• 072920 77839
  • info@smartachievers.in

Topic Question Set

Q 1 :    

Consider the system of a pair of linear equations:

    2/x + 5y = 15
    3/x + 6y = 7

Assertion (A): The given pair of equations can be reduced to a pair of linear equations in two variables.
Reason (R): In the given equations, y can be substituted by 1/p.

  • Both A and R are true, and R is the correct explanation of A.

     

  • Both A and R are true, but R is not the correct explanation of A.

     

  • A is true, but R is false.

     

  • A is false, but R is true.

     

(2)

Rationale: Yes, the given pair of equations can be reduced to a pair of linear equations in two variables (m and y) by putting 1/x = m.
Certainly, we can substitute y by 1/p but that would not help the given equations in reducing to a pair of linear equations.

 

Q 2 :    

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 a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0  is inconsistent if a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

  • Both A and R are true, and R is the correct explanation of A.

     

  • Both A and R are true, but R is not the correct explanation of A.

     

  • A is true, but R is false.

     

  • A is false, but R is true.

     

(3)

Rationale: We have system of linear equations x + 2y + 3 = 0 and 3x + ky + 6 = 0.
For inconsistency, we have
   a₁/a₂ = b₁/b₂ ≠ c₁/c₂
    => 1/3 = 2/k ≠ 3/6
    => 1/3 = 2/k ≠ 1/2
    => k = 6

For k = 6, system of linear equations is inconsistent.
Hence, Assertion (A) is true but Reason (R) is false.

Q 3 :    

Assertion (A): The system of linear equations 2x + 3y = 7 and kx + 9/2 y = 12 have no solution, if k = 3.
Reason (R): The system of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 have no solution, if a₁/a₂ = b₁/b₂.

  • Both A and R are true, and R is the correct explanation of A.

     

  • Both A and R are true, but R is not the correct explanation of A.

     

  • A is true, but R is false.

     

  • A is false, but R is true.

     

(3)

Rationale: The system of linear equations in Reason (R) have no solution, if
 a₁/a₂ = b₁/b₂ ≠ c₁/c₂..
So, Reason (R) is false. The system of linear equations in Assertion (A) will have no solution if
    k/2 = 9/3 ≠ 12/7  or  k/2 = 3/2 ≠ 12/7  or  k = 3.

 

Q 4 :    

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

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

  • Both A and R are true, and R is the correct explanation of A.

     

  • Both A and R are true, but R is not the correct explanation of A.

     

  • ) A is true, but R is false.

     

  • A is false, but R is true.

     

(4)

If two lines are coincident, then the pair of lines is consistent and it has infinitely many solutions.

Therefore, Assertion (A) is not true but Reason (R) is true.

 

Q 5 :    

Assertion (A): A pair of linear equations has no solution(s) if it is represented by intersecting lines graphically.

Reason (R): If two lines are intersecting, then the pair has unique solution and is called consistent pair of equations.

  • Both A and R are true, and R is the correct explanation of A.

     

  • Both A and R are true, but R is not the correct explanation of A.

     

  • A is true, but R is false.

     

  • A is false, but R is true

     

(4)

We know that a pair of linear equations has no solution if it is represented by parallel lines graphically.

Thus, Assertion (A) is not true but Reason (R) is true.