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

done Case Based MCQs - Pair of Linear Equations in Two Variables Total Questions - 30

• question_answer1)

  Directions: Q. 1 to 5

  From Rajiv Chowk Metro Station, if Charu buys 4 tickets to Karol Bagh and 6 tickets to Hauz Khas, then total cost is Rs 92, but if she buys 6 tickets to Karol Bagh and 10 tickets to Hauz Khas, then total cost is Rs 148.

  Consider the fares from Rajiv Chowk to Karol bagh and that to hauz Khas as Rs x and Rs y respectively and answer the following questions.

  1st situation can be represented algebraically as
  A)
  \[3x-5y=74\] done clear
  B)
  \[2x+5y=74\] done clear
  C)
  \[2x-3y=46\] done clear
  D)
  \[2x+3y=46\] done clear
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• question_answer2)
  2nd situation can be represented algebraically as
  A)
  \[5x+3y=74\] done clear
  B)
  \[5x-3y=74\] done clear
  C)
  \[3x+5y=74\] done clear
  D)
  \[3x-5y=74\] done clear
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• question_answer3)
  Fare from Rajiv Chowk to Karol Bagh is
  A)
  Rs 6 done clear
  B)
  Rs 8 done clear
  C)
  Rs 10 done clear
  D)
  Rs 2 done clear
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• question_answer4)
  Fare from Rajiv Chowk to Hauz Khas
  A)
  Rs 10 done clear
  B)
  Rs12 done clear
  C)
  Rs 14 done clear
  D)
  Rs 16 done clear
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• question_answer5)
  The system of linear equations represented by both situation has
  A)
  infinitely many solutions done clear
  B)
  no solution done clear
  C)
  unique solution done clear
  D)
  None of the above done clear
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• question_answer6)

  Directions: Q. 6 to 10
  A test consists of 'True' or 'False' questions. One mark is awarded for every correct answer while \[\frac{1}{4}\] mark is deducted for every wrong answer.
  A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks.
  Type Question	Marks given for correct answer	Marks deducted for wrong answer
  True/False	1	0.25

  If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?
  A)
  96 done clear
  B)
  92 done clear
  C)
  90 done clear
  D)
  None of these done clear
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• question_answer7)
  How many questions did he guess?
  A)
  20 done clear
  B)
  22 done clear
  C)
  24 done clear
  D)
  26 done clear
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• question_answer8)
  If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?
  A)
  40 done clear
  B)
  80 done clear
  C)
  75 done clear
  D)
  70 done clear
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• question_answer9)
  If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?
  A)
  95 done clear
  B)
  100 done clear
  C)
  120 done clear
  D)
  80 done clear
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• question_answer10)
  If answer to all questions he attempted by giving were wrong and answered 90 correctly, then how many marks he got?
  A)
  90 done clear
  B)
  100 done clear
  C)
  95 done clear
  D)
  80 done clear
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• question_answer11)
   

  Directions: Q. 11 to 15

  Mr. Jayant sahu arranged dinner party for some of his friends. The expenses of the dinner are partly constant and partly proportional to the number of guests. The expenses amount to Rs 450 for 5 guest and Rs 850 for 10 guests.

  Denote the constant expense by Rs x and proportional expense per person by Rs y and answer the following questions.

  Represent both the situations algebraically
  A)
  \[x+5y=850,x+10y=450\] done clear
  B)
  \[x-5y=850,x-10y=450\] done clear
  C)
  \[x+5y=450,x+10y=850\] done clear
  D)
  None of the above done clear
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• question_answer12)
  Proportional expense for each person is
  A)
  Rs 50 done clear
  B)
  Rs 80 done clear
  C)
  Rs 90 done clear
  D)
  Rs 100 done clear
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• question_answer13)
  The fixed (or constant) expense for the party is
  A)
  Rs 50 done clear
  B)
  Rs 80 done clear
  C)
  Rs 90 done clear
  D)
  Rs 100 done clear
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• question_answer14)
  If there would be 12 guests at the dinner party, then what amount Mr Jayant has to pay?
  A)
  Rs 1500 done clear
  B)
  Rs 1300 done clear
  C)
  Rs 1200 done clear
  D)
  Rs 1010 done clear
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• question_answer15)
  The system of linear equations representing both the situations will have
  A)
  unique solution done clear
  B)
  no solution done clear
  C)
  infinitely many solutions done clear
  D)
  None of the above done clear
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• question_answer16)
   

  Directions: Q. 16 to 20

  Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq m.

  Based on the above information, answer the following questions:

  Form the pair of linear equations in two variables from this situation.
  A)
  \[2x+y=19,x-y=13\] done clear
  B)
  \[2x+y=19,x+y=13\] done clear
  C)
  \[2x-y=13,x+y=19\] done clear
  D)
  \[2x-y=19,x+y=13\] done clear
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• question_answer17)
  Find the length of the outer boundary of the layout.
  A)
  27m done clear
  B)
  30m done clear
  C)
  54m done clear
  D)
  None of these done clear
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• question_answer18)
  Find the area of each bedroom and kitchen in the layout.
  A)
  \[35{{m}^{2}},\,15\,{{m}^{2}}\] done clear
  B)
  \[~27{{m}^{2}},\text{ }30{{m}^{2}}\] done clear
  C)
  \[40{{m}^{2}},30{{m}^{2}}\] done clear
  D)
  \[30{{m}^{2}},\text{ }35{{m}^{2}}\] done clear
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• question_answer19)
  Find the area of living room in the layout.
  A)
  \[75{{m}^{2}}\] done clear
  B)
  \[65{{m}^{2}}\] done clear
  C)
  \[72{{m}^{2}}\] done clear
  D)
  None of these done clear
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• question_answer20)
  Find the cost of laying tiles in kitchen at the rate of Rs 50 per sq m.
  A)
  1600 done clear
  B)
  1525 done clear
  C)
  1750 done clear
  D)
  1250 done clear
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• question_answer21)
   

  Directions: Q. 21 to 25

  Shivam usually go to a Vegetable shop with his mother. He observes the following two situations.

  On 1st day : The cost of 4 kg of onion and 2 kg of tomato was Rs 3200.

  On 2nd day : The cost of 8 kg of onion and 4 kg of tomato was Rs 6000.

  Denoting the cost of 1 kg onion by Rs x and cost of 1 kg tomato by Rs y and answer the following questions.

  Represent algebraically the situation of day-I.
  A)
  x+2y=1500 done clear
  B)
  2x+y=1600 done clear
  C)
  x-2y=1500 done clear
  D)
  None of these done clear
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• question_answer22)
  Represent algebraically the situation of day-II.
  A)
  2x+y=1500 done clear
  B)
  2x-y=1500 done clear
  C)
  x+2y=1500 done clear
  D)
  2x+y=750 done clear
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• question_answer23)
  The linear equation represented by day-I, intersect the X-axis at
  A)
  (0,800) done clear
  B)
  (0,-800) done clear
  C)
  (800,0) done clear
  D)
  (-800,0) done clear
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• question_answer24)
  The linear equation represented by day-II, intersect the V-axis at
  A)
  (1500,0) done clear
  B)
  (0,-1500) done clear
  C)
  (-1500,0) done clear
  D)
  (0,1500) done clear
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• question_answer25)
  Linear equations represented by day-I and day-II situations, are
  A)
  non-parallel done clear
  B)
  parallel done clear
  C)
  intersect at one point done clear
  D)
  overlapping each other done clear
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• question_answer26)
   

  Directions: Q. 26 to 30
  It is common that Governments revise travel fares from time to time based on various factors such as inflation (a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations.
  Name of the city	Distance travelled (km)	Amount paid (in Rs)
  City A	10	75
  	15	110
  City B	8	91
  	14	145
  Situation 1 In city A, for a journey of 10 km, the charge paid is Rs 75 and for a journey of 15 km, the charge paid is Rs 110.
  Situation 2 In a city B, for a journey of 8 km, the charge paid is Rs 91 and for a journey of 14 km, the charge paid is Rs 145.

  Refer situation 1

  If the fixed charges of auto rickshaw be Rs x and the running charges be Rs y km/h, the pair of linear equations representing the situation is

   
  A)
  \[x+10y=110,x+15y=75\] done clear
  B)
  \[x+10y=75,x+15y=110\] done clear
  C)
  \[10x+y=110,15x+y=75\] done clear
  D)
  \[10x+y=75,15x+y=110\] done clear
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• question_answer27)
  A person travels a distance of 50 km. The amount he has to pay is
  A)
  Rs 155 done clear
  B)
  Rs 255 done clear
  C)
  Rs 355 done clear
  D)
  Rs 455 done clear
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• question_answer28)

  Refer situation 2

  What will a person have to pay for travelling a distance of 30 km?

  A)
  Rs 185 done clear
  B)
  Rs 289 done clear
  C)
  Rs 275 done clear
  D)
  Rs 305   done clear
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• question_answer29)
  The graph of lines representing the conditions are: (situation 2)
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
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• question_answer30)
  The lines representing the conditions situation 2 are
  A)
  Parallel lines done clear
  B)
  Intersecting lines done clear
  C)
  Coincident lines done clear
  D)
  None of the above done clear
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