Please refer to the **MCQ Questions for Class 10 Maths Linear Equations **with Answers. The following Linear Equations Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Linear Equations Class 10 MCQ Questions with Answers

Please see below Linear Equations Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Questions. If 12a + 3b =1 and 7b – 2a = 9 , find the average (arithmetic mean) of ‘a’ and ‘b’.**

(a) 2.5

(b) 1

(c) 0.1

(d) 0.5

## Ans.

D

**Questions.** Which of the respective values of ‘x’ and ‘y’**satisfy the following equations I and II?**

(I) 3x + y = 19

(II) x – y = 9

(a) 7, 2

(b) 7, -2

(c) -7, 2

(d) -7, -2

## Ans.

B

**Questions.** If 3x – 5y = 5 and x/x + y = 5/7, what is the value of x – y ?

(a) 9

(b) 6

(c) 4

(d) 3

## Ans.

D

**Questions.** The sum of Raju’s age and half of Sameer’s age is 4. One-third Raju’s age added to twice Sameer’s age is 5. Find the sum of their ages.

(a) 7 years

(b) 3 years

(c) 5 years

(d) 2 years

## Ans.

C

**Questions.** If 4x + 6y = 32 and 4x – 2y = 4 , find the value

of 8y.

(a) 24

(b) 28

(c) 36

(d) 42

## Ans.

B

**Questions.****If a + b = 5and3a + 2b = 20, find 3a + b .**

(a) 25

(b) 20

(c) 15

(d) 10

## Ans.

A

**Questions.** For the equations ( p + 2) (q- 1/2) = pq – 5 and (p – 2) (q- 1/2) = pq – 5, find the solution set (p, q).

## Ans.

D

**Questions.** Find the values of ‘x’ and y for x – y = 0.9 ;

11/x + y = 2

(a) 3.2, 5.6

(b) 3.2, 2.3

(c) 5.6, 2.3

(d) 4.5, 6.4

## Ans.

B

** Questions. What is the solution of the equations, 3x – y + 1/ 3 = 2x + y + 2/5 = 3x + 2y + 1/6**(a) x = 1,y = – 1

(b) x = 1, y = 1

(c) x = 1, y = 2

(d) x = 2,y = 1

## Ans.

B

**Questions.** Three chairs and two tables cost `1850.Five**chairs and three tables cost `2850. Find the** **total cost of one chair and one table.**

(a) `800

(b) `850

(c) `900

(d) `950

## Ans.

B

**Questions.****The course of an enemy submarine as plotted on a set of rectangular axes gives the equation 2x + 3y = 5. On the same axes. the course of a destroyer is indicated by the equation x – y = 10 . Find the point (x, y) at which the submarine can be destroyed.**

(a) (-7, 3)

(b) (7, -3)

(c) (-3, 7)

(d) (3, -7)

## Ans.

B

**Questions.** Identify the solution of (2/3)x – (3/4) y = 1 and

8x – 9y =16.

(a) x = 6,y = 4

(b) Infinitely many solutions

(c) x = 4,y = 6

(d) No solution

## Ans.

D

**Questions.** Find the solution of the equations 8x – 9y = 6xy 10x + 6y = 19xy .

(a) x = 3/2, y = 3/2

(b) x = 2/3, y = 3/2

(c) x =3/2, y = 2/3

(d) x = 3, y = 2

## Ans.

C

**Questions.** If x + 1/y = 5 and 2x + 3/y = 13, what is the value of (2x – 3y) ?

(a) 1

(b) 2

(c) 3

(d) 5

## Ans.

D

**Questions.****Which of the following is the solution of the system of equations 4/x + 5y = 7 and 3/x + 4y = 5 ?**

(a) x = -(1/3), y = -1

(b) x = 1/3, y = -1

(c) x = 1/3, y = 1

(d) x = 1/3,y = 1

## Ans.

A

**Questions.** The solution of 2x + 3y = 2 and 3x + 2y = 2 can be represented by a point. In which of the following parts of the coordinate plane does the point lie?

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

## Ans.

A

**Questions.****Find the values of ‘x’ and y, for the equations a2/x – b2/y = 0, a2b/x = a + b where x, y ≠ 0 .**

(a) x = a2 , y = b2

(b) x = b2 , y = a2

(c) x = b/a,y = a/b

(d) x = 1/b,y = 1/a

## Ans.

A

**Questions.** cm Find ‘x’ and ‘y’ for the equations x/3 + y/4 = 4 and 5x/3 + y/4 = 8

(a) x = 8,y = 6

(b) x = 3,y = 4

(c) x = 6,y = 8

(d) x = 4,y – 6

## Ans.

C

**Questions.****Find the number of solutions of the equations x + 1/y = 2 and 2xy – 3y = – 2.**

(a) 0

(b) 1

(c) 2

(d) Infinitely many

## Ans.

A

**Questions.** Which of the following solutions do the system of equations2x + y = 5and x + 2y = 4 have?

(a) Consistent and a unique solution

(b) Consistent and infinitely many solutions

(c) Inconsistent

(d) No solution

## Ans.

A

**Questions.** How many solutions does the system of equations, 3x – 4y = 5 and 12x – 16y = 20 have?

(a) More than two solutions

(b) Exactly two solutions

(c) Exactly one solution

(d) No solution

## Ans.

A

**Questions.** If the equations 4x + 7y = 10 and 10x + ky = 25represent coincident lines, what is the value of ‘k’?

(a) 5

(b) 17/2

(c) 27/2

(d) 35/2

## Ans.

D

**Questions.** For what value of ‘k’ will the system of equations 3x + 5y = 2 and kx + 10y = 0 have a non zero solution?

(a) 0

(b) 2

(c) 6

(d) 8

## Ans.

C

**Questions.****For what value of ‘k’, will the equations 4x + 6y = 11and 2x + ky = 7be inconsistent?**

(a) 2

(b) 3

(c) 4

(d) 8

## Ans.

B

**Questions.****The difference between two numbers is 5 and the difference between their squares is 65. Find the larger number.**

(a) 9

(b) 10

(c) 11

(d) 12

## Ans.

A

**Questions.****49 was divided among 150 children. Each girl got 50 paise and a boy 25 paise. How many boys were there?**

(a) 100

(b) 102

(c) 104

(d) 105

## Ans.

C

**Questions.****The area of a rectangle increases by 76 square units, if the length and breadth are each increased by 2 units. However, if the length is increased by 3 units and breadth is decreased by 3 units, the area gets reduced by 21 square units. Find the sum of the length and breadth of the rectangle.**

(a) 40 units

(b) 42 units

(c) 4 units

(d) 36 units

## Ans.

D

**Questions.** If the cost of 3 audio cassettes and 2 VCDs is ` 350 and that of 2 audio cassettes and 3 VCDs is `425, what is the cost of a VCD?

(a) ` 140

(b) ` 125

(c) ` 115

(d) ` 110

## Ans.

C

**Questions.** What number must be added to each of the numbers, 5, 9, 17, 27 to make them proportionate?

(a) 2

(b) 1

(c) 3

(d) 5

## Ans.

C

**Questions.** A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is ` 250 per quintal, the monthly expenses of the family is ` 1000 and when it is ` 240 per quintal, the monthly expenses is ` 980. Find the monthly expenses of the family on wheat when the cost of wheat is ` 350 a quintal.

(a) ` 900

(b) ` 350

(c) ` 650

(d) ` 700

## Ans.

D

**Questions.** The angles A, B, C and D in order in a cyclic quadrilateral are (2x + y)^{o} ,(2(x + y))^{o} , (3x + 2 )^{o} and (4x – 2 )^{o} . Find their measures in the same order.

(a) 70^{o}, 110^{o}, 80^{o}, 100^{O}

(b) 70^{o}, 80^{o}, 110^{o}, 100^{o}

(c) 70^{o}, 80^{o,} 100o, 110^{o}

(d) 80^{o} , 100^{o} , 110^{o }, 70^{o}

## Ans.

B

**Questions.****Two numbers differ by 3 and their product is 54. Find the numbers.**

(a) 9 and 6

(b) -9 and -6

(c) Both (a) and (b)

(d) 9 and -4

## Ans.

C

**Questions.****The smallest angle of a triangle is one-fifth the sum of the other two and the largest angle exceeds the sum of the other two by 20 ^{o} . Find the largest angle of the triangle.**

(a) 100

^{o}

(b) 90

^{o}

(c) 120

^{o}

(d) 110

^{o}

## Ans.

A

**Question. The sum of a two digit number is 8. The number obtained by reversing the digits exceeds thenumber by 18. Then the given number is : **

(a) 53

(b) 35

(c) 26

(d) 62

**Answer**

B

**Question. If x + 5y = 34 and x – 5y = – 6, find the value of 5y – 2x. **

(a) – 8

(b) 14

(c) 8

(d) 20

**Answer**

A

**Question. Find the value of λ = if bx – ay = a + bax + by = a-b. **

(a) 2

(b) 1

(c) 0

(d) – 1

**Answer**

D

**Question. 10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than thenumber of boys, find the number of boys who took part in the quiz. **

(a) 3

(b) 7

(c) 2

(d) 8

**Answer**

A

**Question. For what value of a, the pair of equations, 3x + 2y – 4= 0 and ax – y – 3 = 0 has a unique solutions: **

(a) All real numbers except –3/2

(b) a=-3/2

(c) a=3/2

(d) a=2/3

**Answer**

A

**Question. 5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens cost Rs. 46. Find the costof 2 pencils and 3 pens. **

(a) Rs. 42

(b) Rs. 39

(c) Rs. 21

(d) Rs. 16

**Answer**

C

**Question. A linear equation in two variables has: **

(a) 1 solution

(b) 2 solutions

(c) no solution

(d) infinitely many

**Answer**

D

**Question. A pair of linear equations is not consistent if: **

(a) if has one solution

(b) it has many solutions

(c) graph intersect or coincide

(d) graph is parallel

**Answer**

D

**Question. In a AABC, ∠A = x°, ∠B = (3a – 2)° and ∠C = y°. Also, ∠C – ∠B = 9°. Find the value of ∠B. **

(a) 73°

(b) 82°

(c) 25°

(d) 49°

**Answer**

A

**Question. The perimeter of a rectangle is 44 cm. Its length exceeds twice its breadth by 4 cm. Find the areaof the rectangle. **

(a) 46 cm²

(b) 49 cm²

(c) 96 cm²

(d) 69 cm²

**Answer**

C

**Question. For what value of k, will the equations, x + 2y + (11 – k) = 0 and 2x + ky + (10 + k) = 0 representthe coincident lines : **

(a) k = 12

(b) k = 4

(c) k = 36

(d) k = 2

**Answer**

B

**Question. An equation ax + by + c = 0 is a linear equation in 2 variables, where a, b, c are : **

(a) natural numbers

(b) whole numbers

(c) integers

(d) real numbers

**Answer**

D

**Question. The area of triangle formed by x-y +1 = 0, 3x + 2y -12 = 0 and X-axis is : **

(a) 15/2 sq. units

(b) 9 sq. units

(c) 5 sq. units

(d) 6 sq. units

**Answer**

A

**Question. The pair of equations y = 9 and y = – 7 has: **

(a) one solution

(b) two solutions

(c) infinitely many

(d) no solution solutions

**Answer**

D

**Question. The solutions of the system of equations, x – y + 1 = 0, 3x + 2y -12 = 0 is : **

(a) (0,1)

(b) (4,0)

(c) (2,3)

(d) (0,6)

**Answer**

C

**Question. The system of equations 3x – 5y = 20 and 6x – 10y = 40 has : **

(a) one solution

(b) exactly 2 solutions

(c) infinitely many solutions

(d) no solutions solutions

**Answer**

C

**Question. The given system of equations, – x + 2y + 2 = 0 1/2 x – y – 1= o, has : **

(a) a unique solution

(b) infinite solutions

(c) no solution

(d) 2 solutions

**Answer**

A

**One Word Questions :**

**Question. A person can row downstream 20km in 2 hrs. and upstream 4km is two hours. Find the speed of rowing in still water and the speed of the current?**

**Answer**

6km/hr; 4km/hr

**Question. Find the point on y-axis satisfying the equation 2x – 5y = 10.**

**Answer**

(0, –2)

**Question. What is the value of y satisfying both the equations when x = 1?****2x – y = 3, 4x – y = 5**

**Answer**

y = –1

**Question. If we add 1 in the numerator of a fraction and substract 1 from its denomenator, the fraction becomes 1. If it is also given that the fraction becomes half when we add 1 to its denominator, then what is the fraction?**

**Answer**

3/5

**Question. What is the area of the triangle formed by the lines. 2x – y = –8, 8x + 3y = 24 and x-axis in the figure below? **

**Answer**

28 sq. units

**QuestionTwo audio cassettes and three video cassettes cost Rs. 340. But three audio cassettes and two video cassettes cost Rs. 260. Find the price of a pair of an audio and a video cassette.**

**Answer**

Rs. 120

**Question. What are the coordinates of points where 2x – 7y = 14 intersects y-axis?**

**Answer**

(0, –2)

**Question. Find the two digit number if ratio of digits is 1 : 3 and their sum is 8.**

**Answer**

26 or 62

**Question. What are the coordinates of the point of intersection of two lines****3x + y = 0, 5x – 2y = 0?**

**Answer**

(0, 0)

**Question. If three angles of a triangle are x, 2x, 2x + 5, what is the measure of each angle?**

**Answer**

35°, 70°, 75°

**Question. For what value of a, the pair of linear equations has no solution?****3x – 4y + 7 = 0****ax + 3y – 5 = 0**

**Answer**

a = – 9/4

**Question. Form an equation of a line so that the point x = 1, y = –2 lies on that line?**

**Answer**

2x – 3y = 8

**Question. For rectangular plot having 72 square metre area, find the sides if length is twice the breadth?**

**Answer**

12m, 6m

**Question. If x = y, x = 2, and x-axis from the triangle as shown in the figure below, find the coordinates of the three vertices of the triangle. **

**Answer**

(0, 0), (2, 0), (2, 2)

**Question. A father is 3 times as old as his son. After 12 years his age will be twice as that of the age of his son. Find their present ages.**

**Answer**

36 yrs., 12 yrs.

**Question. If one number is thrice the other and their sum is 16, find the numbers.**

**Answer**

12 and 4

**Question. For what value of m the system of linear equation has unique solution?****2x + 3y = 7****2mx + y = 28**

**Answer**

m ≠ 1/3

**Question. Find x-coordinate of point lying on the line 5x – y – 7 = 0 corresponding to y = 3.**

**Answer**

x = 2

**Question. 3 chairs and 2 tables cost Rs. 2,400. If cost of one chair is Rs. 400, what is the cost of 1 table?**

**Answer**

Rs. 600

**Question. Sum of two number is 35 and their difference is 13. Find the two numbers.**

**Answer**

24, 11

**Question. Find the value of y corresponding to x = 3 in the equation 3x + 2y = 9.**

**Answer**

y = 0

**Question. What should be added to 35 to obtain a number obtained by reversing digits of 35?**

**Answer**

18

**Question. Find coordinates of two points on the line 5x + 3y = 15 in the figure below :– **

**Answer**

(3, 0), (0, 5)

**Question. In ΔABC , ∠A= x°,∠B = y° and ∠C = y+20° . If y – x = 50°, what type of triangle is ΔABC?**

**Answer**

Right angled triangle

**Question. Find the point on x-axis satisfying the equation x + y = 5.**

**Answer**

(5, 0)