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

Question 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?

Accepted Answer

100 m

Answer

200 m

Answer

500 m

Answer

300 m

Question 2

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

Accepted Answer

intersecting or coincident

Answer

always coincident

Answer

parallel

Answer

always intersecting

Question 3

Two equations in two variables taken together are called

Accepted Answer

simultaneous equations

Answer

linear equations

Answer

quadratic equations

Answer

none of these

Question 4

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

Accepted Answer

Infinitely many solutions

Answer

Unique solution

Answer

Exactly two solutions

Answer

No solution

Question 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

Accepted Answer

25 and 25

Answer

35 and 15

Answer

35 and 20

Answer

15 and 35

Question 6

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

Accepted Answer

(2, 4)

Answer

(3, 3)

Answer

(5, -3)

Answer

(4, 0)

Question 7

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

Accepted Answer

k = 10

Answer

k = 5

Answer

k ≠ 10

Answer

k ≠ 5

Question 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.

Accepted Answer

21

Answer

28

Answer

24

Answer

12

Question 9

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

Accepted Answer

15/4

Answer

5/4

Answer

2/5

Answer

3/2

Question 10

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

Accepted Answer

15/4

Answer

4/15

Answer

4/5

Answer

5/4

Question 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

Accepted Answer

19/5, 6/5

Answer

6, -1

Answer

2, 3

Answer

1, 4

Question 12

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

Accepted Answer

10x – 14y = –4

Answer

10x + 14y + 4 = 0

Answer

–10x – 14y + 4 = 0

Answer

–10x + 14y + 4 = 0

Question 13

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

Accepted Answer

intersecting at (- 4, – 5)

Answer

intersecting at (- 5, – 4)

Answer

intersecting at (5, 4)

Answer

intersecting at (4, 5)

Question 14

If the system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28 has infinitely many solutions, then

Accepted Answer

b = 2a

Answer

a = 2b

Answer

a + 2b = 0

Answer

2a + b = 0

Question 15

Which of the following pair of linear equations is inconsistent?

Accepted Answer

2x + 3y = 7; 4x + 6y = 5

Answer

x – 2y = 6; 2x + 3y = 4

Answer

9x – 8y = 17; 18x -16y = 34

Answer

5x – 3y =11; 7x + 2y =13

Question 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

Accepted Answer

55°, 85°

Answer

45°, 75°

Answer

50°, 80°

Answer

55°, 95°

Question 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:

Accepted Answer

40, 48

Answer

40, 42

Answer

42, 48

Answer

44, 50

Question 18

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

Accepted Answer

3 and 1

Answer

4 and 3

Answer

5 and 1

Answer

-1 and -3

Question 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?

Accepted Answer

profit of 3.33 %

Answer

profit of 10%

Answer

less of 6 %

Answer

no profit no loss

Question 20

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

Accepted Answer

1/5 and -2

Answer

1/3 and 1/2

Answer

3 and 1/2

Answer

2 and 1/3

Question 21

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

Accepted Answer

inconsistent

Answer

coincident

Answer

consistent

Answer

none of these

Question 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

Accepted Answer

6 and 36

Answer

4 and 24

Answer

5 and 30

Answer

3 and 24

Question 23

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

Accepted Answer

y-axis

Answer

x-axis

Answer

both x- and y-axis

Answer

none of these

Question 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

Accepted Answer

15u + 30v – 1 = 0; 16u + 28v – 1 = 0

Answer

15x – 30y + 1 = 0; 16x + 28y +1 = 0

Answer

16u + 30v – 1 = 0; 16u + 28v – 1 = 0

Answer

16x + 30y – 1 = 0; 16x + 28y – 1 = 0

Question 25

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

Accepted Answer

a unique solution

Answer

no solution

Answer

infinitely many solutions

Answer

none of these

Question 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:

Accepted Answer

x=20° and y = 30°

Answer

x=20° and y = 10°

Answer

x=44° and y=15°

Answer

x=15° and y=15°

Question 27

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

Accepted Answer

straight line

Answer

vertical line

Answer

horizontal line

Answer

none of these

Question 28

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

Accepted Answer

x – 4y – 14 = 0; 5x – y – 13 = 0

Answer

x + y = -1; 2x – 3y = -5

Answer

2x + 5y = -11; 4x + 10y = -22

Answer

2x – y = 1; 3x + 2y = 0

Question 29

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

Accepted Answer

y-axis

Answer

x-axis

Answer

both x- and y-axis

Answer

none of these

Question 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:

Accepted Answer

6km/hr and 4km/hr

Answer

6km/hr and 3km/hr

Answer

7km/hr and 4km/hr

Answer

10km/hr and 6km/hr

Question 31

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

Accepted Answer

x-axis

Answer

y-axis

Answer

both axis

Answer

none of these

Question 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 –

Accepted Answer

7/9

Answer

5/8

Answer

5/6

Answer

13/16

Question 33

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

Accepted Answer

no solution

Answer

infinitely many solutions

Answer

one solution

Answer

two solutions

Question 34

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

Accepted Answer

15/4

Answer

–5/4

Answer

–2/5

Answer

–3/2

Question 35

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

Accepted Answer

-6x+10y-4=0

Answer

6x-10y-4=0

Answer

6x+10y-4=0

Answer

-6x+10y+4=0

Question 36

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

Accepted Answer

intersecting at (a, b)

Answer

parallel

Answer

intersecting at (b, a)

Answer

coincident

Question 37

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

Accepted Answer

No solution

Answer

Unique solution

Answer

Exactly two solutions

Answer

Infinitely many solutions

Question 38

The value of x, y in the following 2x + 2y – 3y + 1 = 5, 2x + 3y = 17 is

Accepted Answer

3,2

Answer

-2,3

Answer

2, -3

Answer

2, 3

Question 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

Accepted Answer

x = 40, y= 10

Answer

x = 43, y = 13

Answer

x = 37, y = 7

Answer

none

Question 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.

Accepted Answer

140,280

Answer

120, 130

Answer

240,280

Answer

100,120

Question 41

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

Accepted Answer

3 and 1

Answer

4 and 3

Answer

5 and 1

Answer

-1 and -3

Question 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

Accepted Answer

l = 20m, b = 16m

Answer

l = 16m, b= 20m

Answer

l = 18m, b = 18m

Answer

none

Question 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?

Accepted Answer

a ≠ -2

Answer

a = -2

Answer

a = 2

Answer

a ≠ 2

Question 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:

Accepted Answer

5/12

Answer

3/12

Answer

4/12

Answer

7/12

Question 45

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

Accepted Answer

inconsistent

Answer

coincident

Answer

consistent

Answer

none of these

Question 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

Accepted Answer

25 and 25

Answer

35 and 15

Answer

35 and 20

Answer

15 and 35

Question 47

The graph of y = 4x is a line

Accepted Answer

passing through the origin

Answer

parallel to x-axis

Answer

parallel to y-axis

Answer

perpendicular to y-axis

Question 48

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

Accepted Answer

straight line

Answer

vertical line

Answer

horizontal line

Answer

none of these

Question 49

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

Accepted Answer

intersecting at (a, b)

Answer

parallel

Answer

intersecting at (b, a)

Answer

coincident

Question 50

Graphically, the pair of equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0 represents two lines which are

Accepted Answer

Parallel

Answer

Intersecting at exactly one point

Answer

Intersecting at two points

Answer

Coincident

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

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