Class 10 – Maths Chapter – 3 Pair of Linear Equations in two variables

Quiz -1 (1 Mark Questions)

Q-1 **The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:**

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

Ans – (c) Infinitely many solutions

Q-2 Graphically, the pair of equations 7x – y = 5; 21x – 3y = 10 represents two lines which are

(a) intersecting at one point

(b) parallel

(c) intersecting at two points

(d) Coincident

Ans – (b) parallel

Q-3 ** If a pair of linear equations is consistent, then the lines are:**

(a) Parallel

(b) Always coincident

(c) Always intersecting

(d) Intersecting or coincident

Ans – (d) Intersecting or coincident

Q-4 The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have

(a) a unique solution

(b) infinitely many solutions

(c) no solution

(d) two solutions

Ans – (c) no solution

Q-5 **The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have**

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

Ans – (c) no solution

Q-6 The pair of equations x = 0 and x = 5 has

(a) no solution

(b) unique/one solution

(c) two solutions

(d) infinitely many solutions

Ans – (a) no solution

Q-7 The pair of equation x = – 4 and y = – 5 graphically represents lines which are

(a) intersecting at (- 5, – 4)

(b) intersecting at (- 4, – 5)

(c) intersecting at (5, 4)

(d) intersecting at (4, 5)

Ans – (b) intersecting at (- 4, – 5)

Q-8 **If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?**

(a) 4/15

(b) 15/4

(c) 4/5

(d) 5/4

Ans – (b) 15/4

Q-9 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

(a) 6, -1

(b) 2, 3

(c) 1, 4

(d) 19/5, 6/5

Ans – (d) 19/5, 6/5

Q-10 The graph of x = -2 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both x- and y-axis

(d) none of these

Ans – (b) y-axis

Q-11 The graph of y = 3x is a line

(a) parallel to x-axis

(b) parallel to y-axis

(c) perpendicular to y-axis

(d) passing through the origin

Ans – (d) passing through the origin

Q-12 **If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:**

(a) -6x+10y-4=0

(b) 6x-10y-4=0

(c) 6x+10y-4=0

(d) -6x+10y+4=0

Ans – (a) -6x+10y-4=0

Q-13 Two equations in two variables taken together are called

(a) linear equations

(b) quadratic equations

(c) simultaneous equations

(d) none of these

Ans – (a) linear equations

Q-14 If in the equation x + 2y = 10, the value of y is 6, then the value of x will be

(a) -2

(b) 2

(c) 4

(d) 5

Ans – (a) -2

Q-15 **The solution of the equations x-y=2 and x+y=4 is:**

(a) 3 and 1

(b) 4 and 3

(c) 5 and 1

(d) -1 and -3

Ans – (a) 3 and 1

**Q-16 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:**

(a) 3/12

(b) 4/12

(c) 5/12

(d) 7/12

Ans – (c) 5/12

Q-17 The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k – 1 has infinitely many solutions is

(a) 2

(b) 3

(c) 4

(d) 5

Ans – (a) 2

Q-18 The value of k for which the equations (3k + l)x + 3y = 2; (k2 + l)x + (k – 2)y = 5 has no solution, then k is equal to

(a) 2

(b) 3

(c) 1

(d) -1

Ans – (d) -1

**Q-19 The solution of 4/x+3y=14 and 3/x-4y=23 is:**

(a) ⅕ and -2

(b) ⅓ and ½

(c) 3 and ½

(d) 2 and ⅓

Ans – (a) ⅕ and -2

** Q-20 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:**

(a) 6km/hr and 3km/hr

(b) 7km/hr and 4km/hr

(c) 6km/hr and 4km/hr

(d) 10km/hr and 6km/hr

Ans – (c) 6km/hr and 4km/hr

Q-21 The pair of equations x = a and y = b graphically represents lines which are

(a) parallel

(b) intersecting at (b, a)

(c) coincident

(d) intersecting at (a,b)

Ans – (d) intersecting at (a,b)

Q-22 Asha 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) 35 and 15

(b) 15 and 35

(c) 35 and 20

(d) 25 and 25

Ans – (d) 25 and 25

**Q-23 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:**

(a) x=20° and y = 10°

(b) x=20° and y = 30°

(c) x=44° and y=15°

(d) x=15° and y=15°

Ans – (b) x=20° and y = 30°

Q-24 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 of the son and the father are, respectively

(a) 4 and 24

(b) 5 and 30

(c) 6 and 36

(d) 3 and 24

Ans – (c) 6 and 36

Q-25 The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

Ans – (c) infinitely many solutions

Q-26 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) 27

(b) 72

(c) 45

(d) 36

Ans – (d) 36

Q-27 The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

(a) a unique solution

(b) exactly two solutions

(c) infinitely many solutions

(d) no solution

Ans – (d) no solution

Q-28 What will be the value of k, if the lines given by x+ky+3 = 0 and 2x+(k+2)y+6 = 0 are coincident?

a) 4

b) 2

c) 6

d) 8

Ans – b) 2

Q-29 The sum of a two digit number and the number obtained by reversing the order of the digits is 187. If the digits differ by 1, then what will be the number?

a) 67

b) 54

c) 89

d) 67

Ans – c) 89

Q-30 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) -3

(c) -12

(d) no value

Ans – (d) no value

Q-31 If the lines representing the pair of linear equations a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 are coincident, then

(a) a_{1}/a_{2} = b_{1}/b_{2}

(b) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

(c) a_{1}/a_{2} ≠ b_{1}/b_{2}

(d) a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

Ans – (b) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

Q-32 A pair of linear equations which has a unique solution x = 2, y = -3 is

(a) x + y = -1; 2x – 3y = -5

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

(c) 2x – y = 1; 3x + 2y = 0

(d) x – 4y – 14 = 0; 5x – y – 13 = 0

Ans – (b) 2x + 5y = -11; 4x + 10y = -22

Q-33 10 years ago, a woman was thrice the age of her daughter. Two years later her daughter’s age will be 30 more than the age of the mother. What are the present ages of the woman and the daughter?

(a) 70 years, 40 years

(b) 60 years, 40 years

(c) 55 years, 25 years

(d) 45 years, 20 years

Ans – (c) 55 years, 25 years

Q-34 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

(a) 4 and 24

(b) 5 and 30

(c) 6 and 36

(d) 3 and 24

Ans – (c) 6 and 36

Q-35 If the pair of linear equations has a unique solution, then the lines representing these equations will

(a) coincide

(b) intersect at one point

(c) parallel to each other

(d) parallel to x-axis

Ans – (b) intersect at one point

Q-36 In a piggy bank the total number of coins of Rs. 5 and Rs. 1 is 100. If the total coins amount is 300, then what is the number of coins of each denomination?

a) 30, 70

b) 50, 50

c) 45, 55

d) 60, 40

Ans – b) 50, 50

Q-37 Which of the following method(s) is/are used to find the solution of a pair of linear equations algebraically?

(a) Substitution Method

(b) Elimination Method

(c) Cross- multiplication Method

(d) All the above

Ans – (d) All the above

Q-38 A father gives Rs. 500 to his children every month. If the boy gets Rs. 100 then, the girl gets Rs. 200 and if the boy gets Rs. 100 the girl gets Rs. 150. How many children does he have?

(a) 0

(b) 3

(c) 2

(d) 1

Ans – (a) 0

Q-39 The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be

(a) parallel lines

(b) coincident lines

(c) intersecting lines

(d) perpendicular lines

Ans – (a) parallel lines