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

done MCQs - Pair of Linear Equations in Two Variables Total Questions - 50

• question_answer1)
  The pair of equations \[y=0\] and \[y=-7\] has
  A)
  one solution done clear
  B)
  two solutions done clear
  C)
  infinitely many solutions done clear
  D)
  no solution done clear
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• question_answer2)
  The pair of equations x = a and y = b graphically represents lines which are
  A)
  parallel done clear
  B)
  intersecting at (b, a) done clear
  C)
  coincident done clear
  D)
  intersecting at (a, b) done clear
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• question_answer3)
  Akhila went to a fair in her village. She wanted to enjoy rides on the giant wheel and play hoopla. If each ride costs Rs 3 and a game of hoopla costs Rs 4, then she spent Rs 20. The linear equation to represent this condition is
  A)
  \[3x+4y=27\] done clear
  B)
  \[4x+3y=5\] done clear
  C)
  \[3x+4y=20\] done clear
  D)
  None of these done clear
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• question_answer4)
  A fraction becomes \[\frac{4}{5}\], if 2 is added to both numerator and denominator, if however 4 is subtracted from both numerator and denominator, then the fraction becomes \[\frac{1}{2}\]. The algebraical representation of situation is
  A)
  \[5x-4y+2=0,x-y=0\] done clear
  B)
  \[5x-4y+2=0,2x-y-4=0\] done clear
  C)
  \[x+4y=0,y+2x=0\] done clear
  D)
  None of the above done clear
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• question_answer5)
  Romila went to a stationary stall and purchased 2 pencils and 3 erasers for Rs 9. Her friend Sonali saw the new variety of pencils and erasers with Romila, and she also bought 4 pencils and 6 erasers of the same kind for Rs 18. The algebraic representation of situation is
  A)
  \[2x+3y=9,3x+5y=18\] done clear
  B)
  \[2x+4y=8,4x+6y=18\] done clear
  C)
  \[2x+3y=9,4x+6y=18\] done clear
  D)
  None of the above done clear
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• question_answer6)
  \[3x-y=3,\text{ }9x-3y=9\]has infinite solution.
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially true/false done clear
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• question_answer7)
  The number of common solutions for the system of linear equations \[5x+4y+6=0\]and \[10x+8y=12\]is
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  None of these done clear
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• question_answer8)
  On comparing the ratios \[{{a}_{1}}/{{a}_{2}},\,{{b}_{1}}/{{b}_{2}}\]and \[{{c}_{1}}/{{c}_{2}}\]and without drawing them, the pair of linear equation is \[3x-5y+8=0,7x+6y-9=0\]
  A)
  parallel done clear
  B)
  intersecting done clear
  C)
  coincident done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer9)
  If a pair of linear equations is consistent, then the lines will be
  A)
  parallel done clear
  B)
  always coincident done clear
  C)
  intersecting or coincident done clear
  D)
  always intersecting done clear
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• question_answer10)
  If a pair of linear equations is given by \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] and\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]. In this case, the pair of linear equations is consistent.
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially true/false done clear
  View Solution play_arrow

• question_answer11)
  If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is ......... .
  A)
  Consistent done clear
  B)
  Cannot say done clear
  C)
  Inconsistent done clear
  D)
  None of these done clear
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• question_answer12)
  If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is ......... .
  A)
  Consistent done clear
  B)
  Inconsistent done clear
  C)
  Cannot say done clear
  D)
  None of these done clear
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• question_answer13)
  Which of the following pair of equations are inconsistent?
  A)
  \[3x-y=9,\,x-\frac{y}{3}=3\] done clear
  B)
  \[4x+3y=24,\,-2x+3y=6\] done clear
  C)
  \[5x-y=10,\,10x-2y=20\] done clear
  D)
  \[-2x+y=3,\,-4x+2y=10\] done clear
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• question_answer14)
  The pair of linear equations are \[4x-5y-12=0,\,10y+20=8x\]
  A)
  consistent done clear
  B)
  inconsistent done clear
  C)
  can't say done clear
  D)
  None of these done clear
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• question_answer15)
  A pair of linear equations which has a unique solution x = 2 and y = - 3 is
  A)
  \[x+y=1\] and \[2x-3y=-5\] done clear
  B)
  2x+5y=-11 and \[4x+10y=-22\] done clear
  C)
  \[2x-y=1\]and \[3x+2y=0\] done clear
  D)
  \[x-4y-14=0\]and \[5x-y-13=0\] done clear
  View Solution play_arrow

• question_answer16)
  The pair of equations \[x+2y+5=0\]and\[-3x-6y+1=0\]has
  A)
  a unique solution done clear
  B)
  exactly two solutions done clear
  C)
  infinitely many solutions done clear
  D)
  no solution done clear
  View Solution play_arrow

• question_answer17)
  One equation of a pair of dependent linear equations is\[-\text{ }5x+7y-2=0\]. The second equation can be
  A)
  \[10x+14y+4=0\]    done clear
  B)
  \[-10x-14y+4=0\] done clear
  C)
  \[-10x+14y+4=0\] done clear
  D)
  \[10x-14y+4=0\] done clear
  View Solution play_arrow

• question_answer18)
  If the lines given by \[2x+ky=1\] and \[3x-5y=7\] has unique solution, then the value of k is
  A)
  \[-10/3\] done clear
  B)
  \[-5/3\] done clear
  C)
  \[2/3\] done clear
  D)
  for all real value except\[\frac{-10}{3}\] done clear
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• question_answer19)
  The value of k for which the system of linear equations \[x+2y=3\], \[5x+ky+7=0\] is inconsistent is
  A)
  \[-\frac{14}{3}\] done clear
  B)
  \[\frac{2}{5}\] done clear
  C)
  5 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer20)
  The value of 'k' for which the system of equations \[kx-5y=2;\text{ }6x+2y=7\]has no solution is
  A)
  \[-15\] done clear
  B)
  \[\frac{-5}{2}\] done clear
  C)
  \[\frac{2}{7}\] done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer21)
  For what value of k, will the following pair of linear equations have infinitely many solutions? \[2x+3y=4\]and \[\left( k+2 \right)x+6y=3k+2\]
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
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• question_answer22)
  If the lines given by \[3x+2ky=2\]and \[2x+5y=1\] are parallel, then the value of k is
  A)
  \[-\frac{5}{4}\] done clear
  B)
  \[\frac{2}{5}\] done clear
  C)
  \[\frac{15}{4}\] done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer23)
  For what value of p, will the following system of linear equations represent parallel lines? \[-x+py=1\]and \[px-y=1\]
  A)
  2 done clear
  B)
  3 done clear
  C)
  1 done clear
  D)
  None of these done clear
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• question_answer24)
  The value of a for which the lines \[x=1,\text{ }y=2\] and \[{{a}^{2}}x+2y-20=0\] are concurrent, is
  A)
  1 done clear
  B)
  8 done clear
  C)
  -4 done clear
  D)
  -2 done clear
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• question_answer25)
  The value of x and y for the following system of equations \[x+8y=19\]and\[2x+11y=28\], (by substitution method) is
  A)
  3,2 done clear
  B)
  2,3 done clear
  C)
  6,3 done clear
  D)
  3,4 done clear
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• question_answer26)
  Solve the following system of linear equations \[ax+by\text{ }-a+b=0\]and   \[bx-ay-a-b=0\]. The value of x and y are
  A)
  1, -1 done clear
  B)
  -1, 1 done clear
  C)
  1, 0 done clear
  D)
  0, 2 done clear
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• question_answer27)
  The difference between two numbers is 26 and one number is three times the other number. The numbers are
  A)
  39 and 26 done clear
  B)
  39 and 41 done clear
  C)
  39 and 13 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer28)
  Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5, then the numbers are ......... and ......... .
  A)
  48, 20 done clear
  B)
  40, 28 done clear
  C)
  40, 48 done clear
  D)
  20, 24 done clear
  View Solution play_arrow

• question_answer29)
  Using elimination method, all the possible solutions of the following pair of linear equations is \[2x+3y=8\]and \[4x+6y=7\]
  A)
  Consistent done clear
  B)
  \[x=2,y=3\] done clear
  C)
  No solution done clear
  D)
  All real values done clear
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• question_answer30)
  Find the values of x and y in the following equations. \[x-3y=8\]and \[5x+3y=10\]
  A)
  \[x=3,\,y=-\frac{5}{3}\] done clear
  B)
  \[x=-3,\,y=\frac{5}{3}\] done clear
  C)
  \[x=-3,\,y=\frac{-5}{3}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  The values of x and y for the following pair of linear \[41x+53y=135\] and \[53x+41y=147\]
  A)
  \[x=2,y=3\] done clear
  B)
  \[x=1,y=2\] done clear
  C)
  \[x=3,y=2\] done clear
  D)
  \[x=2,y=1\] done clear
  View Solution play_arrow

• question_answer32)
  If \[2x+3y=5\] and \[3x+2y=10\], then x-y= ......... .
  A)
  3 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer33)
  If \[x=a\]and \[y=b\] is the solution of the equations \[x-y=2\]and\[x+y=4\], then the values of a and b are 3 and 2, respectively
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially true/false done clear
  View Solution play_arrow

• question_answer34)
  The pair of equations \[{{3}^{x+y}}=81,\,{{81}^{x-y}}=3\] has
  A)
  no solution done clear
  B)
  unique solution done clear
  C)
  infinitely many solutions done clear
  D)
  \[x=2\frac{1}{8},\,y=1\frac{7}{8}\] done clear
  View Solution play_arrow

• question_answer35)
  If the angles of a triangle are x, y and \[40{}^\circ \] and the difference between the two angles x and y is \[30{}^\circ \]. Then, the value of x and y is \[85{}^\circ \]and \[55{}^\circ \]respectively.
  A)
  True done clear
  B)
  False done clear
  C)
  Can't say done clear
  D)
  Partially true/false done clear
  View Solution play_arrow

• question_answer36)
  The sum of a two-digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Then, the first number is 64.
  A)
  True done clear
  B)
  False done clear
  C)
  Cannot say done clear
  D)
  Partially true/false done clear
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• question_answer37)
   

  The area of a rectangle increases by 76 sq units, if the length and breadth is increased by 2 units. However, if the length is increased by

  3 units and breadth is decreased by

  3 units, the area of sets reduced by

  21 sq units. Find the breadth of the rectangle.

  A)
  9 units done clear
  B)
  16 units done clear
  C)
  18 units done clear
  D)
  21 units done clear
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• question_answer38)
  A fraction becomes 4/5 when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each of them, it becomes 1/2. Then, numerator of the fraction is
  A)
  6 done clear
  B)
  7 done clear
  C)
  8 done clear
  D)
  9 done clear
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• question_answer39)
  Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is
  A)
  28 done clear
  B)
  30 done clear
  C)
  32 done clear
  D)
  34 done clear
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• question_answer40)
  Aruna has only Rs 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Ra 1 and Rs 2 coins is
  A)
  24,24 done clear
  B)
  25,25 done clear
  C)
  26,26 done clear
  D)
  None of these done clear
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• question_answer41)
  From a bus stand in Delhi, if we buy 2 tickets to Pitampura and 3 tickets to Dilshad Garden, the total cost is Rs 46 but if we buy 3 tickets to Pitampura and 5 tickets to Dilshad Garden, the total cost is Rs 74. Then, the fares from the bus stand to Pitampura and to Dilshad Garden is
  A)
  Rs 8 ; Rs 100 done clear
  B)
  Rs 10, Rs 8 done clear
  C)
  Rs 8 ; Rs 10 done clear
  D)
  Rs 20, Rs 5 done clear
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• question_answer42)

  The value of x and y of the following pair of equation is

  \[\frac{2}{x}+\frac{3}{y}=13;\,\frac{5}{x}-\frac{4}{y}=-2\]

  A)
  \[x=2,\,y=3\] done clear
  B)
  \[x=\frac{1}{3},\,y=\frac{1}{2}\] done clear
  C)
  \[x=\frac{1}{2},\,y=\frac{1}{3}\] done clear
  D)
  \[x=3,\,y=2\] done clear
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• question_answer43)

  The value of x and y of the following pairs of equations by reducing them to a pair of linear equations is

  \[\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2;\,\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1\]

   
  A)
  \[x=4,\text{ }y=9\] done clear
  B)
  \[x=2,\,\,y=3\] done clear
  C)
  \[x=8,\,\,y=18\] done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer44)
  The values of x and y in the pair of equation \[x+4y=27xy,\,\]\[x+2y-21xy\]is
  A)
  \[x=3,\,y=15\] done clear
  B)
  \[x=15,\,y=3\] done clear
  C)
  \[x=\frac{1}{15},\,y=\frac{1}{3}\] done clear
  D)
  \[x=\frac{1}{3},\,y=\frac{1}{15}\] done clear
  View Solution play_arrow

• question_answer45)
  The value of x and y in \[\frac{5}{x+1}-\frac{2}{y-1}=\frac{1}{2};\,\frac{10}{x+1}+\frac{2}{y-1}=\frac{5}{2},\]where \[x\ne -1\] and \[y\ne 1\], is
  A)
  \[x=4,y=5\] done clear
  B)
  \[x=5,y=4\] done clear
  C)
  \[x=\frac{1}{4},\,y=\frac{1}{5}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer46)
  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 h less than the scheduled time and if the train was slower by 10 km/h, it would have taken 3 h more than the scheduled time. Then, the distance covered by the train is
  A)
  50km done clear
  B)
  300km done clear
  C)
  600km done clear
  D)
  12km done clear
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• question_answer47)
  The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, then find their monthly incomes. Form a pair of linear equations from the above data and by elimination method, the value of monthly incomes are
  A)
  18000, 14000 done clear
  B)
  20000,12000 done clear
  C)
  22000,10000 done clear
  D)
  None of the above done clear
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• question_answer48)
  A boatman rows his boat 35 km upstream and 55 km downstream in 12 h. He can row 30 km upstream and 44 km downstream in 10 h, then the speed of the boat in still water is
  A)
  8km/h done clear
  B)
  3km/h done clear
  C)
  5km/h done clear
  D)
  11km/h done clear
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• question_answer49)
  Match the Column

  	Column - I		Column - II
  A.	\[2x+3y=40\] \[6x+5y=10\]	1.	Coincident lines
  B.	\[2x+3y=40\] \[6x+9y=50\]	2.	Intersecting lines
  C.	\[2x+3y=10\] \[4x+6y=20\]	3.	Parallel lines

  A)
  A-R,     B-P,     C-Q done clear
  B)
  A-P,     B-R,     C-Q done clear
  C)
  A-R,     B-Q,    C-P done clear
  D)
  None of these done clear
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• question_answer50)
  Column-II give value of x and y for pair of equation given in Column-II.

  	Column - I		Column - II
  A.	\[2x+y=8\], \[x+6y=15\]	1.	(3, 4)
  B.	\[5x+3y=35\], \[2x+4y=28\]	2.	(4, 5)
  C.	\[15x+4y=61\] \[4x+15y=72\]	3.	(3, 2)

  A)
  A-R,     B-P,     C-Q done clear
  B)
  A-P,     B-R,     C-Q done clear
  C)
  A-R,     B-Q,    C-P done clear
  D)
  None of these done clear
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