JEE Main 2025 — 28 January, Morning Shift — Question 68

$\mathrm{I}_{1}=\frac{\mathrm{MR}_{1}^{2}}{4}, \mathrm{I}_{2}=\frac{\mathrm{MR}_{2}^{2}}{2}, \mathrm{I}_{3}=\frac{2 \mathrm{MR}_{1}^{2}}{5}$

According to problem

$\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=2.5 \Rightarrow \frac{\frac{\mathrm{MR}_{1}^{2}}{4}}{\frac{\mathrm{MR}_{2}^{2}}{2}}=\frac{5}{2} \Rightarrow \frac{\mathrm{R}_{1}^{2}}{\mathrm{R}_{2}^{2}}=5$

Now we are provided with information that

$\frac{\mathrm{I}_{3}}{\mathrm{I}_{2}}=\mathrm{n}$

$\Rightarrow \frac{\frac{2 \mathrm{MR}_{1}^{2}}{5}}{\frac{\mathrm{MR}_{2}^{2}}{2}}=\mathrm{n} \Rightarrow \frac{4 \mathrm{R}_{1}^{2}}{5 \mathrm{R}_{2}^{2}}=\mathrm{n}$

From Eq', (1) and (2)

$\Rightarrow \mathrm{n}=4$ MAGES