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Solution


Q.

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.
1 Both A and R are true, and R is the correct explanation of A.  
2 Both A and R are true, but R is not the correct explanation of A.  
3 A is true, but R is false.  
4 A is false, but R is true.  

Ans.

(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.