1
GATE ECE 2026
MCQ (Single Correct Answer)
+1
-0.33

Consider the Friis' transmission equation $P_R=\left(P_T G_T G_R \lambda^2\right) /(4 \pi D)^2$, where $P_R$ and $P_T$ are the received and the transmitted powers, respectively.

$G_T$ and $G_R$ are the gain of transmitting and receiving antennas, respectively, $D$ is the distance between the transmitting and receiving antennas, and $\lambda$ is the wavelength in free space.

Given: $G_T=G_R=1.0, \lambda=0.30 \mathrm{~m}$ and $P_T=+10 \mathrm{dBm}$.

Choose the distance (D), in km , from the following options at which the received power, $P_R=-90 \mathrm{dBm}$ ?

A

$\frac{15}{4 \pi}$

B

$\frac{15}{2 \pi}$

C

$\frac{75}{2 \pi}$

D

$\frac{3}{4 \pi}$

2
GATE ECE 2026
MCQ (Single Correct Answer)
+1
-0.33

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by

$$ \vec{E}(z, t)=E_0[\hat{x} \cos (\omega t-k z)+\hat{y} \sin (\omega t-k z)] $$

in a right-handed orthogonal co-ordinate system.

Which of the following is the correct polarization of the electromagnetic wave?

A

Right-handed circularly polarized

B

Left-handed circularly polarized

C

Linearly polarized

D

Linearly polarized with $-45^{\circ}$ angle to $\hat{x}$

3
GATE ECE 2026
MCQ (More than One Correct Answer)
+1
-0.33

Which option(s) represents/ represent the dielectric loss tangent of a substrate?

A

Ratio of the real to imaginary parts of the total displacement current

B

$\frac{\left(\omega \epsilon^{\prime \prime}+\sigma\right)}{\left(\omega \epsilon^{\prime}\right)}$

C

Ratio of the electric susceptibility to permittivity

D

Ratio of the polarization vector $\vec{P}$ to the displacement vector $\vec{D}$

4
GATE ECE 2026
Numerical
+1
-0.33

The cutoff frequency (in GHz ) for the dominant $\mathrm{TE}_{10}$ mode of an air-filled rectangular waveguide of inner dimension 0.28 inch $\times 0.14$ inch is $\_\_\_\_$ .

(rounded off to two decimal places).

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