clear
  B)
   1 done clear
  C)
   2                             done clear
  D)
          Infinitely many done clear
  View Solution play_arrow

• question_answer50)
  Which of the following solutions do the system of equations\[2x+y=5\]and\[x+2y=4\]have?
  A)
   Consistent and a unique solution done clear
  B)
   Consistent and infinitely many solutions done clear
  C)
   Inconsistent done clear
  D)
   No solution done clear
  View Solution play_arrow

• question_answer51)
  If the equations\[4x+7y=10\]and \[10x+ky=25\]represent coincident lines, what is the value of 'k'?
  A)
   5                                             done clear
  B)
   \[\frac{17}{2}\] done clear
  C)
   \[\frac{27}{2}\]                done clear
  D)
          \[\frac{35}{2}\] done clear
  View Solution play_arrow

• question_answer52)
  For what value of 'k', will the equations\[4x+6y=11\]and\[2x+ky=7\]be inconsistent?
  A)
                   2                                             done clear
  B)
   3 done clear
  C)
   4                             done clear
  D)
          8 done clear
  View Solution play_arrow

• question_answer53)
  For what value of 'k' will the system of equations\[3x+5y=2\]and\[kx+10y=0\] have a non zero solution?
  A)
   0                             done clear
  B)
          2 done clear
  C)
   6                             done clear
  D)
          8 done clear
  View Solution play_arrow

• question_answer54)
  If the cost of 3 audio cassettes and 2 VCDs is Rs. 350 and that of 2 audio cassettes and 3 VCDs is Rs.425, what is the cost of a VCD?
  A)
   Rs. 140                                 done clear
  B)
   Rs. 125 done clear
  C)
   Rs. 115                 done clear
  D)
          Rs. 110 done clear
  View Solution play_arrow

• question_answer55)
  The difference between two numbers is 5 and the difference between their squares is 65. Find the larger number.
  A)
   9            done clear
  B)
   10 done clear
  C)
   11           done clear
  D)
   12 done clear
  View Solution play_arrow

• question_answer56)
  Rs.49 was divided among 150 children. Each girl got 50 paise and a boy 25 paise. How many boys were there?
  A)
   100                                        done clear
  B)
   102 done clear
  C)
   104                        done clear
  D)
          105 done clear
  View Solution play_arrow

• question_answer57)
  The area of a rectangle increases by 76 square units, if the length and breadth are each increased by 2 units. However, if the length is increased by 3 units and breadth is decreased by 3 units, the area gets reduced by 21 square units. Find the sum of the length and breadth of the rectangle.
  A)
   40 units                               done clear
  B)
   42 units done clear
  C)
   4 units                  done clear
  D)
          36 units done clear
  View Solution play_arrow

• question_answer58)
  What number must be added to each of the numbers, 5, 9, 17, 27 to make them proportionate?
  A)
   2                                             done clear
  B)
   1 done clear
  C)
   3                                             done clear
  D)
   5 done clear
  View Solution play_arrow

• question_answer59)
  Two numbers differ by 3 and their product is 54. Find the numbers.
  A)
   9 and 6 done clear
  B)
   -9 and -6 done clear
  C)
   Both [a] and [b] done clear
  D)
   9 and -4 done clear
  View Solution play_arrow

• question_answer60)
  A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is Rs. 250 per quintal, the monthly expenses of the family is Rs. 1000 and when it is Rs. 240 per quintal, the monthly expenses is Rs. 980. Find the monthly expenses of the family on wheat when the cost of wheat is Rs. 350 a quintal.
  A)
   Rs. 900                 done clear
  B)
          Rs. 350 done clear
  C)
   Rs. 650                 done clear
  D)
          Rs. 700 done clear
  View Solution play_arrow

• question_answer61)
  The angles A, B, C and D in order in a cyclic quadrilateral are\[{{(2x+y)}^{o}},{{(2(x+y))}^{o}}\],\[{{(3x+2y)}^{o}}\], and\[{{(4x-2y)}^{o}}\]. Find their measures in the same order.
  A)
   \[\text{7}0{}^\circ ,\text{ 11}0{}^\circ ,\text{ 8}0{}^\circ ,\text{ 1}00{}^\circ \] done clear
  B)
   \[\text{7}0{}^\circ ,\text{ 8}0{}^\circ ,\text{ 11}0{}^\circ ,\text{ 1}00{}^\circ \] done clear
  C)
   \[\text{7}0{}^\circ ,\text{ 8}0{}^\circ ,\text{ 1}00{}^\circ ,\text{ 11}0{}^\circ \] done clear
  D)
   80°, 100°, 110°, 70° done clear
  View Solution play_arrow

• question_answer62)
  The smallest angle of a triangle is one-fifth the sum of the other two and the largest angle exceeds the sum of the other two by\[\text{2}0{}^\circ \]. Find the largest angle of the triangle.
  A)
   \[\text{1}00{}^\circ \]                                   done clear
  B)
   \[\text{9}0{}^\circ \] done clear
  C)
   \[\text{12}0{}^\circ \]                   done clear
  D)
          \[\text{11}0{}^\circ \] done clear
  View Solution play_arrow

• question_answer63)
  The sum of Raju's age and half of Sameer's age is 4. One-third Raju's age added to twice Sameer's age is 5. Find the sum of their ages.
  A)
   7 years                                 done clear
  B)
   3 years done clear
  C)
   5 years                 done clear
  D)
          2 years done clear
  View Solution play_arrow