10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank

done Assertion And Reason (MCQs) - Pair of Linear Equations in Two Variables Total Questions - 22

• question_answer1)

  Directions (Q. Nos. 1 - 22): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:

  Assertion (A): \[\text{x}=\text{2},\text{ y}=\text{1}\]is a solution of pair of equations \[\text{3x}-\text{2y}=\text{4}\]and\[\text{2x}+\text{y}=\text{5}\].

  Reason (R): A pair of values \[(x,y)\] satisfying each one of the equations in a given system of two simultaneous linear equations in x and y is called a solution of the system of equations.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer2)

  Assertion (A): The system of equations \[x+2y-5=0\] and \[\text{2x}-\text{6y}+\text{9}=0\] has infinitely many solutions.

  Reason (R): The system of equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] has infinitely many solutions when \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer3)

  Assertion (A): The system of equations \[x+y-6=0\] and \[\text{x}-\text{y}-\text{2}=0\]has a unique solution.

  Reason (R): The system of equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] has a unique solution when \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer4)

  Assertion (A): If the pair of equations \[x+2y+7=0,\] \[3x+ky+21=0\] represents coincident lines, then the value of k is 6.

  Reason (R): The pair of linear equations are coincident Lines if they have no solution.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer5)

  Assertion (A): The system of equations \[\text{2x}+\text{3y}+\text{5}=0\] and \[\text{4x+ky}+\text{7}=0\] is inconsistent when \[\text{k}=\text{6}\].

  Reason (R): The system of equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] is inconsistent when \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer6)

  Assertion (A): The system of equations are inconsistent:

  \[\text{2x}+\text{4y}=\text{1}0\] \[\text{3x}+\text{6y}=\text{12}\]

  Reason (R): A pair of linear equations which has no solution is called an inconsistent pair of Linear equations.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer7)

  Assertion (A): The system of equations \[\text{3x}-\text{y}-\text{5}=0,\]\[\text{6x}-\text{2y}-\text{k}=0\] has no solution if \[\text{k}=\text{1}0\].

  Reason (R): The pair of equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]has no solution if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}.\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer8)

  Assertion (A): (Graphically, the pair of Linear equations \[\text{2x}-\text{y}-\text{5}=0\]and \[\text{x}-\text{y}-\text{3}=0\]represent intersecting lines.

  Reason (R): The linear equations \[\text{2x}-\text{y}-\text{5}=0\] and \[\text{x}-\text{y}-\text{3}=0\]meet the y-axis at \[(0,3)\] and \[(0,-5)\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer9)

  Assertion (A): \[\text{4x}+\text{3y}=\text{12}\]is a line which is parallel to \[\text{8x}+\text{6y}=\text{48}\]

  Reason (R): The graph of linear equation \[\text{ax}=\text{b},\]where \[a\ne 0\] is parallel to x-axis.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer10)

  Assertion (A): A two digit number, where tens digit is greater than ones digit is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of digits by 13 and adding 2. The number is 41.

  Reason (R): The linear equations used are \[\text{7x}-\text{2y}+\text{1}=0\]and \[\text{l2x}+\text{23y}+\text{2}=0.\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer11)

  Assertion (A): If the system of equations \[\text{2x}+\text{3y}=\text{7}\] and \[2ax+(a+b)y=28\] has infinitely many solutions, then\[\text{2a}-\text{b}=0\].

  Reason (R): The system of equations \[\text{3x}-\text{5y}=\text{9}\] and \[\text{6x}-\text{l0y}=\text{8}\] has a unique solution.

   
  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer12)

  Assertion (A):  \[\text{3x}+\text{4y}+\text{5}=0\]  and   \[\text{6x}+k\text{y}+\text{9}=0\]represent parallel lines if \[k=8.\]

  Reason (R): \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]represent parallel lines if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer13)

  Assertion (A): The value of \[q=\pm 2,\]if \[\text{x}=\text{3},\] \[y=1\]is the solution of the line \[2x+y-{{q}^{2}}-3=0\]

  Reason (R): The solution of the line will satisfy the equation of the line.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer14)

  Assertion (A): For \[k=6,\] the system of linear equations \[x+2y+3=0\]and \[3x+ky+6=0\] is inconsistent.

  Reason (R):   The   system   of   linear  equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] is inconsistent if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer15)

  Assertion (A): If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution.

  Reason (R): If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer16)

  Assertion (A): The value of k for which the system of equations \[\text{kx}-y=\text{2},\]\[\text{6x}-\text{2y}=\text{3}\] has a unique solution in 3.

  Reason  (R): 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 a unique  solutions if \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}.\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer17)

  Assertion (A): \[\text{x}+\text{y}-\text{4}=0\]and \[2x+ky-3=0\]has no solution if \[k=2\]

  Reason (R): \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]are consistent if \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{k}_{1}}}{{{k}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer18)

  Assertion (A): Pair of linear equations: \[9x+3y+12=0,\] \[\text{8x}+\text{6y}+\text{24}=0\] have infinitely many solutions.

  Reason (R): Pair of Linear equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] have infinitely many solutions, if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer19)

  Assertion (A): If \[kx-y-2=0\]and \[\text{6x}-\text{2y}-\text{3}=0\] are inconsistent, then \[k=3\].

  Reason (R): \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]are inconsistent of \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}.\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer20)

  Assertion (A): The lines \[\text{2x}-\text{5y}=\text{7}\]and \[\text{6x}-\text{15y}=\text{8}\] are parallel lines.

  Reason (R):   The   system   of   linear   equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]have infinitely many solutions if \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer21)

  Assertion (A): \[\text{3x}-\text{4y}=7\] and \[\text{6x}-\text{8y}=\text{k}\] have infinite number of solution if \[\text{k}=\text{14}\].

  Reason (R): \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] have a unique solution if \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer22)

  Assertion (A): The Linear equations \[\text{x}-\text{2y}-\text{3}=0\]and \[\text{3x}+\text{4y}-\text{2}0=0\] have exactly one solution.

  Reason (R): The linear equations \[\text{2x}+\text{3y}-\text{9}=0\] and \[\text{4x}+\text{6y}-\text{18}=0\] have a unique solution.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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