This quiz works best with JavaScript enabled. Home > Cbse > Class 10 > Mathematics > Pair Of Linear Equations In Two Variables > Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The value of k for which the system of equations 3x+5y=0 and kx+10y=0 have infinitely many solutions is ..... A) 6. B) 0. C) 8. D) 2. Show Answer Correct Answer: A) 6. 2. Given the linear equation 12x-4y = 20, which of the following linear equations in two variables is such that the geometrical representation of the pair formed is two intersecting lines.1. 6x + 4y =102. 6x-2y = 10 A) 1. B) 2. C) 1 and 2 both. D) Neither. Show Answer Correct Answer: A) 1. 3. The equation y = 3x + 5 has ..... A) A unique solution. B) Only two solutions. C) Three solutions. D) Infinitely many solutions. Show Answer Correct Answer: D) Infinitely many solutions. 4. Twice the difference of the two numbers is 24.If the two numbers are m and n represent this information in the form of a linear equation. A) 2 m-n = 24. B) 2 (m+n) = 24. C) 2 (m-n ) = 24. D) 2 (x-y) = 24. Show Answer Correct Answer: C) 2 (m-n ) = 24. 5. If a pair of linear equations is consistent, then the corresponding lines will be ..... A) Parallel. B) Always coincident. C) Always intersecting in a unique point. D) Intersecting or coincident. Show Answer Correct Answer: D) Intersecting or coincident. 6. There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has? A) D + c = 502d + 4c = 174. B) D + C = 504D + 2C = 174. C) D + c = 1744d + 2c = 50. D) D + c = 1742d + 4c = 50. Show Answer Correct Answer: B) D + C = 504D + 2C = 174. 7. Y =-2x + 18y = 8 A) (-5, 8). B) (-2, 8). C) (5, 8). D) (2, 8). Show Answer Correct Answer: C) (5, 8). 8. The pair of linear equations X + 2y-8 = 0 and 2x + 4y =16 has A) Unique solution. B) No solution. C) Two solutions. D) Infinitely many solutions. Show Answer Correct Answer: D) Infinitely many solutions. 9. A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream. A) 10 km/h, 4 km/h. B) 10 km/h, 40 km/h. C) 1 km/h, 4 km/h. D) 100 km/h, 4 km/h. Show Answer Correct Answer: A) 10 km/h, 4 km/h. 10. 29x+37y=103 and 37x+29y = 95 then A) X = 1, y = 2. B) X = 3, y = 2. C) X = 2, y = 1. D) X = 2, y = 3. Show Answer Correct Answer: A) X = 1, y = 2. 11. If the lines given by 3x+2ky =2 and 2x+5y+1= 0 are parallel then the value of k is ..... A) $\frac{3}{2}$. B) $\frac{15}{4}$. C) $\frac{2}{5}$. D) $\frac{-5}{4}$. Show Answer Correct Answer: B) $\frac{15}{4}$. 12. The system of equations kx-y = 2 and 6x-2y = 3 has a unique solution only when k = ..... A) 0. B) Not equal to 0. C) Not equal to 3. D) 3. Show Answer Correct Answer: C) Not equal to 3. 13. Solve the system by elimination.-4x-4y = 0 4x + 4y = 0 A) (-6, 10). B) (-6, -4). C) Infinite number of solutions. D) (6, 4). Show Answer Correct Answer: C) Infinite number of solutions. 14. The equations 4x + 3y-1 = 5 and 12x + 9y = 15 represent A) No solution. B) Infinite many solution. C) Unique solution. D) None of the above. Show Answer Correct Answer: A) No solution. 15. The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. if 3 students are less in a row, there would be 2 rows more. To find the number of students, the situation can be represented algebraically as A) X-3y + 3 = 0 ;2x-3y + 6 = 0. B) X + 3y + 3 = 0 ; 2x-3y-6 = 0. C) X-3y + 3 = 0 ; 2x-3y-6 = 0. D) X-3y + 3 = 0 ; 2x-3y + 6 = 0. Show Answer Correct Answer: C) X-3y + 3 = 0 ; 2x-3y-6 = 0. 16. When do the lines of a pair of linear equations coincide? A) When a1/a2 = c1/c2. B) When a1/a2 = b1/b2. C) When a1/a2 = b1/b2 = c1/c2. D) When a1/a2 = b1/b2 = c1/c2. Show Answer Correct Answer: A) When a1/a2 = c1/c2. 17. The value of c for which the pair of equations cx-y = 2 and 6x-2y = 3 will have infinitely many solutions is A) 3. B) -12. C) -3. D) No value. Show Answer Correct Answer: D) No value. 18. The linear equation 2x+3=12 has A) One solution. B) Infinitely many solution. C) Two solutions. D) No solution. Show Answer Correct Answer: A) One solution. 19. Solution of the system of equations $\sqrt{2}x-\sqrt{5}y=0$ $\sqrt{5}x+\sqrt{2}y=0$ A) $ x = 0, \\y = 0 $. B) $x=\sqrt{2}, \\y=\sqrt{5}$. C) $x=\sqrt{5}, \\y=\sqrt{2}$. D) $x=-\sqrt{2}, \\y=\sqrt{5}$. Show Answer Correct Answer: A) $ x = 0, \\y = 0 $. 20. The pair of lines 'x = a' and 'y = b' graphically represent lines which are A) Parallel. B) Intersecting at (a, b). C) Coincident. D) Intersecting at (b, a). Show Answer Correct Answer: B) Intersecting at (a, b). 21. ASSERTION:The linear equation x-2y-3=0 and 3x+4y-20=0 have exactly one solutions.REASON:The linear equation 2x+3y-9=0 and 4x+6y-18=0 have a unique solution. A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion. B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. C) Assertion is true but Reason is false. D) Assertion is false but Reason is true. Show Answer Correct Answer: C) Assertion is true but Reason is false. 22. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is A) 15/4. B) -5/4. C) 2/ 5. D) 3/2. Show Answer Correct Answer: A) 15/4. 23. During lockdown, Amar and Birju decided to walk to their village 30 kms away. Amar took 3 hours more than Birju to reach the village. However, if Amar had walked twice as fast he would have reached 3/2 hours before Birju. Find their speed of walking. A) Amar's speed = 10 kmphBirju's speed = 0 kmph. B) Amar's speed = 10/3 kmphBirju's speed = 5 kmph. C) Amar's speed = 3/10 kmphBirju's speed = 1/5 kmph. D) None of the above. Show Answer Correct Answer: B) Amar's speed = 10/3 kmphBirju's speed = 5 kmph. 24. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is A) 63. B) 25. C) 72. D) 36. Show Answer Correct Answer: D) 36. 25. Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k. A) 5. B) 6. C) 8. D) 7. Show Answer Correct Answer: C) 8. 26. Solve the system of equations by substitution.y =-4x + 5y = 3x-16 A) (11, 17). B) (21, 47). C) (3, -7). D) (-3, -25). Show Answer Correct Answer: C) (3, -7). 27. 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) 240, 280. B) 100, 120. C) 140, 280. D) 120, 130. Show Answer Correct Answer: C) 140, 280. 28. Solve $2x+3y=11$ $2x-4y=-24$ $y=mx+3$ A) $m=-1$. B) $m=-2$. C) $m=1$. D) $m=2$. Show Answer Correct Answer: A) $m=-1$. 29. Which of these systems has an infinite number of solutions? A) $y=3x+4$ $-12x+4y=16$. B) $x+2y=10$ $2x+4y=10$. C) $y=2x+6$ $4x-2y=8$. D) $y=-2x+1$ $y=-2x-3$. Show Answer Correct Answer: A) $y=3x+4$ $-12x+4y=16$. 30. A fraction becomes. when subtracted from the numerator and it becomes. when 8 is added to its denominator. Find the fraction. A) $\frac{3}{13}$. B) $\frac{4}{12}$. C) $\frac{11}{7}$. D) $\frac{5}{12}$. Show Answer Correct Answer: D) $\frac{5}{12}$. 31. Which of the following pairs of equations represent an inconsistent system? A) 5x-y = 10, 10x-2y = 20. B) 3x-2Y = 8, 2x + 3Y = 1. C) 3x-y =-8, 3x-y = 24. D) 5x-y = 3, x + 3y = 4. Show Answer Correct Answer: C) 3x-y =-8, 3x-y = 24. 32. The path of a train A is given by the equation $x+2y-4=0$ $2x+4y-12=0$ A) $ x = 2, \\y = 3 $. B) $ x =-2, \\y = 3 $. C) $ x =-2, \\y =-3 $. D) None of these. Show Answer Correct Answer: D) None of these. 33. Which method is used to find the unique solution of a pair of linear equations? A) Graphical Method. B) Algebraic Method. C) Elimination Method. D) Substitution Method. Show Answer Correct Answer: B) Algebraic Method. 34. If a pair of equation is consistent, then the lines will be A) Parallel. B) Always coincident. C) Always intersecting. D) Intersecting or coincident. Show Answer Correct Answer: D) Intersecting or coincident. 35. The equations 4x + 3y = 5 and 12x + 9y = 15 represent A) No solution. B) Infinite many solution. C) Unique solution. D) None of the above. Show Answer Correct Answer: B) Infinite many solution. 36. Write an equation in Standard Form.A store sells t-shirts for $ 12 each and sweatshirts for $ 15 each. You plan to spend $ 120 on t-shirts and sweatshirts. A) 12x + 15 = 120. B) 12 + 15y = 2x. C) X + Kha = 120. D) 12x + 15y = 120. Show Answer Correct Answer: D) 12x + 15y = 120. 37. Ganesh has to pay Rs. 482 for 19 apples and 11 guavas. If he would have exchanged the number of apples and guavas purchased, then he would have paid Rs.64 less. Find how much more amount he has to pay to purchase 1 apple than 1 guava A) Rs.11. B) Rs.19. C) Rs.7. D) Rs.8. Show Answer Correct Answer: D) Rs.8. 38. A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream. A) 2km/hr. B) 2.5Km/h. C) 5Km/h. D) 25Km/h. Show Answer Correct Answer: B) 2.5Km/h. 39. The pair of equations 3x-5y = 7 and 6x + 10y = 7 have A) Intersecting at one point. B) Parallel. C) Intersecting at two points. D) Coincident. Show Answer Correct Answer: A) Intersecting at one point. 40. For what value of k will the following equations have infinitely many solutions? 2x-3y=7, (k+1) x+ (1-2k) y=5k-4 A) 5. B) 2. C) 1. D) 3. Show Answer Correct Answer: A) 5. 41. The graph of x =-2 is a line parallel to the A) Y-axis. B) X-axis. C) Both x-and y-axis. D) None of these. Show Answer Correct Answer: A) Y-axis. 42. The pair of linear equations 6x-7y = 1 and 3x-4y = 5 has( 1 mark ) A) No solution. B) Two solutions. C) Infinitely many solutions. D) Unique solution. Show Answer Correct Answer: D) Unique solution. 43. The dependent equations has A) Infinitely many solution. B) No solution. C) One solution. D) Two solutions. Show Answer Correct Answer: A) Infinitely many solution. 44. If speed of water is x km/hr and that of boat in still water be y km/hr, then the speed of boat while going downstream is ..... km/hr A) (x+y). B) (Y-X). C) (2x+y). D) (x-y). Show Answer Correct Answer: A) (x+y). 45. Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? A) Y = 1550 + xy = x + 4. B) Y-x = 1550y = 4x. C) X + y = 1550y = x + 4. D) X + y = 1550y = 4x. Show Answer Correct Answer: D) X + y = 1550y = 4x. 46. Five year ago, Namita was thrice as old as Mamta. Ten years later, Namita will be twice as old as Mamta. How old is Mamta at present? A) 50 years. B) 30 years. C) 15 years. D) 20 years. Show Answer Correct Answer: D) 20 years. 47. The pair of equations $x+2y+5=0$ $-3x-6y+1=0$ A) No soultion. B) Exactly two solutions. C) Infinitely many solutions. D) A unique solution. Show Answer Correct Answer: A) No soultion. 48. If x=3 in 5x +2y= 10 then y= A) -3.5. B) -2. C) -2.5. D) -3. Show Answer Correct Answer: C) -2.5. 49. If 2 is added to the numerator and denominator of a fraction it becomes 9/10. When 3 is subtracted from the numerator and denominator it becomes 4/5. If x is the numerator and y is the denominator, represent this information as a pair of linear equations. A) 9 (x +2) = 10 (y +2) 5 (x-3) = 4 (y-3). B) 10 (x +2) = 9 (y +2) 4 (x-3) = 5 (y-3). C) 10 (x +2) = 9 (y +2) 5 (x-3) = 4 (y-3). D) 9 (x+2) = 10 (y+2) 4 (x-3) = 5 (y-3). Show Answer Correct Answer: C) 10 (x +2) = 9 (y +2) 5 (x-3) = 4 (y-3). 50. I we add1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction. This situation can be represented algebraically as A) X-y + 2 =0 ; 2x-y +1= 0. B) X-y + 2 = 0 ; 2x + y-1=0. C) X-y + 2 = 0 ; 2x-y-1 =0. D) X +y + 2 = 0 ; 2x-y-1 = 0. Show Answer Correct Answer: C) X-y + 2 = 0 ; 2x-y-1 =0. 51. Anjali finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?3x + 2y = 3152x + 4y = 450 A) 90 minutes. B) 30 minutes. C) 60 minutes. D) 45 minutes. Show Answer Correct Answer: D) 45 minutes. 52. Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines. Find the number of students in the class. A) 40. B) 60. C) 70. D) 50. Show Answer Correct Answer: B) 60. 53. The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box. A) Rs 10, Rs 10. B) Rs 100, Rs 15. C) Rs 10, Rs 15. D) Rs 15, Rs 15. Show Answer Correct Answer: C) Rs 10, Rs 15. 54. What is pair of linear equations in two variables? A) A set of two or more linear equations in the same two variables. B) A polynomial with three terms. C) Set of two linear equations in same two variables. D) None of the above. Show Answer Correct Answer: C) Set of two linear equations in same two variables. 55. Which method is used to find infinitely many solutions of a pair of linear equations? A) Graphical Method. B) Algebraic Method. C) Substitution Method. D) Elimination Method. Show Answer Correct Answer: A) Graphical Method. 56. The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. He also buys 3 bats and 5 balls for ₹ 1750. We need to find the cost of one bat and one ball. The situation can be expressed algebraically as A) SA +ZI = 3800;ZKS + 5 = 1750. B) Ss + shi = 3800;ZKS + 5 = 1750. C) S-shi = 3800;ZKS + 5 = 1750. D) SA + Shi = 1750;ZKS + 5 = 3800. Show Answer Correct Answer: B) Ss + shi = 3800;ZKS + 5 = 1750. 57. The pair of equations 5x-15y = 8 and 3x-9y = 24/5 has: A) No solution. B) Two solutions. C) Infinitely many solutions. D) One solution. Show Answer Correct Answer: C) Infinitely many solutions. 58. A fruit seller sells apples at rupees 2 each and oranges at rupees 4 each. On Monday, his sold a total of 57 fruits and earned a revenue of rupees 158. Find out the total number of apples sold on Monday. A) 35. B) 43. C) 15. D) 22. Show Answer Correct Answer: A) 35. 59. What will be the solution of these equations ax+by=a-b, bx-ay=a+b A) X = 2, y =-1. B) X = 1, y =-1. C) X=-2, y=-2. D) X = 1, y = 2. Show Answer Correct Answer: B) X = 1, y =-1. 60. For what values of k will the following pair of linear equations have infinitely many solutions? $kx+3y-\left(k-3\right)=0$ $12x+ky-k=0$ A) $k=-4$. B) $k=6$. C) $k=2$. D) $k=-3$. Show Answer Correct Answer: B) $k=6$. Next →Related QuizzesMathematics QuizzesClass 10 QuizzesClass 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables Quiz 2Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables Quiz 3 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books