CBSE Class 10 Mathematics Pairs of Linear Equations in Two Variables MCQs Set 03

Question: The number of solutions of the pair of equations 2x + 5y = 10 and 6x + 15y – 30 = 0 is
a) 0
b) 1
c) 2
d) infinite
Answer: d

Question: If a pair of linear equations has infinitely many solutions, then the lines representing them will be
a) parallel
b) intersecting or coincident
c) always intersecting
d) always coincident
Answer: a

Question: If the sum of the ages (in years) of a father and his son is 65 and twice the difference of their ages (in years) is 50, what is the age of the father?
a) 45 years
b) 40 years
c) 50 years
d) 55 years
Answer: a

Question: A pair of linear equations which has x = 0, y = -5 as a solution is
a) x + y = 0; 2x – 3y = 10
b) x + y = 3; 2x – y = 5
c) 2x + 3y + 5 = 0; 3x + 2y = 0
d) x – 4y = 14; 5x – y = 13
Answer: c

Question: The pair of equations 6x – 7y = 1 and 3x – 4y = 5 has
a) a unique solution
b) two solutions
c) infinitely many solutions
d) no solution
Answer: a

Question: If a + b = 5 and 3a + 2b = 20, find 3a + b.
a) 25
b) 20
c) 15
d) 10
Answer: a

Question: The value of k for which the pair of equations kx + y = 3 and 3x + 6y = 5 has a unique solution is
a) –1/2
b) 2
c) –2
d) all the above
Answer: d

Question: The pair of equations x = 2 and y = 3 has
a) one solution
b) two solutions
c) many solutions
d) no solution
Answer: a

Question: If the pair of linear equations 2x + ky – 3 = 0 and 6x + (2/3)y + 7 = 0 has a unique solution, which of the following is true?
a) k = 2/3
b) k ≠ 2/3
c) k = 2/9
d) k ≠ 2/9
Answer: d

Question: The value of k for which the system of equations x + 3y – 4 = 0 and 2x + ky = 7 is inconsistent is
a) 21/4
b) 1/6
c) 6
d) 4/21
Answer: c

Question: Sanya’s age is three times her sister’s age. Five years hence, her age will be twice her sister’s age. The present ages (in years) of Sanya and her sister are respectively
a) 12 and 4
b) 15 and 5
c) 5 and 15
d) 4 and 12
Answer: b

Question: A’s age is six times B’s age. Four years hence, the age of A will be four times B’s age. The present ages, in years, of A and B are, respectively
a) 3 and 24
b) 36 and 6
c) 6 and 36
d) 4 and 24
Answer: b

Question: Divya has only ₹2 and ₹5 coins with her. If the total number of coins that she has is 25 and the amount of money with her is ₹80, then the number of ₹2 and ₹5 coins are, respectively
a) 15 and 10
b) 10 and 15
c) 12 and 10
d) 13 and 12
Answer: b

Question: How many solutions does the system of equations p + 2q = 4 and 2p + 4q – 12 = 0 have?
a) 0
b) 1
c) 2
d) 3
Answer: a

Question: The value of k for which the lines (k + 1)x + 3ky + 15 = 0 and 5x + ky + 5 = 0 are coincident is
a) 14
b) 2
c) –14
d) –2
Answer: a

Question: The pair of equations y = a and y = b graphically represents lines which are
a) intersecting at (a, b)
b) intersecting at (b, a)
c) parallel
d) coincident
Answer: c

Question: The pair of equations x + 3y – 4 = 0 and 2x + 6y = 7 has
a) 0 solutions
b) 1 solution
c) 2 solutions
d) infinite solutions
Answer: a

Question: The sum of the digits of a two-digit number is 8. If 18 is added to it, the digits of the number get reversed. The number is
a) 53
b) 35
c) 62
d) 26
Answer: b

Question: The pair of equations 4x – 3y + 5 = 0 and 8x – 6y –10 = 0 graphically represents two lines which are
a) coincident
b) parallel
c) intersecting at exactly one point
d) intersecting at exactly two points
Answer: b

Question: If a pair of linear equations is inconsistent, then the lines representing them will be
a) parallel
b) always coincident
c) intersecting or coincident
d) always intersecting
Answer: a

Question: The pair of equations 3x – 2y = 5 and 6x – y = 3 have
a) no solution
b) a unique solution
c) two solutions
d) infinitely many solutions
Answer: b

Question: 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
Answer: c

Question: A pair of linear equations which has a unique solution x = –1, y = –2 is
a) x – y = 1; 2x + 3y = 5
b) 2x – 3y = 4; x – 5y = 9
c) x + y – 3 = 0; x – y = 1
d) x + y + 3 = 0; 2x – 3y + 5 = 0
Answer: b

Question: The pair of equations x = a and y = b graphically represent lines which are
a) parallel
b) intersecting at (b, a)
c) coincident
d) intersecting at (a, b)
Answer: d

Question: If x = a and y = b is the solution of the equations x + y = 5 and x – y = 7, then values of a and b are respectively
a) 1 and 4
b) 6 and –1
c) –6 and 1
d) –1 and –6
Answer: b

Question: If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is
a) –5/4
b) 2/5
c) 15/4
d) 3/2
Answer: c

Question: A pair of linear equations in two variables cannot have
a) a unique solution
b) no solution
c) infinitely many solutions
d) exactly two solutions
Answer: d

Question: A pair of linear equations which has a unique solution x = 3, y = –2 is
a) x + y = –1; 2x – 3y = 12
b) 2x + 5y + 4 = 0; 4x + 10y + 8 = 0
c) 2x – 3y = 0; 3x + 2y = 0
d) x – 4y = 14; 5x – y = 13
Answer: b

Question: 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
Answer: b

Question: Five years ago, a father’s age was seven times his son’s age. Five years from now, the father’s age will be thrice the son’s age. What are the respective present ages of father and son?
a) 40 years, 10 years
b) 10 years, 40 years
c) 25 years, 5 years
d) 30 years, 8 years
Answer: a

Question: The side of a square is 4m more than the side of another square. The sum of their areas is 208 sq. m. What is the side of the larger square?
a) 12m
b) 8m
c) 9m
d) 5m
Answer: a

Question: If the system of equations 4x + y = 3 and (2k – 1)x + (k – 1)y = 2k + 1 is inconsistent, then k =
a) 2/3
b) –2/3
c) –3/2
d) 3/2
Answer: d

Question: If am ≠ bl, then the system of equations ax + by = c and lx + my = n
a) has a unique solution
b) has no solution
c) has infinitely many solutions
d) may or may not have a solution
Answer: a

Question: If the system of equations 4x + 3y = 9 and 2ax + 3(a + b)y = 18 has infinitely many solutions, then
a) b = 2a
b) a = 2b
c) a + 2b = 0
d) 2a – b = 0
Answer: b

Question: The value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution is
a) 0
b) 3
c) ≠ 0
d) ≠ 3
Answer: d

Question: 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 expense is ₹ 1000; when it is ₹ 240, the expense is ₹ 980. What is the monthly expense on wheat if the cost is ₹ 350 per quintal?
a) ₹ 900
b) ₹ 350
c) ₹ 650
d) ₹ 700
Answer: d

Question: If the system of equations 2x + 3y = 7 and (a + b)x + (2a – b)y = 21 has infinitely many solutions, then
a) a = 1, b = 5
b) a = –1, b = 5
c) a = 5, b = 1
d) a = 5, b = –1
Answer: c

Question: Find the unique solution of the system of simultaneous equations 2x – y = 2 and 4x – y = 4.
a) x = 0, y = 1
b) x = 0, y = 0
c) x = 1, y = 0
d) x = 1, y = 1
Answer: c

Question: If 2x – 3y = 7 and (a + b)x – (a + b – 3)y = 4a + b represent coincident lines, then a and b satisfy the equation
a) a + 5b = 0
b) 5a + b = 0
c) a – 5b = 0
d) 5a – b = 0
Answer: c