GATE EC 2026 Question Paper (15-Feb-2026) (Shift 1)

Consider the Friis' transmission equation $P_R=(P_T{G}_T{G}_R{\lambda }^2)/(4\pi D{)}^2$, 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: $G_T=G_R=1.0,\lambda =0.30\text{ m}$ and $P_T=+10\text{ dBm}$.
Choose the distance ($D$), in km, from the following options at which the received power, $P_R=-90\text{ dBm}$?

Consider a discrete memoryless source with an alphabet of four source symbols.
$s(t)$ is a multi-level (-1, 0, +1, +2) signal representing a long sequence of random symbols from the above source which is generating $10^4$ symbols per second.
Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$?

The relation between the input current ($I$) and the output voltage ($V$) of a circuit is governed by the equation: $C\frac{dV}{dt}=I(t)-m(t)$. The circuit is excited by $I(t)=q\delta (t)$, where $q$ is a real valued constant. $V$ at $t=0^{-}$ is $V_0$.
Which of the following is an equivalent representation of the above case?

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

$$\vec{E}(z,t)=E_0[\hat{x}\cos (\omega t-kz)+\hat{y}\sin (\omega t-kz)]$$
in a right-handed orthogonal co-ordinate system.
Which of the following is the correct polarization of the electromagnetic wave?

Consider a p-n junction diode when it is forward biased with 2 V.
Which of the following is/are the correct magnitude(s) of the energy difference between quasi Fermi-levels, $E_{fn}$ in the n-side and $E_{fp}$ in the p-side?