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MCQs for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

1. A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?

(a) 200 m

(b) 500 m

(c) 100 m

(d) 300 m

Answer:  (c) 100 m

2. If a pair of linear equations is consistent, then the lines will be

(a) always coincident

(b) parallel

(c) always intersecting

(d) intersecting or coincident

Answer: (d) intersecting or coincident

3. Two equations in two variables taken together are called

(a) linear equations

(b) quadratic equations

(c) simultaneous equations

(d) none of these

Answer: (c) simultaneous equations

4. The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

Answer: (c) Infinitely many solutions

5. 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 Rs 1 and Rs 2 coins are respectively

(a) 35 and 15

(b) 35 and 20

(c) 15 and 35

(d) 25 and 25

Answer: (d) 25 and 25

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6.  Which of following is not a solution of 3a + b = 12?​

(a) (3, 3)

(b) (5, -3)

(c) (4, 0)

(d) (2, 4)

Answer: (d) (2, 4)

7. The pair of linear equations 3x + 5y = 3, 6x + ky = 8 do not have any solution if –

(a) k = 5

(b) k = 10

(c) k ≌ 10

(d) k ≌ 5

Answer: (b) k = 10

8. The sum of ages of A and B is 49 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B.

(a) 28

(b) 21

(c) 24

(d) 12

Answer:  (b) 21

9.  If the lines given by

3x + 2ky = 2

2x + 5y + 1 = 0

are parallel, then the value of k is

(a) 5/4                                                            

(b) 2/5

(c) 15/4                                                          

(d) 3/2

Answer: (c) 15/4

10. If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?

(a) 4/15

(b) 15/4

(c) ⅘

(d) 5/4

Answer: (b) 15/4

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11.  If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and b are respectively

(a) 6, -1

(b) 2, 3

(c) 1, 4

(d) 19/5,  6/5

Answer: (d) 19/5,  6/5

12. One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0. The second equation can be

(a) 10x + 14y + 4 = 0                                                

(b) –10x – 14y + 4 = 0

(c) –10x + 14y + 4 = 0                                  

(d) 10x – 14y = –4

Answer: (d) 10x – 14y = –4

13.  The pair of equation x = – 4 and y = – 5 graphically represents lines which are

(a) intersecting at (- 5, – 4)

(b) intersecting at (- 4, – 5)

(c) intersecting at (5, 4)

(d) intersecting at (4, 5)

Answer: (b) intersecting at (- 4, – 5)

14. If the system of equations 2x + 3y = 7

2ax + (a + 6)y = 28 has infinitely many solutions, then

(a) a = 2b

(b) b = 2a

(c) a + 2b = 0

(d) 2a + b = 0

Answer: (b) b = 2a

15. Which of the following pair of linear equations is inconsistent?​

(a) 2x + 3y = 7; 4x + 6y = 5

(b) x – 2y = 6; 2x + 3y = 4

(c) 9x – 8y = 17; 18x -16y = 34

(d) 5x – 3y =11; 7x + 2y =13

Answer: (a) 2x + 3y = 7; 4x + 6y = 5

16. The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are

(a) 45°, 75°

(b) 50°, 80°

(c) 55°, 85°

(d) 55°, 95°

Answer: (c) 55°, 85°

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17. 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:

(a) 40, 42                                           

(b) 42, 48

(c) 40, 48                                           

(d) 44, 50

Answer: (c) 40 , 48 

18. The solution of the equations x-y=2 and x+y=4 is:

(a) 3 and 1

(b) 4 and 3

(c) 5 and 1

(d) -1 and -3

Answer: (a) 3 and 1

19.  By selling a wrist watch of Rs.405 the shopkeeper incurs a loss of 10%. What is the gain or loss percentage if he sells the same watch at Rs. 465?

(a) profit of 10%

(b) less of 6 %

(c) profit of 3.33 %

(d) no profit no loss

Answer: (c) profit of 3.33 %

20. The solution of 4/x+3y=14 and 3/x-4y=23 is:

(a) ⅕ and -2

(b) ⅓ and ½

(c) 3 and ½

(d) 2 and ⅓

Answer: (a) ⅕ and -2

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21.   If the pair of equation has no solution, then the pair of equation is :

(a) inconsistent

(b) coincident

(c) consistent

(d) none of these

Answer: (a) inconsistent

22.The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively

(a) 4 and 24                                       

(b) 5 and 30

(c) 6 and 36                                       

(d) 3 and 24

Answer:  (c) 6 and 36  

23. The graph of x = -2 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both x- and y-axis

(d) none of these

Answer: (b) y-axis

24. 3 women and 6 men can together finish a tailoring job in 5 days, while 4 women and 7 men can finish it in 4 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone. The linear equations(in standard form) to solve this problem algebraically are​

(a) 15u + 30v – 1 = 0; 16u + 28v – 1 = 0

(b) 15x – 30y + 1 = 0; 16x + 28y +1 = 0

(c) 16u + 30v – 1 = 0; 16u + 28v – 1 = 0

(d) 16x + 30y – 1 = 0; 16x + 28y – 1 = 0

Answer: (a) 15u + 30v – 1 = 0; 16u + 28v – 1 = 0

25. If am bl then the system of equations ax + by = c, lx + my = n, has

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) none of these

Answer: (a) a unique solution

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26. The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)°, C = (x+y)° and D=(3y-10)°. The value of x and y is:

(a) x=20° and y = 10°

(b) x=20° and y = 30°

(c) x=44° and y=15°

(d) x=15° and y=15°

Answer: (b) x=20° and y = 30°

27. The graph of the equation 2x + 3y = 5 is a

(a) vertical line

(b) straight line

(c) horizontal line

(d) none of these

Answer: (b) straight line

28.A pair of linear equations which has a unique solution x = 2, y = -3 is

(a) x + y = -1

2x – 3y = -5

(b) 2x + 5y = -11

4x + 10y = -22

(c) 2x – y = 1

3x + 2y = 0

(d) x – 4y – 14 = 0

5x – y – 13 = 0

Answer: (d) x – 4y – 14 = 0

5x – y – 13 = 0

29.  The graph of x = -2 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both x- and y-axis

(d) none of these

Answer: (b) y-axis

30. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Her speed of rowing in still water and the speed of the current is:

(a) 6km/hr and 3km/hr

(b) 7km/hr and 4km/hr

(c) 6km/hr and 4km/hr

(d) 10km/hr and 6km/hr

Answer: (c) 6km/hr and 4km/hr

31.  The graph of y = 5 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both axis

(d) none of these

Answer: (a) x-axis

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32. A fraction becomes  4/5 when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each then it becomes 1/2. The fraction is –

(a) 5/8

(b) 5/6

(c) 7/9

(d) 13/16

Answer; (c) 7/9

33. The pair of equations y = 0 and y = -7 has :

(a) no solution

(b) infinitely many solutions

(c) one solution

(d) two solutions

Answer: (a) no solution

34. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is

(a) –5/4

(b) –2/5

(c) 15/4

(d) –3/2

Answer: (c) 15/4

35. If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:

(a) -6x+10y-4=0

(b) 6x-10y-4=0

(c) 6x+10y-4=0

(d) -6x+10y+4=0

Answer: (a) -6x+10y-4=0

36.  The pair of equations x = a and y = b graphically represents lines which are

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

Answer: (d) intersecting at (a, b)

37. The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

Answer: (d) No solution

38. The value of x, y in the following 2x + 2 – 3y + 1 = 5 ………(1) , 2x + 3y = 17 ………(2)​

(a) -2,3

(b) 2, -3

(c) 2, 3

(d) 3,2

Answer: (d) 3,2

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39.  Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. Then their present ages are 

(a) x = 43, y = 13

(b) x = 40, y= 10

(c) x = 37, y = 7

(d) none

Answer: (b) x = 40, y= 10

40. 8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.       

(a) 120, 130       

(b) 140,280       

(c) 240,280       

(d) 100,120

Answer: (b) 140,280

41. The solution of the equations x-y=2 and x+y=4 is:

(a) 3 and 1

(b) 4 and 3

(c) 5 and 1

(d) -1 and -3

Answer: (a) 3 and 1

42.  Half the perimeter of a rectangular garden, whose length is 4m more than its width, is 36 m, then the dimensions of the garden is 

(a) l = 20m, b = 16m

(b) l = 16m, b= 20m

(c) l = 18m, b = 18m

(d) none 

Answer: (a) l = 20m, b = 16m

43. Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?​

(a) a ≠ -2

(b) a = -2

(c) a = 2

(d) a ≠ 2

Answer: (a) a ≠ -2

44. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:

(a)3/12

(b)4/12

(c)5/12

(d)7/12

Answer: (c)5/12

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45. If the pair of equation has no solution, then the pair of equation is :

(a) inconsistent

(b) coincident

(c) consistent

(d) none of these

Answer: (a) inconsistent

46. Rakshita 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 Rs.1 andRs.2 coins is, respectively

(a) 35 and 15                                     

(b) 35 and 20

(c) 15 and 35                                     

(d) 25 and 25

Answer:  (d) 25 and 25 

47. The graph of y = 4x is a line

(a) parallel to x-axis

(b) parallel to y-axis

(c) perpendicular to y-axis

(d) passing through the origin

Answer: (d) passing through the origin

48. The graph of the equation 2x + 3y = 5 is a

(a) vertical line

(b) straight line

(c) horizontal line

(d) none of these

Answer: (b) straight line

49. The pair of equations x = a and y = b graphically represents lines which are

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

Answer: (d) intersecting at (a, b)

50. Graphically, the pair of equations 6x – 3y + 10 = 0

2x – y + 9 = 0 represents two lines which are

(a) Intersecting at exactly one point

(b) Intersecting at two points

(c) Coincident

(d) Parallel

Answer: (d) Parallel

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