AIIMIIT education by naveen rachuri: linear equations 10th cbse mcqs

Class 10 Maths MCQs Chapter 3 Pair of Linear Equations in Two Variables

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

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

3. 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

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

5. The pair of equations x = 0 and x = 5 has
(a) no solution
(b) unique/one solution
(c) two solutions
(d) infinitely many solutions

6. 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)

7. For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines

8. If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is

9. One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be
(a) 2x + 5y = 6
(b) 3x + 5y = 3
(c) -10x – 25y + 15 = 0
(d) 10x + 25y = 15

10. 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

11. 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

12. 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

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

14. Two equations in two variables taken together are called
(a) linear equations
(b) quadratic equations
(c) simultaneous equations
(d) none of these

15. If am bl then the system of equations ax + by = c, lx + my = n, has
(a) a unique solution
(b) no solution
(c) infinitely many solutions
(d) none of these

16. 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

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

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

19. 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

20. 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

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)

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

23. 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

24. 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

25. The linear equation 3x-11y=10 has:

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d.No solutions

26) 3x+10 = 0 will has:

a. Unique solution

b. Two solutions

c. Infinitely many solutions

d.No solutions

27) The solution of equation x-2y = 4 is:

a. (0,2)

b. (2,0)

c. (4,0)

d. (1,1)

28) Find the value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.

a. 5

b. 6

c. 7

d. 85

29) Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:

a. 4/3

b. 5/3

c. 3

d. 7/3

30) The graph of linear equation x+2y = 2, cuts the y-axis at:

a. (2,0)

b. (0,2)

c. (0,1)

d. (1,1)

31) Any point on line x = y is of the form:

a. (k, -k)

b. (0, k)

c. (k, 0)

d. (k, k)

32) The graph of x = 3 is a line:

a. Parallel to the x-axis at a distance of 3 units from the origin

b. Parallel to the y-axis at a distance of 3 units from the origin

c. Makes an intercept 3 on the x-axis

d. Makes an intercept 3 on the y-axis

33) In equation, y = mx+c, m is:

a. Intercept

b. Slope

c. Solution of the equation

d. None of the above

34) If x and y are both positive solutions of equation ax+by+c=0, always lie in the:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Answer: a

35) A linear equation in two variables is of the form ax + by + c = 0, where

(a) a = 0, c = 0

(b) a ≠ 0, b = 0

(d) a ≠ 0, b ≠ 0

Ans.d

36) Any point on the x-axis is of the form

(a) (x, y)

(b) (0, y)

(d) (x, x)

37) Any point on the y-axis is of the form

(a) (y, y)

(b) (0, y)

(d) (x, 0)

38) The linear equation 2x – 5y = 7 has

(a) No solution

(b) unique solution

(d) Infinitely many solutions

39. The linear equation 3x – y = x – 1 has

(a) No solution

(b) unique solution

(d) Infinitely many solutions

40) The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point

(a) (2, 0)

(b) (0, 2)

(d) (0, 0

41) The equation 2x + 5y = 7 has a unique solution, if x, y are:

(a) Rational numbers

(b) Real numbers

(d) Positive real numbers

42. The point of the form (a, a) always lies on:

(a) On the line x + y = 0

(b) On the line y = x

(d) y-axis

43) If we multiply or divide both sides of a linear equation with the same non-zero number, then the solution of the linear equation:

(a) Remains the same

(b) Changes

(d) Changes in case of division only

44) If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is

(a) 2

(b) 4

(d) 6

45. Graphically, the pair of equations

6x – 3y + 10 = 0

2x – y + 9 = 0

Represents two lines which are:

(A) Intersecting at exactly one point.

(B) Intersecting at exactly two points.

(C) Coincident.
D.parallel

46.. The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:

(A) A unique solution

(B) Exactly two solutions

(C) Infinitely many solutions

(D) No solution

47. If a pair of linear equations is consistent, then the lines will be:

(A) Parallel

(B) Always coincident

(C) Intersecting or coincident

(D) Always intersecting

48. The pair of equations y = 0 and y = –7 has

(A) One solution

(B) Two solutions

(C) Infinitely many solutions
(D) No solution

49. If the lines given by

3x + 2ky = 2

2x + 5y + 1 = 0

are parallel, then the value of k is

(A) 5/4

(B) 2/5

(C)15/4
(D) 3/2

50. 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

51. One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0. The second equation can be

(A) 10x + 14y + 4 = 0

(B) –10x – 14y + 4 = 0

(C) –10x + 14y + 4 = 0

(D) 10x – 14y = –4

52. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Then the numbers are:

(A) 40, 42

(B) 42, 48

(C) 40, 48

(D) 44, 50

53. The solution of the equations x – y = 2 and x + y = 4 is:

(A) 3 and 5

(B) 5 and 3

(C) 3 and 1

(D) –1 and –3

54. For which values of a and b, will the following pair of linear equations have infinitely many solutions?

x + 2y = 1

(a – b)x + (a + b)y = a + b – 2

(A) a = 2 and b = 1

(B) a = 2 and b = 2

(C) a = ̶ 3 and b = 1

(D) a = 3 and b = 1

55. 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

56. Rakshita 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 andRs.2 coins is, respectively

(A) 35 and 15

(B) 35 and 20

(C) 15 and 35

(D) 25 and 25

57. In a competitive examination, one mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

(A) 100

(B) 95

(C) 90

(D) 60

58. The angles of a cyclic quadrilateral ABCD are:

A=6x+10
B=5x
C=x+y
D=3y-10
Then value of x and y are:

(A) x = 20o and y = 30o

(B) x = 40o and y = 10o

(C) x = 44o and y=15o

(D) x = 15o and y = 15o

59. A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Reema paid Rs. 22 for a book kept for six days, while Ruchika paid Rs 16 for the book kept for four days, then the charge for each extra day is:

(A) Rs 5

(B) Rs 4

(C) Rs 3

(D) Rs.2

60.  Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines. Find the number of students in the class.

       (a)  40

       (b)  50

       (c)  60

       (d)  70

61.  8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.

       (a)  120, 130

       (b)  140,280

       (c)  240,280

       (d)  100,120

62.  The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.

       (a)  46

       (b)  48

       (c)  64

       (d)  84

63.  A fraction becomes . when subtracted from the numerator and it becomes . when 8 is added to its denominator. Find the fraction.

       (a)  4/12

       (b)  3/13

       (c)  5/12

       (d)  11/7

64. Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.

       (a)  20

       (b)  50

       (c)  60

       (d)  40

65.  What will be the solution of these equations ax+by=a-b, bx-ay=a+b

       (a)  x=1, y=2

       (b)  x=2,y=-1

       (c)  x=-2, y=-2

       (d)  x=1, y=-1

66.  If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 then what will be value of a and b

       (a)  2,1

       (b)  3,1

       (c)  4,6

       (d)  1,2

67.  Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?

       (a)  6km/hr

       (b)  4km/hr

       (c)  3km/hr

       (d)  7km/hr

68. The linear equation 3x-11y=10 has:
a) Unique solution
b) Two solutions
c) Infinitely many solutions
d) No solutions

69. 3x+10 = 0 will has:
a) Unique solution
b) Two solutions
c) Infinitely many solutions
d) No solutions

70. The solution of equation x-2y = 4 is:
a) (0,2)
b) (2,0)
c) (4,0)
d) (1,1)

71. The value of k, if x = 1, y = 2 is a solution of the equation 2x + 3y = k.
a) 5
b) 6
c) 7
d) 8

72. Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:
a) 4/3
b) 5/3
c) 3
d) 7/3

73. The graph of linear equation x+2y = 2, cuts the y-axis at:
a) (2,0)
b) (0,2)
c) (0,1)
d) (1,1)

74. Any point on the line x = y is of the form:
a) (k, -k)
b) (0, k)
c) (k, 0)
d) (k, k)

75. The graph of x = 3 is a line:
a) Parallel to x-axis at a distance of 3 units from the origin
b) Parallel to y-axis at a distance of 3 units from the origin
c) Makes an intercept 3 on x-axis
d) Makes an intercept 3 on y-axi

76. In equation, y = mx+c, m is:
a) Intercept
b) Slope of the line
c) Solution of the equation
d) None of the above

77. If x and y are both positive solutions of equation ax+by+c=0, always lie in:
a) First quadrant
b) Second quadrant
c) Third quadrant
d) Fourth quadran

78. The linear equation 4x – 10y = 14 has:
a) A unique solution
b) Two solutions
c) Infinitely many solutions
d) No solutions

79. Find the number of solutions of the following pair of linear equations. x + 2y – 8 = 0 and 2x + 4y = 16:
a) 0
b) 1
c) 2
d) Infinite

80. If (2, 0) is a solution of the linear equation 2x +3y = k, then the value of k is:
a) 4
b) 6
c) 5
d) 2

81 . The graph of the linear equation 2x +3y = 6 cuts the y-axis at the point:
a) (2, 0)
b) (0, 3)
c) (3, 0)
d) (0, 2)

82. The equation y = 5, in two variables, can be written as:
a) 1 .x + 1 .y = 5
b) 0 .x + 0 .y = 5
c) 1 .x + 0 .y = 5
d)0 .x + 1 .y = 5

83. Any point on the line y = x is of the form:
a) (a, –a)
b) (0, a)
c) (a, 0)
d) (a, a)

84. The graph of x = 5 is a line:
a) Parallel to x-axis at a distance 5 units from the origin
b) Parallel to y-axis at a distance 5 units from the origin
c) Making an intercept 5 on the x-axis
d) Making an intercept 5 on the y-axis
85. x = 9, y = 4 is a solution of the linear equation:
a) 2x + y = 17
b) x + y = 17
c) x + 2y = 17
d) 3x – 2y = 17

86. Any point on the x-axis is of the form:
a) (0, y)
b) (x, 0)
c) (x, x)
d) (x, y)

87. If a linear equation has solutions (–3, 3), (0, 0) and (3, –3), then it is of the form:
a)y – x = 0
b)x + y = 0
c) –2x + y = 0
d) –x + 2y = 0

88. The positive solutions of the equation ax + by + c = 0 always lie in the:
a) 1st quadrant
b) 2nd quadrant
c) 3rd quadrant
d) 4th quadrant

89. The graph of the linear equation 5x + 3y = 10 is a line which meets the x-axis at the point:
a) (0, 3)
b) (3, 0)
c) (2, 0)
d) (0, 2)

90. The point of the form (a, –a) always lies on the line:
a) x = a
b) y = –a
c) y = x
d) x + y = 0

91. The graph of x = 9 is a straight line:
a) Intersecting both the axes
b) parallel to y-axis
c) parallel to x-axis
d) Passing through the origin

92. Equation of the line parallel to x-axis and 6 units above the origin is:
a) x = 6
b) x = –6
c)y = 6
d)y = –6

93.The value of y at x = -1 in the equation 5y = 2 is

(a) 52
(b) 25
(c) 10
(d) 0

94.Equation of a line which is 5 units distance above the x-axis is
(a) x = 5
(b) x + 5 = y
(c) y – 5
(d) x – y = 0

95.x = 3 and y = -2 is a solution of the equation 4px – 3y = 12, then the value of p is
(a) 0
(b) 12
(c) 2
(d) 3

96.Which of the following is the equation of a line parallel to y-axis?
(a) y = 0
(b) x + y = z
(c) y = x
(d) x = a

97.Any point on the line y = 3x is of the form
(a) (a, 3a)
(b) (3a, a)
(c) (a, a3)
(d) (a3, -a)

98.To which equation does the graph represent?
(a) 3x – 7y = 10
(b) y – 2x = 3
(c) 8y – 6x = 4
(d) 5x +352y = 25

99.Any point of the form (a, – a) always lie on the graph of the equation
(a) x = -a
(b) y = a
(c) y = x
(d) x + y = 0

100.The graph of the equation 2x + 3y = 6 cuts the x-axis at the point
(a) (0, 3)
(b) (3, 0)
(c) (2, 0)
(d) (0, 2)

101.Graph of linear equation ax + by + c = 0, a * 0, 6*0 cuts x-axis and y-axis respectively at the points.
(a) (−ca, 0), (0, −cb)
(b) (0, −cb, 0), (−ca, 0)
(c) (-c, 0) (0, -c)
(d) (x, 0) (y, 0)

102.Which of the following ordered pairs is a solution of the equation x – 2y – 6?
(a) (2, 4)
(b) (0, 3)
(c) (-4, 1)
(d) (4, -1)

103.How many linear equation in x and y can be satisfied by x = 1 and y = 2?
(a) only one
(b) two
(c) infinitely many
(d) three

104.Solution of linear equation 2x + 0.y + 9 = 0 is
(a) (92, m)
(b) (n, −92)
(c) (0, −92)
(d) (−92, 0)

105.If (3, 2) is the solution 3x – ky = 5, then k equals of the equation
(a) 2
(b) 4
(c) 3
(d) 12

106.Cost of book (x) exceeds twice the cost of pen (y) by Rs 10. This statement can be expressed as linear equation.
(a) x – 2y – 10 = 0
(b) 2x – y – 10 = 0
(c) 2x + y – 10 = 0
(d) x – 2y + 10 = 0

107.If x represents the age of father and y represents the present age of the son, then the statement for ‘present age of father is 5 more than 6 times the age of the son’ in terms of mathematical equation is
(a) 6x + y = 5
(b) x = 6y + 5
(c) x + 6y = 5
(d) x – 6 = 5

108.Equation of a line passing through origin is
(a) x + y = 1
(b) x = 2y – 4
(c) x + y = 0
(d) y = x – 1

109.The condition that the equation ax + by + c = 0 represents a linear equation in two variables is
(a) a ≠ 0, b = 0
(b) b ≠ 0, a = 0
(c) a = 0, b = 0
(d) a ≠ 0, b ≠ 0

110.The maximum number of points that lie on the graph of a linear equation in two variables is.
(a) two
(b) definite
(c) infinitely many
(d) three

111.Straight line passing through the points (-1, 1), (0, 0) and (1, -1) has equation
(a) y – x
(b) x + y = 0
(c) y = 2x
(d) 2 + 3y = 7x

112. The pair of equations 6x – 10y = 7 and – 6x + 10y = 9 have
(a) a unique solution
(b) infinitely many solutions
(c) no solution
(d) two solutions

113. Graphically, the pair of equations 7x – y = 5; 28x – 4y = 11 represents two lines which are
(a) intersecting at one point
(b) parallel
(c) intersecting at two points
(d) coincident

114. 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

115. 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)

116. If in the equation x + 3y = 10, the value of y is 4, then the value of x will be
(a) -2
(b) 2
(c) 4
(d) 5

117. One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be
(a) 2x + 5y = 6
(b) 3x + 5y = 3
(c) -10x – 25y + 15 = 0
(d) 10x + 25y = 15

118. 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

119. 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

120. 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

121. 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

122. The value of k for which the equations (3k + 1)x + 3y = 2; (k2 + 1)x + (k – 2)y = 5 has no solution, then k is equal to
(a) 2
(b) 3
(c) 1
(d) -1

123. 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

124. If a pair of linear equations is consistent, then the lines are:
(a)Parallel
(b)Always coincident
(c)Always intersecting
(d)Intersecting or coincident

125. The pair of equations 9x – 5y – 7=0 and 3x – 10y – 9=0 have
(a) a unique solution
(b) infinitely many solutions
(c) no solution
(d) two solutions

126. If 29x + 37y = 103, 37x + 29y = 95 then :
(a) x = 1, y = 2
(b) x = 2, y = 1
(c) x = 2, y = 3
(d) x = 3, y = 2

127)The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

A x+2y=0

b.x – 2y = 0

c.2x-y=0

D. 2x+y=0

128)The reason that a degree one polynomial equation ax + by + c =0 is called a linear equation is that

The geometrical representation is a straight line.
A.It has infinitely many solution.
B.It has two variables.
C.Both a and b.

129)Solve the given equation 7x + 3 = 52.

A x = 7

B. x = 9

c.x = 14

d.x = 54

130)Find out which of the following equation have x=2, y=1 as solution.

A.2x + 5y = -9

B.2x + 3y = 7

C.5x + 3y = 14

131)If the point (3,4) lies on the graph of the equation 3y = ax + 7 find the value of "a"

a.a = 4/5

b.a = 7/3

c.a= 5/3

d a = 3/5

132)A number is three times the other. Write a linear equation in two variables to represent this statement

A. x + 3y = 1

B. x - 3y = 0

C 3x - y = 0

d.x - y = 3

133)x = −5 can be written in as equation in two variable __.

A. 1.X + 1.Y = 5

b.1.x + 0.y = -5

c.1.x + 0.y + 5 = 0

d.Both ii and iii

134)(-4,-1) lies on a line which is a graph of the equation ____

A. 2x + 3y = 4

b.2x - 3y = 5

C. x - 4y = 0

d.4x - 2y = 6

135.The linear equation 4x – 10y = 14 has:

• A. A unique solution

• B. Two solutions

• C. Infinitely many solutions

• D. No solutions

136.The equation 2x – 3y = 5 has a unique solution, if x, y are:

• A. Natural numbers

• B. Positive real numbers

• C. Real numbers

• D. Rational numbers

137.If (2, 0) is a solution of the linear equation 2x +3y = k, then the value of k is:

• A. 4

• B. 6

• C. 5

• D. 2

138.The graph of the linear equation 2x +3y = 6 cuts the y-axis at the point:

• A. (2, 0)

• B. (0, 3)

• C. (3, 0)

• D. (0, 2)

139.The equation y = 5, in two variables, can be written as:

• A. 1 . x + 1 . y = 5

• B. 0 . x + 0 . y = 5

• C. 1 . x + 0 . y = 5

• D. 0 . x + 1 . y = 5

140.Any point on the line y = x is of the form:

• A. (a, –a)

• B. (0, a)

• C. (a, 0)

• D. (a, a)

141.The graph of x = 5 is a line:

• A. Parallel to x-axis at a distance 5 units from the origin

• B. Parallel to y-axis at a distance 5 units from the origin

• C. Making an intercept 5 on the x-axis

• D. Making an intercept 5 on the y-axis

142.x = 9, y = 4 is a solution of the linear equation:

• A. 2x + y = 17

• B. X + y = 17

• C. X + 2y = 17

• D. 3x – 2y = 17

143.Any point on the x-axis is of the form:

• A. (0, y)

• B. (x, 0)

• C. (x, x)

• D. (x, y)

144.If a linear equation has solutions (–3, 3), (0, 0) and (3, –3), then it is of the form:

• A. Y – x = 0

• B. X + y = 0

• C. –2x + y = 0

• D. –x + 2y = 0

145. The positive solutions of the equation ax + by + c = 0 always lie in the:
A. Ist quadrant
B. 2nd quadrant
C. 3rd quadrant
D. 4th quadrant

146. The graph of the linear equation 5x + 3y = 10 is a line which meets the x-axis at the point:

• A. (0, 3)

• B. (3, 0)

• C. (2, 0)

• D. (0, 2)

147. The point of the form (a, –a) always lies on the line:

• A. X = a

• B. Y = –a

• C. Y = x

• D. X + y = 0

148.The graph of x = 9 is a straight line:

• A. Intersecting both the axes

• B. Parallel to y-axis

• C. Parallel to x-axis

• D. Passing through the origin

149. Equation of the line parallel to x-axis and 6 units above the origin is:

• A. X = 6

• B. X = –6

• C. Y = 6

• D. Y = –6

150) Every linear equation in two variables has

• an infinite number of solutions

• no solution

• two solutions

• one solution

151) Ten students of class X took part in Mathematics quiz. The number of girls is 4 more than that of the boys. The algebraic representation of the above situation is

A• x + y = 10 and x – y = 4

B• x + y = – 10 and x – y = – 4

C• x – y = 10 and x + y = 4

D• none of these

152) A system of two linear equations in two variables is inconsistent, if their graphs

A• coincide

B• cut the x – axis

C• do not intersect at any point

D• intersect only at a point

153) A system of two linear equations in two variables has no solution, if their graphs

A• coincide

B• intersect only at a point

C• cut the x – axis

D• do not intersect at any point

154) A system of two linear equations in two variables has a unique solution, if their graphs

A• coincide

B• do not intersect at any point

C• cut the x – axis

D• intersect only at a point

155) A system of two linear equations in two variables has infinitely many solutions, if their graphs

A• coincide

B• do not intersect at any point

C• cut the x – axis

D• intersect only at a point

156) A system of two linear equations in two variables is consistent, if their graphs

A• cut the x – axis

B• coincide

C• intersect only at a point

D• do not intersect at any point

157) A system of two linear equations in two variables is dependentconsistent, if their graphs

A• intersect only at a point

B• coincide

C• cut the x – axis

D• do not intersect at any point

158) The lines representing the pair of equations 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0

A• intersect at a point

B• are parallel

C• none of these

D• are coincident

159) The lines representing the pair of equations 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0

A• are parallel

B• none of these

C• are coincident

D• intersect at a point

160) The lines representing the pair of equations 6x – 3y + 10 = 0 and 2x – y + 9 = 0

A• intersect at a point

B• none of these

C• are coincident

D• are parallel

161) The pair of linear equations 3x + 2y = 5 and 2x – 3y = 7 are

A• inconsistent

B• none of these

C• consistent

D• dependent(consistent)

162) The pair of linear equations 5x – 3y = 11 and – 10x + 6y = – 22 are

A• none of these

B• consistent

C• dependent(consistent)

D• inconsistent

Q.163) The pair of linear equations 4x – 6y = 9 and 2x – 3y = 8 are

• none of these

• inconsistent

• dependent(consistent)

• consistent

Q.164) The lines representing the pair of equations x + 3y = 6 and 2x – 3y = 12 intersect at

• (1, 6)

• (0, 6)

• (6, 1)

• (6, 0)

165.Graphically, the pair of equations 6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) Intersecting at exactly one point
(b) Intersecting at two points
(c) Coincident
(d) Parallel

166.The pair of linear equations x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has
(а) a unique solution
(b) exactly two solutions
(c) infinitely many solutions
(d) no solutions

167.If a pair of linear equations is consistent, then
the lines will be
(a) parallel
(b) always coincident
(c)

168.The pair of equations y = 0 and y = -7 has
(а) one solution
(b) two solutions
(c) infinitely many solutions
(d) no solution

169.The pair of equations x = a and y = b graphically represents lines which are
(а) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)

170.For what value of k, for the equations 3x – y + 8 = 0 and 6x – ky = -16 represents coincident lines?
(a) 12
(b) –12
(c) 2
(d) -2

171.If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is
(a) –54
(b) –25
(c) 154
(d) –32

172.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

173.One equation of a pair of dependent linear equation 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

174.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

175.If x = a, y = b is the solution of the equation x – y = 2 and x + y = 4, then the value of a and b are respectively
(a) 3 and 5
(b) 5 and 3
(c) 3 and 1
(d) -1 and -3

176.Aruna 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

177.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, in years, are respectively
(a) 4 and 24
(b) 5 and 30
(c) 6 and 36
(d) 3 and 24

178.If the system of equations 2x + 3y = 7
2ax + (a + 6)y = 28
has infinitely many solutions, then
(a) a = 2b
(b) b = 2a
(c) a + 2b = 0
(d) 2a + b = 0

179.The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are
(a) 45°, 75°
(b) 50°, 80°
(c) 55°, 85°
(d) 55°, 95°