Pair Of Linear Equations In Two Variables Test

Pair Of Linear Equations In Two Variables

This is Pair of Linear Equations in Two Variables Test-03 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Determine graphically the co-ordinates of the vertices of the triangle, the equations of whose sides are: \(y = x,{\text{ }}3y = x,{\text{ }}x + y = 8\)
  • A
    13 sq. units
  • B
    12 sq. units
    Correct
  • C
    11 sq. unit
  • D
    21 sq. units
2
The area of the triangle formed by the lines 2x + 3y = 12 with the co – ordinate axes is
  • A
    20 sq. units
  • B
    10 sq. unit
  • C
    12 sq. units
    Correct
  • D
    16 sq. units
3
A system of linear equations is said to be consistent, if it has
  • A
    one solution
  • B
    at least one solution
    Correct
  • C
    two solutions
  • D
    no solution
4
A system of linear equations is said to be inconsistent, if it has
  • A
    at least one solution
  • B
    no solution
    Correct
  • C
    two solutions
  • D
    one solution
5
If the system 6x – 2y = 3, kx – y = 2 has a unique solution, then
  • A
    \(k \ne 4\)
  • B
    \(k \ne 3\)
    Correct
  • C
    k = 3
  • D
    k = 4
6
The system of equations x – 4y = 8, 3x – 12y = 24
  • A
    may or may not have a solution
  • B
    has infinitely many solutions
    Correct
  • C
    has a unique solution
  • D
    has no solution
7
The system of linear equations \({a_1}x + {b_1}y + {c_1} = 0\) and \({a_2}x + {b_2}y + {c_2} = 0\) has no solution if
  • A
    \(\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}\)
  • B
    \(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} = \frac{{{c_1}}}{{{c_2}}}\)
  • C
    none of these
  • D
    \(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\)
    Correct
8
The system of linear equations \({a_1}x + {b_1}y + {c_1} = 0\) and \({a_2}x + {b_2}y + {c_2} = 0\) has infinitely many solutions if
  • A
    none of these
  • B
    \(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} = \frac{{{c_1}}}{{{c_2}}}\)
    Correct
  • C
    \(\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}\)
  • D
    \(\frac{{{a_1}}}{{{a_2}}} = \frac{{{b_1}}}{{{b_2}}} \ne \frac{{{c_1}}}{{{c_2}}}\)
9
The pair of equations 5x – 15y = 8 and 3x – 9y = \(\frac{{24}}{5}\) has
  • A
    one solution
  • B
    two solutions
  • C
    no solution
  • D
    infinitely many solutions
    Correct
10
The pair of equations x = 2 and y = – 3 has
  • A
    no solution
  • B
    one solution
    Correct
  • C
    two solutions
  • D
    infinitely many solutions
11
The value of ‘k’ so that the system of equations 3x – 4y – 7 = 0 and 6x – ky – 5 = 0 have a unique solution is
  • A
    \(k \ne -8\)
  • B
    \(k \ne -4\)
  • C
    \(k \ne 4\)
  • D
    \(k \ne 8\)
    Correct
12
The value of ‘k’ so that the system of linear equations kx – y – 2 = 0 and 6x – 2y – 3 = 0 have no solution is
  • A
    k = 3
    Correct
  • B
    k = – 4
  • C
    k = 4
  • D
    k = – 3
13
The value of ‘k’ so that the system of equations 3x – y – 5 = 0 and 6x – 2y – k = 0 have infinitely many solutions is
  • A
    k = 8
  • B
    k = – 10
  • C
    k = – 8
  • D
    k = 10
    Correct
14
The pair of linear equations ax + by = c and px + qy = r has a unique solution then
  • A
    aq \( \ne \) bp
    Correct
  • B
    ap = bq
  • C
    aq = bp
  • D
    ap \( \ne \) bq
15
If 6x + 3y = c – 3 and 12x + cy = c has infinitely many solutions, then c =
  • A
    4
  • B
    6
    Correct
  • C
    5
  • D
    3