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

done Linear Equation in two Variables Total Questions - 40

• question_answer1)
  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
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• question_answer2)
  For what value of k, do the equations \[3(k-1)x+4y=24\] and \[15x+20y=8(k+13)\]have infinite solutions?
  A)
   1/2                               done clear
  B)
   6              done clear
  C)
   1/3                               done clear
  D)
   2 done clear
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• question_answer3)
  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
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• question_answer4)
  If the system of equations \[4x+py=21\] and \[px-2y=15\] has unique solution, then which of the following could be the value of p?

  (I) 6	(II) 66
  (III) 125	(IV) 6666

  A)
   Both (I) and (II)             done clear
  B)
   Both (III) and (IV) done clear
  C)
   (I), (II) and (III)              done clear
  D)
   All of (I), (II), (III) and (IV) done clear
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• question_answer5)
  What is the number of solutions of the pair of linear equations \[4p-6q+18=0\] and \[2p-3q+9=0\]?
  A)
   0                                 done clear
  B)
   1              done clear
  C)
   2                                 done clear
  D)
   Infinitely many done clear
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• question_answer6)
  If (p, p) is the solution of equations \[ax+by+(t-s)=0\]and \[bx+ay+(s-r)=(0\ne b)\] then, which of the following must be true?
  A)
   \[2r=s+t\]                     done clear
  B)
   \[2t=r+s\] done clear
  C)
   \[2s=r+t\]         done clear
  D)
   \[r+s+t=0\] done clear
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• question_answer7)
  If the pair of linear equations \[5x+ky-3=0\] and \[8x+\frac{2}{5}y+k=0\] has a unique solution, which of the following is true?
  A)
   \[k=\frac{8}{3}\]                      done clear
  B)
   k is not an integer done clear
  C)
   \[k=\frac{6}{7}\]                      done clear
  D)
   \[k\ne \frac{1}{4}\] done clear
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• question_answer8)
  If an ordered pair satisfying the equations \[2x-3y=18\] and \[4x-y=16\] also satisfies the equations \[5x-py-23=0\], then find the value of p.
  A)
   1, - 2   done clear
  B)
   6, - 5 done clear
  C)
   2, 0                              done clear
  D)
   1, 2 done clear
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• question_answer9)
  What number must be subtracted from each of the numbers 10, 11, 17, 19 to them proportionate?
  A)
   1                                 done clear
  B)
   8            done clear
  C)
   3          done clear
  D)
   7 done clear
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• question_answer10)
  A father said to his son, 'the sum of our present ages is twice my age 12 years ago and nine years hence, the sum of our ages will be thrice my age 14 years ago?. What is his son's present age?
  A)
   16 years                       done clear
  B)
   12 years     done clear
  C)
   14 years                       done clear
  D)
   6 years done clear
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• question_answer11)
  The angles A, B, C and D in order in a cyclic quadrilateral are \[(2x+y){}^\circ ,(2(x+y)){}^\circ ,(3x+2y){}^\circ ,\] and \[(4x-2y){}^\circ \]. Find their measures in the same order.
  A)
   \[70{}^\circ ,\text{ }110{}^\circ ,\text{ }80{}^\circ ,\text{ }100{}^\circ \]        done clear
  B)
   \[70{}^\circ ,\text{ }80{}^\circ ,\text{ }110{}^\circ ,\text{ }100{}^\circ \] done clear
  C)
   \[70{}^\circ ,\text{ }80{}^\circ ,\text{ }100{}^\circ ,\text{ }110{}^\circ \]                  done clear
  D)
   \[80{}^\circ ,\text{ }100{}^\circ ,\text{ }110{}^\circ ,\text{ }70{}^\circ \] done clear
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• question_answer12)
  Shyam has twice as many sisters as he has brothers. If Reena, Shyam's sister has the same number of brothers as she has sisters, then Reena has how many brothers?
  A)
   6                                 done clear
  B)
   3              done clear
  C)
   1                                 done clear
  D)
   5 done clear
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• question_answer13)
  The sum of the speeds of a boat in still water and the speed the currents is 10 kmph. If the boat takes 40% of the time to travel downstream when compared to that upstream, then finds the difference of the speeds of the boat when travelling upstream and downstream,
  A)
   3 kmph                         done clear
  B)
   6 kmph   done clear
  C)
   4 kmph             done clear
  D)
   5 kmph done clear
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• question_answer14)
  A two-digit number is formed by either subtracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits. Find the number.
  A)
   46                                done clear
  B)
   73       done clear
  C)
   23                                done clear
  D)
   16 done clear
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• question_answer15)
  The following sentences are the steps involved in solving the in equation, \[6x+3>2x-5\]. Given that x is whole number less than 5, arrange them in sequential order from first to last.

  (I) Solution set =\[\left\{ 0,\text{ }1,\text{ }2,\text{ }3,\text{ }4 \right\}\left( \therefore \text{ }x\in W \right)\]

  (II) \[4x>-8\]

  (III) \[6x-2x>-5-3\]

  (IV) \[x>-2\]

  A)
   CBAD                          done clear
  B)
   BCDA         done clear
  C)
   CBDA    done clear
  D)
   ABCD done clear
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• question_answer16)
  In \[\Delta ABC,\] if \[\angle A=x{}^\circ ,\angle B=3x{}^\circ ,\angle C=y{}^\circ \] and \[3y{}^\circ -5x{}^\circ =30\]. Then \[\Delta ABC\] is
  A)
   A right angled triangle        done clear
  B)
   An isosceles triangle done clear
  C)
   An equilateral triangle               done clear
  D)
   A right angled isosceles triangle done clear
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• question_answer17)
  Subodh and Sudheer start from Dwarka and R.K. Puram towards R.K. Puram and Dwarka respectively, at the same time. After they meet at dhaula kuan on the way from R.K. Puram to Dwarka, Subodh reduces his speed by 33.333% and returns back to Dwarka and Sudheer increases his speed by the same percentage and returns back to R.K. Puram. If the time taken by Subodh for his total journey is 120 minutes, then what is the time taken by Sudheer to complete his entire journey?
  A)
   132 minutes      done clear
  B)
   108 minutes      done clear
  C)
   92 minutes                    done clear
  D)
   84 minutes done clear
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• question_answer18)
  A rectangle with perimeter 132 m is partitioned into 5 congruent rectangles, as indicated in the diagram. The perimeter of each of the congruent rectangle is,
  A)
   50 m                            done clear
  B)
   60 m    done clear
  C)
   96 m                done clear
  D)
   66 m done clear
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• question_answer19)
  The equations representing the given graph is
  A)
   \[5x-6y=13;\,\,3x-2y=6\]           done clear
  B)
   \[~x\text{ }+\text{ }\frac{1}{2}y=1;2x+2y=1\] done clear
  C)
   \[3+3x=y;-x-y=6\]             done clear
  D)
   \[3x-4y=1,8y-6x=4\] done clear
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• question_answer20)
  Which of the following is true about the statements given below?

  Assertion (A): Homogeneous system of linear equations is always consistent.

  Reason (R): x = 0, y = 0 is always a solution of the homogeneous system of equations with unknowns x and y.

  A)
   A is true and R is also true.         done clear
  B)
   A is false and R is also false. done clear
  C)
   A is true and R is false              done clear
  D)
   A is false and R is true done clear
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• question_answer21)
  The graph of x = a where 'a' is a constant is perpendicular to
  A)
   x - axis        done clear
  B)
   y - axis          done clear
  C)
   Line y - x                     done clear
  D)
   Line x + y = 0 done clear
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• question_answer22)
  The value of 'K' for which the system of equations \[x+2y-3=0\] and \[6x+Ky+7=0\]has no solution, is
  A)
   12       done clear
  B)
   15             done clear
  C)
   8                                 done clear
  D)
   13 done clear
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• question_answer23)

  The value of K for which the system of equations

  \[\begin{align}   & \,\,\,\,\,\,x+Ky=3 \\  & 11x-77y=87 \\ \end{align}\]

  has a unique solution, is

  A)
   \[K=13\]                       done clear
  B)
   \[K\ne -7\]      done clear
  C)
   \[K=87\]                       done clear
  D)
   \[K\ne 0\]           done clear
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• question_answer24)
  Choose the dependent system from the following.
  A)
   \[m+n=7,3m+3n=21\]         done clear
  B)
   \[5x-7y,6x-3y=8\] done clear
  C)
   \[x-3y=18,-x-y=11\] done clear
  D)
   \[9x+y=-2,8x-2y=0\] done clear
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• question_answer25)
  If the pair of linear equations \[13x+15y=3\] and \[65x+ky=6\] do not, have any solution, which of the following is true?
  A)
   \[k\ne 80\]                     done clear
  B)
   \[k=75\] done clear
  C)
   \[k\ne 65\]                     done clear
  D)
   \[k\ne 75\] done clear
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• question_answer26)
  What is the solution of the equations, \[\frac{3x+y+2}{6}=\frac{2x+2y+3}{7}=\frac{13x-2y-3}{8}\]?
  A)
   \[x=-6,\,y=-7\]  done clear
  B)
   \[x=1,y=1\] done clear
  C)
   \[x=6,y=7\]                  done clear
  D)
   \[x=2,y=3\] done clear
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• question_answer27)
  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
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• question_answer28)
  If \[\frac{1}{x}+\frac{1}{y}=k\] and \[\frac{1}{x}-\frac{1}{y}=k\], then the value of y ________.
  A)
   0                                 done clear
  B)
   \[\frac{1}{k}\]             done clear
  C)
   1000 k              done clear
  D)
   Does not exist done clear
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• question_answer29)
  What is the solution set of \[\frac{12}{2x+3y}+\frac{5}{3x-2y}=-7\] and \[\frac{8}{2x+3y}+\frac{6}{3x-2y}=-10\]?
  A)
   (0.5, 1) done clear
  B)
   (6, 2)    done clear
  C)
   (12, 5)              done clear
  D)
   (8, 6) done clear
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• question_answer30)
  Ramesh has some cows and some parrots in his shed. The total number of legs is 130 and the total number of heads is 40. Find the number of cows in his shed.
  A)
   35                                done clear
  B)
   15            done clear
  C)
   25     done clear
  D)
   40 done clear
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• question_answer31)
  The sum of the successors of two numbers is 40 and the difference of their predecessors is 8. Find the numbers.
  A)
   23, 13                          done clear
  B)
   23, 15        done clear
  C)
   40, 8                done clear
  D)
   21, 15 done clear
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• question_answer32)
  In a fraction, if numerator is increased by 20 and denominator is decreased by 4, then the fraction becomes 2. Instead, if numerator is decreased by 4 and denominator is increased by 20, then the fraction becomes\[\frac{2}{5}\]. Find the fraction.
  A)
   \[\frac{21}{25}\]                                   done clear
  B)
   \[\frac{6}{19}\] done clear
  C)
   \[\frac{8}{17}\]                         done clear
  D)
   \[\frac{22}{25}\] done clear
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• question_answer33)
  If\[x+y=(a-b),y+z=(b-c),z+x=(c-a),\]then the average of\[\left( x+y+z \right)\]is..........
  A)
   \[b-a+c\]                      done clear
  B)
   \[0\]           done clear
  C)
   \[a-b-c\]            done clear
  D)
   \[a+b+c\] done clear
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• question_answer34)
  The area of a rectangle decreases by 10 units, if its length is lowered by 2 units and breadth is increased by 1 unit. If we increase the length by 1 unit and the breadth decrease by 1 unit, the area decreases by 5 units. Find the dimensions of the rectangle.
  A)
   \[18\times 16\]                           done clear
  B)
   \[16\times 12\] done clear
  C)
   \[17\times 19\]               done clear
  D)
   \[17\times 17\] done clear
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• question_answer35)
  \[2x+3y=0\] and \[3x+2y=0\] has how many solutions?
  A)
   No solution       done clear
  B)
   1 solution (trivial)   done clear
  C)
   2 solution          done clear
  D)
   None done clear
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• question_answer36)
  Ritu can row 20 km downstream in 2 hours, and 4 km upstream in 2 hours. The pair of equations, which correctly represents the word problem stated as above is:
  A)
   u + 2v = 15              u - v = 6 done clear
  B)
   u + v =16       u - v = 8 done clear
  C)
   u + v = 10                        u -  v = 2   done clear
  D)
   2u + v = 18        u - 2v = 3 done clear
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• question_answer37)
  A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time and, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
  A)
   75 km                          done clear
  B)
   150 km        done clear
  C)
   300 km             done clear
  D)
   600 km done clear
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• question_answer38)
  A boat goes 30 km upstream and 44 km downstream in 10 hours. If one of the distance time relationships is represented by the following equation\[\frac{30}{P}+\frac{44}{Q}=10\]; then, which of the following correctly represents P and Q?
  A)
   \[P=(x+y)\]and \[Q=(x-y)\] done clear
  B)
   \[P=x-y\] and \[Q=x+y\] done clear
  C)
   \[P=\frac{1}{x+y}\] and \[Q=\frac{1}{x-y}\] done clear
  D)
   \[P={{x}^{2}}-{{y}^{2}}\] and \[Q={{x}^{2}}+{{y}^{2}}\] done clear
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• question_answer39)
  It is also given that in 13 hrs, the boat can go 40 km upstream and 55 km downstream. Using the data given in Q 38, find the speed of stream and that of boat in still water (in km/hr.).
  A)
   3, 8                  done clear
  B)
   8, 3            done clear
  C)
   10, 5                done clear
  D)
   5, 10 done clear
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• question_answer40)
  Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions?
  A)
   \[x-3y-3=0\]  \[3x-9y-2=0\] done clear
  B)
   \[2x+y=5\] \[3x+2y=8\] done clear
  C)
  \[\left\{ {{a}^{2}}-{{b}^{2}} \right\}x+\left\{ \left( {{b}^{3}}-{{a}^{3}} \right) \right\}y+c=0\] \[\left\{ {{\left( a+b \right)}^{3}}-a{{b}^{2}}-{{a}^{2}}b \right\}y-\left\{ {{\left( a+b \right)}^{2}} \right\}x+2c=0\] Where \[c\ne 0\] done clear
  D)
   None of these done clear
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