Maths MCQ Ch-3 Class 10 | Pair of Linear Equations

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Chapter 3 | Class X

Pair of Linear Equations in Two Variables

MCQ Based on Pair of linear equations in two variables

MCQ  Based on the Unique solution or intersecting lines.

MCQ Based on the Infinitely many solutions or coincident lines.

MCQ Based on the No solution or Parallel lines.

MCQ Based on the consistency or inconsistency of pair of linear equations.

MCQ Based from the CBSE Sample Questions

In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. Solution Hints are also given to some difficult problems. Each MCQ contains four options from which one option is correct. On the right hand side column of the pdf Answer option is given.

Action Plan

First of all students should Learn and write all basic points and Formulas of Pair of Linear Equations in two variables.

Start solving  the NCERT Problems with examples.

Solve the important assignments on the Pair of Linear Equations in Two Variables.

Then start solving the following MCQ.

MCQ | CHAPTER 3 | CLASS 10

PAIR OF LINEAR EUATIONS IN TWO VARIABLES

Q 1)What will be the nature of the graph lines of the equations 5x - 2y = 9 and 15x - 6y = 1 ?
a) Parallel
b) Coincident
c) Intersecting
d) Perpendicular to each other
Ans: a

Q 2)The equations 2x - 3y = 5 and 4x + 6y = 10 has
a) Unique sol.
b) No Sol.
c) Infinitely many sol
d) Inconsistent 

Ans: a

Q 3)What will be the nature of the graph lines of the equations x + 3y – 2 = 0 and 2x – y + 5 = 0 ?
a) Parallel
b) Coincident
c) Intersecting
d) Perpendicular to each other 

Ans: c

Q 4) If a pair of linear equations is consistent, then the lines will be
(a) always coincident
(b) parallel
(c) always intersecting
(d) intersecting or coincident 

Ans: d

Q 5) What will be the nature of the graph lines of the equations 2x + 5y + 15 = 0 and 6x + 15y + 45 = 0 ? 

a) Parallel
b) Coincident
c) Intersecting
d) Perpendicular to each other 

Ans: b

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

Q 7) What will be the value of k, if the lines given by (5 + k)x – 3y + 15 = 0 and (k – 1)x – y + 19 = 0 are parallel?
a) 5
b) 4
c) 6
d) 7 

Ans: b

Q 8) What will be the value of k, if the lines given by 3x + ky – 4 = 0 and 5x + (9 + k)y + 41 = 0 represent two lines intersecting at a point?

 

  
 Ans: d

Q 9) 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

Q 10) 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

Q 11) 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

Q 12) It takes 10 men and 6 women to finish a piece of work in 4 days, while it takes 5 men and 7 women to finish the same job in 6 days. What will be the time taken by 1 man and 1 woman to finish the job?
a) Man = 34 days, Woman = 45 days
b) Man = 45 days, Woman = 34 days
c) Man = 53 days, Woman = 96 days
d) Man = 54 days, Woman = 96 days 

Ans: d

Q 13) 10 years ago, a woman was thrice the age of her daughter. Two years later daughter’s age will be 30 less 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

Q 14) The sum of two numbers is 13 and the sum of their reciprocals is 13/ 40What are the two numbers?
a) 5, 8
b) 10, 3
c) 12, 1
d) 9, 4 

Ans: a

Q 15) 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

Q 16) 5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is
a) 50 years
b) 45 years
c) 47 years
d) 40 years 

Ans: d

Q 17) 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. 200 the girl gets Rs. 150. How many children does he have?
a) 0
b) 3
c) 2
d) 1 

Ans: b

Q 18) For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines
a) -9/2
b) -11
c) 9/2
d) -7 

Ans: a

Q 19) A pair of linear equations a₁x + b₁y + c₁ = 0; a₂x + b₂y + c₂ = 0 is said to be inconsistent, if

Ans: b

Q 20) 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

Q 21) If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is
a) -10/3
b) 10/3
c) -13
d) -7
Ans a

Q 22) 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

Q 23) The graph of y = 4x 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

Q 24) The graph of y = 5 is a line parallel to the
a) x-axis
b) y-axis
c) both axis
d) none of these 

Ans: a

Q 25) The graph of the equation 2x + 3y = 5 is a
a) vertical line
b) straight line
c) horizontal line
d) none of these 

Ans: b

Q 26) 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

Q 27) The value of k, for which equations 3x + 5y = 0 and kx + l0y = 0 has a non-zero solution is
a) 6
b) 0
c) 2
d) 5 

Ans: a

Q 28) 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

Q 29) 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

Q 30) 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

Q 31) 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

Q 32) 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

Q 33) 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

Q 34) 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

Q 35) Rohin 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
Q 36) Find the points where the lines 3x – 4y – 12 = 0 and 4x + 3y = 8 meet the x – axis
a) (- 4, 0), (2, 0)
b) ( 4, 0), (2, 0)
c) ( 4, 0), (- 2, 0)
d) (3, 0), (1, 0)
Ans: b

Q 37) 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

Q 38) Solve x + y = 7 and 2x – y = 5
a) (3, 4)
b) (5, 2)
c) (4, 3)
d) (2, 5) 

Ans: c

Q 39) 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

Q 40) Solve : 65x – 33y = 97 and 33x – 65y = 1
a) 2, 1
b) 1, 2
c) 2, 3
d) 3, 2 

Ans: a

Q 41) Solve : x + y = 7 and 2x – y = 5
a) (3, 4)
b) (5, 2)
c) (4, 3)
d) (2, 5) 

Ans: c

Q 42) If graph of two lines meet at (- 5, 4) and ax + 3y = 17 then a² + 1 =
a) 0
b) 2
c) 4
d) 1
Ans: b

Q 43) Solve x – y = 1 and 2x + 3y = - 8
a) (1, 2)
b) (-1, -2)
c) (2, 1)
d) (1, - 2) 

Ans: b

Q 44) The equations 2x – 3y = 5 and 4x + 6y = 10 has
a) Unique sol.
b) No Sol
c) Infinitely many sol.
d) Inconsistent 

Ans: a

Q 45) For what value of p, the equations 4x + py + 8 = 0 and 2x + 2y + 1 = 0 has unique solution
a) p = 4
b) p ≠ 2
c) p = 2
d) p ≠ 4 

Ans: d

Q 46) The equations 3x – 5y = 7 and 9x – 10y = 14 has
a) Unique sol.
b) No Sol
c) Infinitely many sol.
d) Inconsistent 

Ans: a

Q 47) For what value of k, the equations kx + 3y – k + 3 = 0 and 12x + ky – k = 0 has coincident lines
a) k = - 6
b) k ≠ 6

c) k = 6
d) p  ≠ - 6 

Ans: c

Q 48) For what value of k, the equations 5x + 2ky = 2 and 3x + 5y + 1 = 0 has parallel lines
a) k = - 5/ 4
b) k = 2/ 5
c) k = 25/6
d) k = 3/ 2
Ans: c

Q 49) Given the linear equations 2x – 3y = 5, which of the following will be another linear equation such that both have unique solutions
a) 2x – 3y = 10
b) 4x + 6y = 3
c) 4x – 6y = 10
d) 4x – 6y = 5 

Ans: b

Q 50) Given the linear equations 5x + 3y = 8, which of the following will be another linear equation such that both have no solutions
a) 10x – 6y = 16
b) 10x + 6y = 15
c) 10x + 6y = 16
d) 10x – 6y = 15 

Ans: b

Q 51) The difference between two numbers is 26 and one number is three times the other. Find the numbers.
a) 12, 36
b) 14, 42
c) 13, 39
d) 10, 30 

Ans: c

Q 52) In △ ABC, ∠C = 3∠B = 2(∠A+∠B then ∠C =

a) 60^o
b) 120^o
c) 100^o
d) 90^o
Ans: b

Q 53) Solve: 101x + 99y = 499 and 99x + 101y = 501
a) 3, 2
b) – 2, 5
c) 2, -5
d) 2, 3 

Ans: d

Q 54) If the following figure ABCD is a rectangle then find x and y

a) (4, 1)
b) (2, 3)
c) (3, 2)
d) (1, 4) 

Ans: d

Questions from CBSE Sample Paper 2021-22
Basic Maths SP (241)

Q 55) The pair of linear equations y = 0 and y = - 5 has
(a) One solution
(b) Two solutions
(c) Infinitely many solutions
(d) No solution 

Ans: d

Q 56) 8 chairs and 5 tables cost Rs.10500, while 5 chairs and 3 tables cost Rs.6450. The cost of each chair will be
(a) Rs. 750
(b) Rs.600
(c) Rs. 850
(d) Rs. 900 

Ans: a

Q 57) There are 20 vehicles-cars and motorcycles in a parking area. If there are 56 wheels together, how many cars are there?
(a) 8
(b) 10
(c) 12
(d) 20
Ans: a
Solution Hint
Let no of Cars = x
Let no of motorcycles = y
x + y = 20
4x + 2y = 56
Solving the above equations No of cars = x = 8

Q 58) What is the age of father, if the sum of the ages of a father and his son in years is 65 and twice the difference of their ages in years is 50 ?
(a) 40 years
(b) 45 years
(c) 55 years
(d) 65 years 

Ans: b

Q 59) What is the solution of the pair of linear equations 37x + 43y = 123, 43x + 37y = 117 ?
(a) x = 2, y = 1
(b) x = -1, y = 2
(c) x = -2, y = 1
(d) x = 1, y = 2
Ans:d
Solution Hint
37x + 43y = 123 ____(1)
43x + 37y = 117 ____(2)
Adding (1) and (2)
x + y = 3 ______(3)
Subtracting (2) from (1)
-x + y = 1..............(4)
Adding (3) and (4),
2y = 4 ⇒ y = 2 ⇒ x = 1 ∴ 

Solution is x = 1 and y = 2

Q 60) The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 do not have a solution if
(a) K = 5
(b) K = 10
(c) k ≠ 10
(d) k ≠ 5 

Ans:b

Q 61)If ABCD is a rectangle , find the values of x and y

a) x = 10, y = 2
b) x = 12, y = 8
c) x = 2, y = 10
d) x = 20, y = 0 

Ans: a

Standard Maths SP (041)

Q 62) The value of k for which the lines 5x + 7y = 3 and 15x + 21y = k coincide is
a) 9
b) 5
c) 7
d) 18 

Ans: a

Q 63) 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 – 14y + 4 = 0
c) –10x + 14y + 4 = 0
(d) 10x – 14y = – 4
Ans: d

Q 64) If 217x + 131y = 913,
131x + 217y = 827, then x + y is
(a) 5
(b) 6
(c) 7
(d) 8 

Ans: a

Q 65) The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is
(a) 2x – y + 7 = 0
(b) 3x +2 y – 7 = 0
(c) 3x – y – 7 = 0
(d) 3x + y – 7 = 0 

Ans: d

Q 66) The number of solutions of 3^x+y = 243 and 243^x-y = 3 is
(a) 0
(b) 1
(c) 2
(d) infinite 

Ans: b

Q 67) The lines x = a and y = b, are
(a) intersecting
(b) parallel
(c) overlapping
(d) (None of these)
Ans: a
Solution Hint 

Lines x = a is a line parallel to y axis and y = b is a line parallel to x axis. So they will intersect.

Questions from CBSE Final Question Paper 2021-22 (Basic)

Q 68) The pair of equations y = 0 and y = - 7 has :
a) one solution
b) two solutions
c) no solution
d) infinitely many solutions 

Ans: c

Q 69) If ax + by = a² – b² and bx + ay = 0, then the value of (x + y) is :
a) a² – b²
b) b – a
c) a – b
d) a² + b²
Ans: c


Q 70) If x = a, y = b is the solution of the equations 3x - y = 8 and x + y = 4, then the values of a and b are respectively :
a) 3 and 1
b) 3 and 5
c) 5 and 3
d) -1 and – 3
Ans: a


Q 71) The area of the triangle formed by the lines 2x + 3 y = 12 and x - y - 1= 0 and x = 0 (as shown in the figure) is :

a) 7.5 sq units
b) 5 sq units
c) 6.5 sq units
c) 6 sq units
Ans: a

Questions from CBSE Final Question Paper 2021-22 (Standard)

Q 72) The line represented by 4x – 3y = 9 intersects the y - axis at :
a) (0, -3)
b) (5,0)
c) (- 3,0)
d (0, 5) 

Ans: a

Q 73) The pair of lines represented by the linear equations 3x + 2y = 7 and 4x + 8y – 11 = 0 are :
a) perpendicular
b) parallel
c) intersecting
d) coincident 

Ans: c

Q 74) If 17x – 19y = 53 and 19x – 17y = 55, then the value of (x + y) is :
a) 1
b) -1
c) 3
d) - 3 

Ans: a

Q 75) A father is three times as old as his son. In 12 years time, he will be twice as old as his son. The sum of the present ages of the father and the son is :
a) 36 years
b) 48 years
c) 60 years
d) 42 years 

Ans: b

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