NTSE Stage 2 SAT 2017 Question Paper

Reason :
We know that condition for infinitely many solutions is :
$\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$
⇒ $\frac{\mathrm{p}}{12}=\frac{3}{\mathrm{p}}=\frac{\mathrm{p}-3}{\mathrm{p}}$
using $\frac{\mathrm{p}}{12}=\frac{3}{\mathrm{p}}$ ⇒ $\mathrm{p}=\pm 6$ ...(1)
using $\frac{3}{\mathrm{p}}=\frac{\mathrm{p}-3}{3}$ ⇒ $\mathrm{p}=+6$ ...(2)
Hence from (1) & (2) p = + 6 is a common solution. Hence option (1) is correct.