ISRO EC 2025 Q.28: solution and answer

ISRO 2025 · ECQ.28 · 1 mark · MCQ

According to Friis Transmission Equation, the received power P_r is directly proportional to :

(A)
The square of the distance between antennas
(B)
The square of wavelength
(C)
The square of frequency
(D)
The cube of the transmitted power

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Answer and solution

ANSWER

The received power is directly proportional to the square of the wavelength, option (b).

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

The Friis transmission equation for free space is $P_{r} = P_{t} G_{t} G_{r} (\frac{λ}{4 π R})^{2}$ , where $G_{t}$ and $G_{r}$ are the antenna gains and $R$ is the separation.
Reading off the dependence: $P_{r} \propto P_{t}$ (first power), $P_{r} \propto G_{t} G_{r}$ , $P_{r} \propto λ^{2}$ and $P_{r} \propto 1/ R^{2}$ .
(a) Wrong: $P_{r}$ is inversely proportional to $R^{2}$ , so it falls as the distance grows.
(b) Correct: $P_{r} \propto λ^{2}$ , which is direct proportionality to the square of the wavelength.
(c) Wrong: with $λ = c / f$ , $P_{r} \propto 1/ f^{2}$ , so received power decreases with the square of frequency (for fixed antenna gains).
(d) Wrong: $P_{r}$ is linear in $P_{t}$ , not cubic.
Hence the received power is directly proportional to the square of the wavelength.

KEY IDEA

Friis equation: $P_{r} = P_{t} G_{t} G_{r} (λ /4 π R)^{2}$ . Only the $λ^{2}$ factor is a direct (positive) power-law dependence among the options; distance and frequency appear in the denominator, and transmitted power appears to the first power.

WATCH OUT FOR

Confusing "proportional to the square" with "inversely proportional to the square": the distance term $R^{2}$ sits in the denominator, so option (a) is the inverse relation. Also forgetting that $λ = c / f$ turns the wavelength dependence into an inverse dependence on frequency.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 4 ISRO Antennas questions, with notes

ISRO EC 2025 Q.28: solution and answer

Answer and solution

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