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

Question. If \(3x - 5y = 5\) and \(\frac{x}{x + y} = \frac{5}{7}\), what is the value of \(x - y\)?
(a) 9
(b) 6
(c) 4
(d) 3
Answer: D

Question. If \(12a + 3b = 1\) and \(7b - 2a = 9\), find the average (arithmetic mean) of 'a' and 'b'.
(a) 2.5
(b) 1
(c) 0.1
(d) 0.5
Answer: D

Question. If \(4x + 6y = 32\) and \(4x - 2y = 4\), find the value of 8y.
(a) 24
(b) 28
(c) 36
(d) 42
Answer: B

Question. For the equations \((p + 2)(q - \frac{1}{2}) = pq - 5\) and \((p - 2)(q - \frac{1}{2}) = pq - 5\), find the solution set (p, q).
(a) \((-10, -\frac{1}{2})\)
(b) \((-10, \frac{1}{2})\)
(c) \((10, -\frac{1}{2})\)
(d) \((10, \frac{1}{2})\)
Answer: D

Question. Identify the solution of \(\frac{2}{3}x - \frac{3}{4}y = 1\) and \(8x - 9y = 16\).
(a) \(x = 6, y = 4\)
(b) Infinitely many solutions
(c) \(x = 4, y = 6\)
(d) No solution
Answer: D

Question. Find the values of 'x' and y for \(x - y = 0.9\); \(\frac{11}{x + y} = 2\)
(a) 3.2, 5.6
(b) 3.2, 2.3
(c) 5.6, 2.3
(d) 4.5, 6.4
Answer: B

Question. What is the solution of the equations, \(\frac{3x - y + 1}{3} = \frac{2x + y + 2}{5} = \frac{3x + 2y + 1}{6}\)?
(a) \(x = -1, y = -1\)
(b) \(x = 1, y = 1\)
(c) \(x = 1, y = 2\)
(d) \(x = 2, y = 1\)
Answer: B

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. Find the solution of the equations \(8x - 9y = 6xy\) and \(10x + 6y = 19xy\).
(a) \(x = \frac{3}{2}, y = \frac{3}{2}\)
(b) \(x = \frac{2}{3}, y = \frac{3}{2}\)
(c) \(x = \frac{3}{2}, y = \frac{2}{3}\)
(d) \(x = 3, y = 2\)
Answer: C

Question. Find the values of 'x' and y, for the equations \(\frac{a^2}{x} - \frac{b^2}{y} = 0\); \(\frac{a^2b}{x} + \frac{b^2a}{y} = a + b\) where \(x, y \neq 0\).
(a) \(x = a^2, y = b^2\)
(b) \(x = b^2, y = a^2\)
(c) \(x = \frac{b}{a}, y = \frac{a}{b}\)
(d) \(x = \frac{1}{b}, y = \frac{1}{a}\)
Answer: A

Question. If \(x + \frac{1}{y} = 5\) and \(2x + \frac{3}{y} = 13\), what is the value of \((2x - 3y)\)?
(a) 1
(b) 2
(c) 3
(d) 5
Answer: D

Question. Which of the following is the solution of the system of equations \(\frac{4}{x} + 5y = 7\) and \(\frac{3}{x} + 4y = 5\)?
(a) \(x = -\frac{1}{3}, y = -1\)
(b) \(x = \frac{1}{3}, y = -1\)
(c) \(x = -\frac{1}{3}, y = 1\)
(d) \(x = \frac{1}{3}, y = 1\)
Answer: B

Question. The solution of \(2x + 3y = 2\) and \(3x + 2y = 2\) can be represented by a point. In which of the following parts of the coordinate plane does the point lie?
(a) First quadrant
(b) Second quadrant
(c) Third quadrant
(d) Fourth quadrant
Answer: A

Question. Find 'x' and 'y' for the equations \(\frac{x}{3} + \frac{y}{4} = 4\) and \(\frac{5x}{3} + \frac{y}{4} = 8\).
(a) \(x = 8, y = 6\)
(b) \(x = 3, y = 4\)
(c) \(x = 6, y = 8\)
(d) \(x = 4, y = -6\)
Answer: C

Question. How many solutions does the system of equations, \(3x - 4y = 5\) and \(12x - 16y = 20\) have?
(a) More than two solutions
(b) Exactly two solutions
(c) Exactly one solution
(d) No solution
Answer: A

Question. Find the number of solutions of the equations \(x + \frac{1}{y} = 2\) and \(2xy - 3y = -2\).
(a) 0
(b) 1
(c) 2
(d) Infinitely many
Answer: A

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. If the equations \(4x + 7y = 10\) and \(10x + ky = 25\) represent coincident lines, what is the value of 'k'?
(a) 5
(b) \(\frac{17}{2}\)
(c) \(\frac{27}{2}\)
(d) \(\frac{35}{2}\)
Answer: D

Question. For what value of 'k', will the equations \(4x + 6y = 11\) and \(2x + ky = 7\) be inconsistent?
(a) 2
(b) 3
(c) 4
(d) 8
Answer: B

Question. For what value of 'k' will the system of equations \(3x + 5y = 2\) and \(kx + 10y = 0\) have a non zero solution?
(a) 0
(b) 2
(c) 6
(d) 8
Answer: C

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. The difference between two numbers is 5 and the difference between their squares is 65. Find the larger number.
(a) 9
(b) 10
(c) 11
(d) 12
Answer: A

Question. ₹ 49 was divided among 150 children. Each girl got 50 paise and a boy 25 paise. How many boys were there?
(a) 100
(b) 102
(c) 104
(d) 105
Answer: C

Question. The area of a rectangle increases by 76 square units, if the length and breadth are each increased by 2 units. However, if the length is increased by 3 units and breadth is decreased by 3 units, the area gets reduced by 21 square units. Find the sum of the length and breadth of the rectangle.
(a) 40 units
(b) 42 units
(c) 4 units
(d) 36 units
Answer: D

Question. What number must be added to each of the numbers, 5, 9, 17, 27 to make them proportionate?
(a) 2
(b) 1
(c) 3
(d) 5
Answer: C

Question. Two numbers differ by 3 and their product is 54. Find the numbers.
(a) 9 and 6
(b) -9 and -6
(c) Both (a) and (b)
(d) 9 and -4
Answer: C

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 expenses of the family is ₹ 1000 and when it is ₹ 240 per quintal, the monthly expenses is ₹ 980. Find the monthly expenses of the family on wheat when the cost of wheat is ₹ 350 a quintal.
(a) ₹ 900
(b) ₹ 350
(c) ₹ 650
(d) ₹ 700
Answer: D

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

Question. The smallest angle of a triangle is one-fifth the sum of the other two and the largest angle exceeds the sum of the other two by \(20^{\circ}\). Find the largest angle of the triangle.
(a) \(100^{\circ}\)
(b) \(90^{\circ}\)
(c) \(120^{\circ}\)
(d) \(110^{\circ}\)
Answer: A

Question. The sum of Raju's age and half of Sameer's age is 4. One-third Raju's age added to twice Sameer's age is 5. Find the sum of their ages.
(a) 7 years
(b) 3 years
(c) 5 years
(d) 2 years
Answer: C