Q 1 – 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
(d) Parallel
Q 2 – If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of the homogeneous
system of equations with unknowns x and y, then which of the following statement is true?
(a) A is true and R is the correct explanation of A
(b) A is false and R is not a correct explanation of A
(c) A is true and R is false
(d) A is false and R is true
(a) A is true and R is the correct explanation of A
Q 3 – 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
(c) intersecting or coincident
Q 4 – 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
(c) intersecting or coincident
Q 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
(c) two solutions
Q 6 – Find the solution to the following system of linear equations:
2p+3q = 9 p – q = 2
(a) (4,2)
(b) (3,1)
(c) (2,-3)
(d) (-4,1)
(b) (3,1)
Q 7 – The pair of equations y = 0 and y = – 7 has
(а) one solution
(b) two solutions
(c) infinitely many solutions
(d) no solution
(d) no solution
Q 8 – Which of the following pair of linear equations is inconsistent?
(a) 2x + 3y = 7; 4x + 6y = 5
(b) x – 2y = 6; 2x + 3y = 4
(c) 9x – 8y = 17; 18x -16y = 34
(d) 5x – 3y =11; 7x + 2y =13
(a) 2x + 3y = 7; 4x + 6y = 5
Q 9 – 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)
(d) intersecting at (a, b)
Q 10 – 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
(b) 140, 280
Q 11 – 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
(c) intersecting or coincident
Q 12 – 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
(d) 36
Q 13 – 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
(d) no value
Q 14 – 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
(d) 25 and 25
Q 15 – 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
(a) –2
Q 16 – 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
(d) 10x – 14y = –4
Q 17 – 10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys who took part in the quiz.
(a) 3
(b) 7
(c) 2
(d) 8
(a) 3
Q 18 – 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
(c) 3 and 1
Q 19 – 5 pencils and 7 pens together cost Rs. 50 whereas 7 pencils and 5 pens cost Rs. 46. Find the cost of 2 pencils and 3 pens.
(a) Rs. 42
(b) Rs. 39
(c) Rs. 21
(d) Rs. 16
(c) Rs. 21
Q 20 – 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
(c) 6 and 36
Q 21 – The perimeter of a rectangle is 44 cm. Its length exceeds twice its breadth by 4 cm. Find the area of the rectangle.
(a) 46 cm²
(b) 49 cm²
(c) 96 cm²
(d) 69 cm²
(c) 96 cm²
Q 22 – 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
(b) b = 2a
Q 23 – Equation of line m is :
(a) x = – 2
(b) x = 2
(c) y = 2
(d) y = – 2
(c) y = 2
Q 24 – 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
(d) passing through the origin
Q 25 – 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°
(c) 55°, 85°
Q 26 – One equation of a pair of dependent linear equations is –5x + 7y = 2, the second equation can be :
(a) –10x + 14y + 4 = 0
(b) –10x – 14x + 4 = 0
(c) 10x – 14y = –4
(d) 10x + 14y + 4 = 0
(c) 10x – 14y = –4
Q 27 – 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
(d) no solutions
Q 28 – Which of following is not a solution of 3a + b = 12?
(a) (3, 3)
(b) (5, -3)
(c) (4, 0)
(d) (2, 4)
(d) (2, 4)
Q 29 – Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?
(a) a ≠ -2
(b) a = –2
(c) a = 2
(d) a ≠ 2
(a) a ≠ –2
Q 30 – Which of the following pair of linear equations is inconsistent?
(a) 2x + 3y = 7; 4x + 6y = 5
(b) x – 2y = 6; 2x + 3y = 4
(c) 9x – 8y = 17; 18x -16y = 34
(d) 5x – 3y =11; 7x + 2y =13
(a) 2x + 3y = 7; 4x + 6y = 5