CBSE Class 10 Mathematics Pairs of Linear Equations in Two Variables MCQs Set 01

Question: The pair of equations 6x -7y =1 and 3x - 4 y = 5 has

a) a unique solution

b) infinitely many solutions

c) two solutions

d) no solution

Answer: a unique solution

Question: The number of solutions of the pair of equations 2x +5y =10 and 6x +15y -30 = 0 is

a) infinite

b) 2

c) 1

d) 0

Answer: infinite

Question: The value of k for which the system of equations x +3y - 4 = 0 and 2x + ky = 7 is inconsistent is

a) 6

b) 4/21

c) 1/6

d) 21/4

Answer: 6

Question: The value of k for which the system of equations kx - y = 2, 6x -2y = 3 has a unique solution is

a) ≠3

b) ≠0

c) = 3

d) = 0

Answer: ≠3

Question: If the system of equations 2x +3y = 7 (a + b)x +(2a - b)y = 21 has infinitely many solutions, then

a) a = 5, b = 1

b) a= 5, b = -1

c) a = –1, b = 5

d) a = 1, b = 5

Answer: a = 5, b = 1

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

a) has a unique solution

b) has infinitely many solutions

c) has no solution

d) may or may not have a solution

Answer: has a unique solution

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) 5a+ b = 0

d) a +5b = 0

Answer: a -5b = 0

Question: The pair of equations x = a and y = b graphically represent lines which are

a) intersecting at (a, b)

b) coincident

c) intersecting at (b, a)

d) parallel

Answer: intersecting at (a, b)

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

a) 15/4

b) 3/2

c) 2/5

d) -5/4

Answer: 15/4

Question: Gunjan 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

a) 35 and 15

b) 35 and 20

c) 15 and 35

d) 25 and 25

Answer: 35 and 15

Question: If a pair of linear equations is inconsistent, then the lines representing them will be

a) parallel

b) intersecting or coincident

c) always coincident

d) always intersecting

Answer: parallel

Question: If a pair of linear equations has infinitely many solutions, then the lines representing them will be

a) always coincident

b) intersecting or coincident

c) parallel

d) always intersecting

Answer: always coincident

Question: The number of solutions of the pair of linear equations x +3y - 4 = 0 and 2x +6 y = 7 is

a) 0

b) 1

c) 2

d) infinite

Answer: 0

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: 14

Question: The value of g for which the system of equations 5gx -2y =1 and 10x + y = 3 has a unique solution is

a) ≠ – 4

b) =– 4

c) = 4

d) None of these

Answer: ≠ – 4

Question: The value of k for which the system of equations 2x + y -3 = 0 and 5x + ky +7= 0 has no solution is

a) 5/2

b) 3/7

c) 2

d) 5

Answer: 5/2

Question: If the system of equations 4x + y = 3 and (2k -1) x +(k -1)y = 2k +1 is inconsistent, then k =

a) 3/2

b) -3/2

c) -2/3

d) 2/3

Answer: 3/2

Question: The value of k for which the system of equation 2x +3y = 7 and 8x +(k + 4)y -28 = 0 has infinitely many solution is

a) 8

b) 3

c) –3

d) –8

Answer: 8

Question: If x = a and y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b are respectively

a) 3 and 1

b) –1 and –3

c) 5 and 3

d) 3 and 5

Answer: 3 and 1

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) 36 and 6

b) 6 and 36

c) 4 and 24

d) 3 and 24

Answer: 36 and 6

Question: The sum of the digits of a two digit number is 14. If 18 is added to the number, the digits get reversed. The number is

a) 68

b) 86

c) 59

d) 95

Answer: 68

Question: Two numbers are in the ratio 1 : 3. If 5 is added to both the numbers, the ratio becomes 1 : 2. The numbers are

a) 5 and 15

b) 6 and 18

c) 7 and 21

d) 4 and 12

Answer: 5 and 15

Question: A pair of linear equations in two variables cannot have

a) exactly two solutions

b) no solution

c) a unique solution

d) infinitely many solutions

Answer: exactly two solutions

Question: The pair of equations 3x -2y = 5 and 6x - y = 3 have

a) a unique solution

b) infinitely many solutions

c) no solution

d) two solutions

Answer: a unique solution

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