ISRO EC 2025 Q.5: solution and answer

Official answer: CSource: ISRO's final answer key of 15 May 2026

1. EIRP is the power an ideal isotropic radiator would need to radiate to give the same peak intensity as the actual antenna in its direction of maximum radiation: $\text{EIRP}=P_{rad}G$, or in decibels ${\text{EIRP}}_{\mathrm{dBW}}=P_{\mathrm{dBW}}+G_{\mathrm{dBi}}$.

2. Convert the gain from dBi to a ratio: $G=10^{3/10}=1.995\approx 2$.

3. Compute: $\text{EIRP}=20\text{W}\times 2=40\text{W}$.

4. Check in decibels: $20\text{W}=10{\log }_{10}(20)\approx 13\mathrm{dBW}$, so $13+3=16\mathrm{dBW}$, and $10^{16/10}\approx 40\text{W}$.

5. The gain is quoted relative to an isotropic radiator (dBi), so no extra conversion such as 2.15 dB is needed. The option $10\text{W}$ divides by the gain and $20\text{W}$ ignores it. The option $60\text{W}$ comes from treating 3 dBi as a gain of 3 (a factor of 3) instead of a factor of about 2. The correct option is $40\text{W}$.