CBSE Class 10 Mathematics Pairs of Linear Equations in Two Variables MCQs Set E

Question. The value of k for which the given system has unique solution 2x + 3y – 5 = 0, kx – 6y – 8 = 0 is
(a) k = 2
(b) k ≠ 4
(c) k = 4
(d) k ≠ 4

Answer: D

Question. For what value of k, the following system of equations have infinite solutions: 2x – 3y = 7, (k + 2)x – (2k + 1)y = 3 (2k – 1)?
(a) k = 2
(b) k = 3
(c) k = 4
(d) k = 8

Answer: C

Question. The value of m for which the pair of linear equations 2x + 3y – 7 = 0 and (m – 1) x + (m + 1) y = (3m – 1) has infinitely many solutions is
(a) 5
(b) 8
(c) – 5
(d) 8

Answer: A

Question. The value(s) of k for which the pair of linear equations kx + y = k² and x + ky = 1 have infinitely many solutions is
(a) 1
(b) 2
(c) 3
(d) 4

Answer: A

Question. For what values of p and q, the following pair of linear equations have infinitely many solutions?
4x + 5y = 2; (2p + 7q)x + (p + 8q)y = 2q – p + 1
(a) p = 1, q = 3
(b) p = 3, q = 4
(c) p = –2, q = 5
(d) p = –1, q = 2

Answer: D

Question. If a pair of linear equations is consistent, then the line represented by them are
(a) parallel
(b) intersecting or coincident
(c) always coincident
(d) always intersecting

Answer: B

Question. The system of simultaneous equations 3m+ n =1 and (2k -1) m+ (k -1)n = 2k +1 , is inconsistent. What is the value of 'k'?
(a) 3
(b) 1
(c) 2
(d) 0

Answer: C

Question. Which of the following is not a solution of the pair of equations 3x – 2y = 4 and 6x – 4y = 8?
(a) x = 2, y = 1
(b) x = 4, y = 4
(c) x = 6, y = 7
(d) x = 5, y = 3

Answer: D

Question. If 2x + y = 35 and 3x + 2y = 65, the value of x y is
(a) 1/ 2
(b)1/ 3 
(c) 1/ 4 
(d) 1 / 5

Answer: D

Question. If 44/x+y + 30/x−y = 10 and 55/x+y + 40/x−y = 13 , then
(a) x = 7 , y = 7
(b) x = 2, y = 3
(c) x = 5 , y = 2
(d) x = 8, y = 3

Answer: D

Question. Aruna 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) 35 and 20
(c) 15 and 35
(d) 25 and 25

Answer: D

Question. The vertices of the triangle formed by the graphs of the equations 4x – 3y – 6 = 0, x + 3y – 9 and y-axis are
(a) (1, 3), (2, 4), (–3, 5)
(b) (0, 3), (3, 2), (0, –2)
(c) (0, 4), (3, 3), (2, 6)
(d) None of the options

Answer: B

Question. The nature of the system of equations 2x – 2y – 2 = 0 and 4x – 4y – 5 = 0 is
(a) Unique
(b) Consistent
(c) Inconsistent
(d) None of the options

Answer: C

Question. The area of the quadrilateral formed by the lines x = 3, x = 6, 2x – y – 4 = 0 and x-axis is
(a) 8 sq. units
(b) 12 sq. units
(c) 15 sq. units
(d) None of the options

Answer: C

Question. The lines represented by the equations 9x + 3y + 12 = 0 and 18x + 6y + 24 will
(a) intersect at a point
(b) be parallel
(c) be coincident
(d) None of the options

Answer: C

Question. If a pair of linear equations is consistent, then the line represented by them are
(a) parallel
(b) intersecting or coincident
(c) always coincident
(d) always intersecting

Answer: B

Question. If 2x + 5y – 1 = 0, 2x + 3y – 3 = 0, then
(a) x = 1, y = – 3
(b) x = 3, y = –1
(c) x = 2, y = 5
(d) x = 5, y = – 3

Answer: B

Question. If 7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2, then
(a) x = 1, y = 4
(b) x = 3, y = 5
(c) x = 5, y = 1
(d) None of the options

Answer: C

Question. The pair of linear equations 3x/2 +5y/3 = 7 and 9x + 10y = 14 is
(a) consistent
(b) inconsistent
(c) consistent with one solution
(d) consistent with many solutions

Answer: B

Question. The value of p if the lines represented by the equations 3x – y – 5 = 0 and 6x – 2y – p = 0 are parallel is
(a) only 8
(b) only 10
(c) only 15
(d) All values of ‘p’ except 10

Answer: C

Question. The value of k for which the given system has unique solution 2x + 3y – 5 = 0, kx – 6y – 8 = 0 is
(a) k = 2
(b) k ≠ 4
(c) k = 4
(d) k ≠ 4

Answer: D

Question. Rajesh buys 7 books and 6 pens for `3800 and Amar buys 3 books and 5 pens of the same kind for ₹ 1750. What are the respective costs of a book and a pen?
(a) ₹ 350, ₹ 50
(b) ₹ 500, ₹ 75
(c) ₹ 250, ₹ 100
(d) ₹ 500, ₹ 50

Answer: D

Question. The angles A, B, C and D in order in a cyclic quadrilateral are (2x + y)^o ,(2(x + y))^o , (3x + 2y )^o , and (4x + 2y )^o . Find their measures in the same order.
(a) 70°, 110°, 80°, 100°
(b) 70°, 80°, 110°, 100°
(c) 70°, 80°, 100°, 110°
(d) 80° , 100° , 110° , 70°

Answer: B

Question. If 3 – (x – 5) = y + 2, 2(x + y) = 4 – 3y, then
(a) x = 13 /4 , y = 9/ 10
(b) x = 7/ 16 , y = 5 /8
(c) x = 4/ 9 , y = 9 /12
(d) x = 26 /3 , y = −8/ 3

Answer: D

Question. The value of x satisfying both the equations 4x – 5 = y and 2x – y = 3, when y = –1 is
(a) 1
(b) –1
(c) 2
(d) –2

Answer: A

Question. The solution of the following system of equations when solved graphically is:
2x – 3y – 6 = 0 2x + y + 10 = 0
(a) (3, 4)
(b) (–3, –4)
(c) (4, 5)
(d) (–4, –5)

Answer: B

Question. Given: 5 pencils and 7 pens together cost ` 50, whereas 7 pencils and 5 pens together cost ` 46. The pair of linear equations representing the above situation and the cost of one pencil and that of one pen, respectively are
(a) 5x – 7y = 50, 7x – 5y = 46; (3, 5)
(b) 5x + 7y = 50, 7x + 5y = 46; (3, 5)
(c) 3x – 8y = 48, 3x + 8y = 48; (5, 3)
(d) None of the options

Answer: B

Question. If 2x + 3y = 11 and 2x – 4y = –24, then the value of ‘m’ for which y = mx + 3 is
(a) 0
(b) 1
(c) –1
(d) – 2

Answer: C

Question. If 2x + 3y = 11 and x – 2y = –12, then the value of ‘m’ for which y = mx + 3 is
(a) 1
(b) –1
(c) 2
(d) – 2

Answer: B

Question. Which of the following solutions do the system of equations 2x + y = 5 and x + 2y = 4 have?
(a) Consistent and a unique solution
(b) Consistent and infinitely many solutions
(c) Inconsistent
(d) No solution

Answer: A

Question. Choose the dependent system from the following.
(a) m+ n = 7, 3m+3n = 21
(b) 3x - 2y = 5 , 2x - 3y = 7
(c) 3x - 3y =18 , x - y =10
(d) 2x + y = 6 , 4x - 2y = 4

Answer: A

Question. The two consecutive odd positive integers, sum of whose squares is 290 are
(a) 5, 13
(b) 11, 13
(c) 13, 17
(d) None of the options

Answer: B

Question. Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. The present age of father and son, respectively are
(a) 40 years, 12 years
(b) 30 years, 6 years
(c) 32 years, 8 years
(d) 42 years, 10 years

Answer: D

Question. The nature of graphs of equations x + 4y = 3, 2x + 8y = 6 and the number of their solutions are
(a) Consistent, one
(b) Consistent, two
(c) Dependent, many
(d) Inconsistent, no solution

Answer: C

Question. The number of solutions of the following pair of linear equations is
x + 2y – 8 = 0
2x + 4y = 16
(a) No solutions
(b) One solution
(c) Two solutions
(d) Infinitely many solutions

Answer: D

Question. If 4/x +5y =7 ;3/x+4y = 5 , then
(a) x = 1 3 y = –1
(b) x = 8, y = 3
(c) x = 4, y = 7
(d) x = 5, y = 9

Answer: A

Question. The value of k for which the system of equations kx + 4y = k – 4, 16x + ky = k have infinite number of solutions is
(a) k = 2
(b) k = 4
(c) k = 6
(d) k = 8

Answer: D

Question. If 2x + 3y = 11 and 2x – 4y = –24, then the value of ‘m’ for which y = mx + 3 is
(a) 0
(b) 1
(c) –1
(d) – 2

Answer: C

Question. If 2x + 3y = 11 and x – 2y = –12, then the value of ‘m’ for which y = mx + 3 is
(a) 1
(b) –1
(c) 2
(d) – 2

Answer: B

Question. Solution of the simultaneous linear equations: 2x/y -y/2 =-1/6 and x/2 +2y/3 =3 is
(a) x = 2, y = – 3
(b) x = – 2, y = 3
(c) x = 2, y = 3
(d) x = – 2, y = – 3

Answer: C

Question. The value of x satisfying both the equations 4x – 5 = y and 2x – y = 3, when y = –1 is
(a) 1
(b) –1
(c) 2
(d) –2

Answer: A

Question. 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)

Answer: B

Question. The sum of a two-digit number and the number obtained by reversing its digits is 154. If the digits differ by 4, find the number.
(a) 95
(b) 73
(c) 84
(d) 62

Answer: A

Question. On comparing a₁/a₂ , b₁/b₂ , c₁/ c₂ , the graphical representation of equations 3x + 2y = 5, 2x – 3y = 7 will be
(a) Intersecting
(b) Coincident
(c) Parallel
(d) None of the options

Answer: A

Question. The lines represented by the equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0 will
(a) intersect at a point
(b) be parallel
(c) be coincident
(d) None of the options

Answer: B

Question. For what value of k, the following system of equations have infinite solutions:
2x – 3y = 7, (k + 2)x – (2k + 1)y = 3 (2k – 1)?
(a) k = 2
(b) k = 3
(c) k = 4
(d) k = 8

Answer: C

Question. The value of k for which the following pair of linear equations have infinitely many solutions:
2x + 3y = 7, (k – 1)x + (k + 2)y = 3k is
(a) 2
(b) 4
(c) 7
(d) 9

Answer: C

Question. If 2x + 5y – 1 = 0, 2x + 3y – 3 = 0, then
(a) x = 1, y = – 3
(b) x = 3, y = –1
(c) x = 2, y = 5
(d) x = 5, y = – 3

Answer: B

Question. If 3 chairs and 1 table costs ` 1500 and 6 chairs and 1 table costs ` 2400, the pair of linear equations to represent this situation is
(a) 6x + y = 1500, 3x + y = 2400
(b) x 3 + y = 1500, x 6 + y = 2400
(c) 3x + y = 1500, 6x + y = 2400
(d) None of the options

Answer: C

Question. 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

Answer: D

Question. The value of m and n so that the pair of linear equations (2m – 1)x + 3y = 5; 3x + (n – 1)y = 2 has infinite number of solutions respectively are
(a) 15/ 4 , 13/ 8 
(b) 17, 4 , 11/ 5 
(c) 11/ 8, 11/ 9 
(d) None of the options

Answer: B

Question. The values of a and b for which the following pair of linear equations have infinitely many solutions:
2x + 3y = 7, (a + b)x + (2a – b)y = 21, respectively are
(a) a = 5, b = 1
(b) a = 2, b = 3
(c) a = 4, b = 7
(d) None of the options

Answer: A

Question. What type of straight lines will be represented by the system of equations 2x + 3y = 5 and 4x + 6y = 7?
(a) Intersecting
(b) Parallel
(c) Conincident
(d) None of the options

Answer: B

Question. The vertices of the triangle formed by the lines, 5x – y = 5, x + 2y = 1 and 6x + y = 17 are
(a) (1, 0), (3, –1), (2, 5)
(b) (2, 3), (5, 6), (3, –1)
(c) (1, 2), (2, 5), (3, 6)
(d) None of the options

Answer: A

Assertion and Reason:
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : 3x + 4y + 5 = 0 and 6x + ky + 9 = 0 represent parallel lines if k = 8
Reason : a₁x + b₁y + c₁ = 0 and a₂x + b²y + c₂ = 0 represent parallel lines if a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Answer: A

Question. Assertion : If kx – y – 2 = 0 and 6x – 2y – 3 = 0 are inconsistent, then k = 3
Reason : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are inconsistent if a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Answer: A

Question. Assertion : The linear equations x – 2y – 3 = 0 and 3x + 4y – 20 = 0 have exactly one solution
Reason : The linear equations 2x + 3y – 9 = 0 and 4x + 6y – 18 = 0 have a unique solution

Answer: C

Question. Assertion : 3x – 4y = 7 and 6x – 8y = k have infinite number of solution if k = 14
Reason : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 have a unique solution if a₁/a₂ ≠ b₁/b₂

Answer: B