Below you will find **MCQ Questions of Chapter 3 Pair of Linear Equations in Two Variables Class 10 Math**s that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 10 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables with Answers

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

► (c) 100 m

2. The pair of linear equations x + 2y = 5, 7x + 3y = 13 has a unique solution -

(a) x = 1, y = 2

(b) x = 2, y = 1

(c) x = 3, y = 1

(d) x = 1, y = 3

► (a) x = 1, y = 2

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

(a) inconsistent

(b) coincident

(c) consistent

(d) none of these

► (a) inconsistent

4. The values of x and y which satisfy the equations: 47x + 31y = 63 and 31x + 47y = 15 are ____________

(a) -2 and -1

(b) 2 and -1

(c) 2 and 1

(d) -2 and 1

► (b) 2 and -1

5. The pair of linear equations x + y = 3, 2x + 5y = 12 has a unique solution x = x_{1}, y = y_{1} then value of x_{1} is –

(a) 1

(b) 2

(c) -1

(d) -2

► (a) 1

6. 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

► (b) 21

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

► (b) k = 10

8. 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

► (c) profit of 3.33 %

9. A lending library has a fixed charge for the first two days and an additional charge for each day thereafter. Sunil paid Rs 28 for a book kept for seven days, while Sohail paid Rs 32 for the book he kept for nine days. Find the charge for each extra day.

(a) Rs 3

(b) Rs 20

(c) Rs 2

(d) Rs 18

► (c) Rs 2

10. The pair of linear equations 13x + ky = k, 39x + 6y = k + 4 has infinitely many solutions if –

(a) k = 1

(b) k = 2

(c) k = 4

(d) k = 6

► (b) k = 2

11. 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

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

12. The pair of linear equations 7x + ky = k, 14x + 2y = k + 1 has infinitely many solutions if –

(a) k = 1

(b) k ≌ 1

(c) k = 2

(d) k = 4

► (a) k = 1

13. Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?

(a) 6km/hr

(b) 4km/hr

(c) 3km/hr

(d) 7km/hr

► (a) 6km/hr

14. The pair of linear equations 3x – 5y + 1 = 0, 2x – y + 3 = 0 has a unique solution x = x1, y = y1 then y1 =

(a) 1

(b) - 1

(c) - 2

(d) - 4

► (b) - 1

15. The value of x, y in the following 2^{x + 2} – 3^{y + 1} = 5 ………(1) , 2x + 3y = 17 ………(2)

(a) -2,3

(b) 2, -3

(c) 2, 3

(d) 3,2

► (d) 3,2

16. One equation of a pair of dependent linear equations is -5x + 7y = 2, the second equation can be :

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

(b) -10x – 14x + 4 = 0

(c) 10x – 14y = -4

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

► (c) 10x – 14y = -4

17. 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

► (c) 7/9

18. If 6x + 3y = 6xy; 2x + 4y = 5xy, then the values of x and y are

(a) 1 and 2

(b) 2 and 1

(c) 1 and 1/2

(d) 1/2 and 1

► (a) 1 and 2

19. For what value of ‘K’ will the system of equations: 3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1 have no solution

(a) 3

(b) 2

(c) 1

(d) -2

► (b) 2

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

(a) -5/4

(b) 2/5

(c) 15/4

(d) 3/2

► (c) 15/4

21. The pair of linear equations 3x + 7y = k, 12x + 2ky = 4k + 1 do not have any solution if

(a) k = 7

(b) k = 14

(c) k = 21

(d) k = 28

► (b) k = 14

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

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

► (d) no solution

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Pair of Linear Equations in Two Variables MCQ Questions** will help you in practising more and more questions in less time.