Linear Equations in Two Variables Class 10 MCQ is one of the best strategies to prepare for the CBSE Class 10 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Linear Equations in Two Variables class 10, which will help them all through their board test.

## Linear Equations in Two Variables Class 10 MCQ

Class 10 Math MCQ with answers are given here to chapter 3 Linear Equations in Two Variables. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 10 Mathematics syllabus. By Solving these Class 10 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 10 Annual exam.

Learn Linear Equations in Two Variables Class 10 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 10 Mathematics Linear Equations in Two Variables MCQ with answers given below.

**Question 1. The pair of equations y = a and y = b graphically represents lines which are **

(a) intersecting at (a, b)

(b) intersecting at (b, a)

(c) parallel

(d) coincident

**Answer**

C

**Question 2. Divya has only ≠ 2 and ≠ 5 coins with her. If the total number of coins that she has is 25 and the amount of money with her is ≠ 80, then the number of ` 2 and ≠ 5 coins are , respectively **

(a) 15 and 10

(b) 10 and 15

(c) 12 and 10

(d) 13 and 12

**Answer**

B

**Question 3. The pair of equations 6x -7y =1 and 3x – 4 y = 5 has **

(a) a unique solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

**Answer**

A

**Question 4. The pair of equations 4x -3y +5 = 0 and 8x -6 y -10 = 0 graphically represents two lines which are **

(a) coincident

(b) parallel

(c) intersecting at exactly one point

(d) intersecting at exactly two points

**Answer**

B

**Question 5. A’s age is six times B’s age. Four years hence, the age of A will be four times B’s age. The present ages, in years, of A and B are, respectively **

(a) 3 and 24

(b) 36 and 6

(c) 6 and 36

(d) 4 and 24

**Answer**

B

**Question 6. The value of k for which the lines (k +1)x +3ky +15 = 0 and 5x + ky +5 = 0 are coincident is **

(a) 14

(b) 2

(c) –14

(d) –2

**Answer**

A

**Question 7. A pair of linear equations which has x = 0, y = -5 as a solution is **

(a) x+y=0/2x-3y=10

(b) x+y=3/2x-y=5

(c) 2x+3y+5=0/3x+2y=0/x-4y=0

(d) x-4y=14/5x-y=13

**Answer**

C

**Question 8. The number of solutions of the pair of linear equations x +3y – 4 = 0 and 2x +6 y = 7 is **

(a) 0

(b) 1

(c) 2

(d) infinite

**Answer**

A

**Question 9. If a pair of linear equations has infinitely many solutions, then the lines representing them will be **

(a) parallel

(b) intersecting or coincident

(c) always intersecting

(d) always coincident

**Answer**

A

**Question 10. The value of k for which the pair of equations kx + y = 3 and 3x +6 y = 5 has a unique solution is **

(a) – 1/2

(b) 2

(c) –2

(d) all the above

**Answer**

D

**Question 11. The pair of equations x = 2 and y = 3 has **

(a) one solution

(b) two solutions

(c) many solutions

(d) no solution

**Answer**

A

**Question 12. If a pair of linear equations is inconsistent, then the lines representing them will be **

(a) parallel

(b) always coincident

(c) intersecting or coincident

(d) always intersecting

**Answer**

A

**Question 13. Sanya’s age is three times her sister’s age. Five years hence, her age will be twice her sister’s age. The present ages (in years) of Sanya and her sister are respectively **

(a) 12 and 4

(b) 15 and 5

(c) 5 and 15

(d) 4 and 12

**Answer**

B

**Question 14. The sum of the digits of a two digit number is 8. If 18 is added to it, the digits of the number get reversed. The number is **

(a) 53

(b) 35

(c) 62

(d) 26

**Answer**

B

**Question 15. If the system of equations 4x + y = 3 and (2k -1) x +(k -1)y = 2k +1 is inconsistent, then k = **

(a) 2/3

(b) -2/3

(c) -3/2

(d) 3/2

**Answer**

D

**Question 16. The number of solutions of the pair of equations 2x +5y =10 and 6x +15y -30 = 0 is **

(a) 0

(b) 1

(c) 2

(d) infinite

**Answer**

D

**Question 17. The value of k for which the system of equations x +3y – 4 = 0 and 2x + ky = 7 is inconsistent is **

(a) 21/4

(b) 1/6

(c) 6

(d) 4/21

**Answer**

C

**Question 18. If the system of equations 2x +3y = 7 **

(a + b)x +(2a – b)y = 21

has infinitely many solutions, then

(a) a = 1, b = 5

(b) a = –1, b = 5

(c) a = 5, b = 1

(d) a= 5, b = -1

**Answer**

C

**Question 19. If am¹ bl, then the system of equations **

ax + by = c, lx + my = n

(a) has a unique solution

(b) has no solution

(c) has infinitely many solutions

(d) may or may not have a solution

**Answer**

A

**Question 20. If the system of equations **

4x+3y=9

2ax+3(a+b)y=18

has infinitely many solutions, then

(a) b = 2a

(b) a = 2b

(c) a +2b = 0

(d) 2a- b = 0

**Answer**

B

**Question 21. The value of k for which the system of equations kx – y = 2, 6x -2y = 3 has a unique solution is **

(a) = 0

(b) = 3

(c) ¹ 0

(d) ¹ 3

**Answer**

**Question 22. A pair of linear equations in two variables cannot have **

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) exactly two solutions

**Answer**

D

**Question 23. The pair of equations 3x -2y = 5 and 6x – y = 3 have **

(a) no solution

(b) a unique solution

(c) two solutions

(d) infinitely many solutions

**Answer**

B

**Question 24. If 2x -3y = 7 and (a + b)x -(a + b -3)y = 4a + b represent coincident lines, then a and b satisfy the equation **

(a) a +5b = 0

(b) 5a+ b = 0

(c) a -5b = 0

(d) 5a- b = 0

**Answer**

C

Whoever needs to take the CBSE Class 10 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 10 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Linear Equations in Two Variables class 10 MCQ are ready by the subject specialists themselves.

**Question 25. The pair of equations x = a and y = b graphically represent lines which are **

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a, b)

**Answer**

D

**Question 26. 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

**Question 27. A pair of linear equations which has a unique solution x = 3, y = -2 is **

(a) x+y=-1/2x-3y+12

(b) 2x+5y+4=0/4x+10y+8=0

(c) 2x-3y=0/3x+2y=0/x-4y=0

(d) x-4y=14/5x-y=13

**Answer**

B

**Question 28. If x = a and y = b is the solution of the equations x + y = 5 and x – y = 7, then values of a and b are respectively **

(a) 1 and 4

(b) 6 and –1

(c) – 6 and 1

(d) –1 and –6

**Answer**

B

**Question 29. A pair of linear equations which has a unique solution x = -1, y = -2 is **

(a) x – y =1; 2x +3y = 5

(b) 2x -3y = 4; x -5y = 9

(c) x + y -3 = 0; x – y =1

(d) x + y +3= 0; 2x -3y +5 = 0

**Answer**

B

**Question 30. The value of g for which the system of equations 5gx -2y =1 and 10x + y = 3 has a unique solution is **

(a) = 4

(b) ¹ 4

(c) =– 4

(d) ¹ – 4

**Answer**

D

**Question 31. The value of k for which the system of equations 2x + y -3 = 0 and 5x + ky +7= 0 has no solution is **

(a) 2

(b) 5

(c) 5/2

(d) 3/7

**Answer**

C

**Question 32. The value of k for which the system of equation 2x +3y = 7 and 8x +(k + 4)y -28 = 0 has infinitely many solution is **

(a) –8

(b) 8

(c) 3

(d) –3

**Answer**

B

**Question 33. 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 respectively **

(a) 3 and 5

(b) 5 and 3

(c) 3 and 1

(d) –1 and –3

**Answer**

C

**Question 34. Gunjan has only ` 1 and ` 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ` 75, then the number of ` 1, and ` 2 coins are respectively **

(a) 25 and 25

(b) 15 and 35

(c) 35 and 15

(d) 35 and 20

**Answer**

A

**Question 35. One equation of a pair of dependent linear equations is 3x – 4 y = 7. The second equation can be **

(a) – 6x +8 y =14

(b) –6x +8 y +14 = 0

(c) 6x +8 y =14

(d) -6x -8 y -14 = 0

**Answer**

B

**Question 36. If a pair of linear equations is consistent, then the lines will be **

(a) always intersecting

(b) always coincident

(c) intersecting or coincident

(d) parallel

**Answer**

B

**Question 37. If x = a, y = b is the solution of the equation x + y = 3 and x – y = 5, then the values of a and b are, respectively **

(a) 4 and –1

(b) 1 and 2

(c) –1 and 4

(d) 2 and 3

**Answer**

C

**Question 38. The sum of the digits of a two digit number is 12. If 18 is subtracted from it, the digits of the number get reversed. The number is **

(a) 57

(b) 75

(c) 84

(d) 48

**Answer**

B

**Question 39. If the lines given by 3x +2ky = 2 and 2x +5y +1 = 0 are parallel, then the value of k is **

(a) 3/2

(b) 15/4

(c) 2/5

(d) – 5/4

**Answer**

B

**Question 40. The value of c for which the pair of equations 4x -5y +7 = 0 and 2cx -10 y +8 = 0 has no solution is **

(a) 8

(b) – 8

(c) 4

(d) – 4

**Answer**

A

**Question 41. The pair of equations x = a and y = b graphically represents lines which are **

(a) coincident

(b) parallel

(c) intersecting at (a, b)

(d) intersecting at (b, a)

**Answer**

C

**Question 42. If we add 1 to the numerator and denominator of a fraction, it becomes 1/2 . It becomes 1/3 if we only add 1 to the denominator. The fraction is **

(a) 3/4

(b) 2/5

(c) 3/5

(d) 1/4

**Answer**

C

**Question 43. The pair of equations x +2y -3 = 0 and 4x +5y = 8 has **

(a) no solution

(b) infinitely many solutions

(c) a unique solution

(d) exactly two solutions

**Answer**

C

**Question 44. The pair of equations 6x – 4 y +9 = 0 and 3x -2y +10 = 0 has **

(a) a unique solution

(b) no solution

(c) exactly two solutions

(d) infinitely many solutions

**Answer**

C

**Question 45. If the lines given by 2x -5y +10 = 0 and kx +15y -30 = 0 are coincident, then the value of k is **

(a) –6

(b) 6

(c) 1/3

(d) -1/3

**Answer**

C

**Question 46. A pair of linear equations which has a unique solution x =1, y = -3 is **

(a) x – y = 4; 2x +3y = 5

(b) 2x – y = -5; 5x -2y =11

(c) 3x + y = 0; x +2y = -5

(d) x + y = -2; 4x +3y = 5 2

**Answer**

B

**Question 47. Anmol’s age is six times his son’s age. Four years hence, the age of Anmol will be four times his son’s age. The present age in years, of the father and the son are respectively **

(a) 24 and 4

(b) 30 and 5

(c) 36 and 6

(d) 24 and 3 2

**Answer**

B

You can easily get good marks If you study with the help of Class 10 Linear Equations in Two Variables MCQ. We trust that information provided is useful for you. NCERT MCQ Questions for Class 10 Linear Equations in Two Variables PDF Free Download would without a doubt create positive results.

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### Frequently Asked Question (FAQs)

## How many MCQ questions are there in Class 10 Chapter 3 Mathematics?

In Class 10 chapter 3 Mathematics, we have provided 47 Important MCQ Questions, But in the future, we will add more MCQs so that you can get good marks in the Class 10 exam.

## Can we score good marks in Class 10 Mathematics with the help of Linear Equations in Two Variables MCQ Questions?

Yes, MCQ Question is one of the best strategies to make your preparation better for the CBSE Board Exam. It also helps to know the student’s basic understanding of each chapter. So, You can score good marks in the Class 12 Mathematics exam.