List of top Questions asked in GATE Electronics and Communication Engineering

Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E$. Assuming $\omega_0=10B$, the energy in the signal $m(t)\cos \omega_0 t$ is

The synchronous sequential circuit shown below works at a clock frequency of 1 GHz. The throughput, in Mbits/s, and the latency, in ns, respectively, are 

In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

In the circuit shown below, $V_1$ and $V_2$ are bias voltages. Based on input and output impedances, the circuit behaves as a

For a MOS capacitor, $V_{fb}$ and $V_t$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width ($W_{\text{dep}}$) for varying gate voltage ($V_g$) is best represented by

Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\{\lambda_k \mid 1 \le k \le n\}$ and $\{\mathbf{v}_k \mid 1 \le k \le n\}$, respectively. For any invertible matrix $P$, the sets of eigenvalues and eigenvectors of the matrix $A$, where $B=P^{-1}AP$, respectively, are
The value of the contour integral, $\displaystyle \oint_{C}\left(\frac{z+2}{z^{2}+2z+2}\right)dz$, where the contour $C$ is $\left\{ z:\; \left| z+1-\tfrac{3}{2}j \right| = 1 \right\}$, taken in the counter clockwise direction, is
Let \(\mathbf{v}_1=\begin{bmatrix}1 \\ 2 \\ 0\end{bmatrix}\) and \(\mathbf{v}_2=\begin{bmatrix}2 \\ 1 \\ 3\end{bmatrix}\) be two vectors. The value of the coefficient \(\alpha\) in the expression \(\mathbf{v}_1=\alpha \mathbf{v}_2+\mathbf{e}\), which minimizes the length of the error vector \(\mathbf{e}\), is

Which one of the following options can be inferred from the given passage alone? When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.
[Excerpt from The Truth about Stories by T. King]

Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to: 
(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.
(ii) Mix the samples within each set and test the mixed sample for covid.
(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.
(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.
Given this strategy, no more than _____________testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

A 100 cm $\times$ 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm $\times$ 1 cm.

The total number of creases visible when the sheet is unfolded is ___________.
 

Which one of the following options represents the given graph? 

What is the smallest number with distinct digits whose digits add up to 45? 

Courts : _________ :: Parliament : Legislature ; (By word meaning)

“I cannot support this proposal. My ___________ will not permit it.”

A transparent dielectric coating is applied to glass $(\varepsilon_r=4,\ \mu_r=1)$ to eliminate the reflection of red light $(\lambda_0=0.75~\mu\text{m})$. The minimum thickness of the dielectric coating, in $\mu$m, that can be used is __________ (rounded off to two decimal places).}
Let an input $x[n]$ having discrete-time Fourier transform \[ X(e^{j\Omega}) = 1 - e^{-j\Omega} + 2e^{-j3\Omega} \] be passed through an LTI system whose frequency response is \[ H(e^{j\Omega}) = 1 - \tfrac12 e^{-j2\Omega}. \] The output $y[n]$ of the system is
The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is ______ bits (rounded off to the nearest integer).
For a real signal, which of the following is/are valid power spectral density/densities?
The open loop transfer function of a unity negative feedback system is \[ G(s) = \frac{k}{s(1+sT_1)(1+sT_2)}, \] where $k$, $T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in rad/s, is
A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when
Consider a narrow band signal, propagating in a lossless dielectric medium $(\varepsilon_r = 4, \mu_r = 1)$, with phase velocity $v_p$ and group velocity $v_g$. Which of the following statement is true? ($c$ is the velocity of light in vacuum.)
For an intrinsic semiconductor at temperature $T=0K$, which of the following statement is true?
A series RLC circuit has a quality factor $Q$ of 1000 at a center frequency of $10^{6}$ rad/s. The possible values of $R$, $L$ and $C$ are
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as