Assertion (A) : The pair of linear equations $px + 3y + 59 = 0$ and $2x + 6y + 118 = 0$ will have infinitely many solutions if $p = 1$.
Reason (R) : If the pair of linear equations $px + 3y + 19 = 0$ and $2x + 6y + 157 = 0$ has a unique solution, then $p \neq 1$.
Select the correct answer from the codes (A), (B), (C) and (D) given below.
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Verification of A: For $px+3y+59=0$ and $2x+6y+118=0$: $\frac{p}{2}=\frac{3}{6}=\frac{59}{118}$ → $\frac{p}{2}=\frac{1}{2}$ → $p=1$. ✓ (Infinitely many solutions)
Verification of R: For unique solution, $\frac{p}{2}\neq\frac{3}{6}$ → $p\neq1$. ✓
Both are true, but R explains a different pair of equations, so R is not the correct explanation of A.
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Explanation
- A is true: Applying the condition $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ gives $p=1$.
- R is true: For a unique solution, $\frac{a_1}{a_2}\neq\frac{b_1}{b_2}$, which gives $p\neq1$.
- However, R refers to a completely different pair of equations (with constants 19 and 157), so it cannot explain why A holds. Hence option (B) is correct.