GATE ECE 2024
Paper was held on Sun, Feb 11, 2024 4:00 AM
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GATE ECE

In the circuit below, assume that the long channel NMOS transistor is biased in saturation. The small signal trans-condu
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For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is
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In the circuit shown, the n : 1 step-down transformer and the diodes are ideal. The diodes have no voltage drop in forwa
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As shown in the circuit, the initial voltage across the capacitor is 10 V, with the switch being open. The switch is the
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The opamps in the circuit shown are ideal, but have saturation voltages of ±10 V. Assume that the initial inductor curre
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In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of $R_
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In the circuit shown below, the transistors $M_1$ and $M_2$ are biased in saturation. Their small signal transconductanc
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Which of the following statements is/are true for a BJT with respect to its DC current gain $\beta$?
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An NMOS transistor operating in the linear region has $I_{D}$ of 5 $\mu$A at $V_{DS}$ of 0.1 V. Keeping $V_{GS}$ constan
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A digital communication system transmits through a noiseless bandlimited channel $[-W, W]$. The received signal $z(t)$ a
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A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order R
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An amplitude modulator has output (in Volts) $$s(t) = A \cos(400 \pi t) + B \cos(360 \pi t) + B \cos(440 \pi t)$$. The c
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A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _______ .
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A source transmits a symbol $s$, taken from $\\{-4, 0, 4\\}$ with equal probability, over an additive white Gaussian noi
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The information bit sequence {1 1 1 0 1 0 1 0 1} is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4)
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Let $X(t) = A\cos(2\pi f_0 t+\theta)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of eac
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In the context of Bode magnitude plots, 40 dB/decade is the same as ______.
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In the feedback control system shown in the figure below $G(s) = \dfrac{6}{s(s+1)(s+2)}$. $R(s), Y(s),$ and $E(s)$ are t
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Consider a unity negative feedback control system with forward path gain $G(s) = \frac{K}{(s + 1)(s + 2)(s + 3)}$ as sho
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A satellite attitude control system, as shown below, has a plant with transfer function $G(s) = \frac{1}{s^2}$ cascaded
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Consider a system $S$ represented in state space as$$\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \
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For the Boolean function $F(A, B, C, D) = \sum m(0,2,5,7,8,10,12,13,14,15)$, the essential prime implicants are ________
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A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set o
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In a number system of base $r$, the equation $x^2 - 12x + 37 = 0$ has $x = 8$ as one of its solutions. The value of $r$
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A 4-bit priority encoder has inputs $D_3, D_2, D_1,$ and $D_0$ in descending order of priority. The two-bit output $AB$
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The propagation delay of the 2 x 1 MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as
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The sequence of states $(Q_1 Q_0)$ of the given synchronous sequential circuit is ________.
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A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a norm
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Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards
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Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant.
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A uniform plane wave with electric field $\vec{E}(x)=A_y \hat{a}_y e^{-j \frac{2 \pi x}{3}} \mathrm{~V} / \mathrm{m}$ is
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A lossless transmission line with characteristic impedance $Z_0 = 50 \Omega$ is terminated with an unknown load. The mag
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For non-degenerately doped n-type silicon, which one of the following plots represents the temperature ($T$) dependence
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The free electron concentration profile $n(x)$ in a doped semiconductor at equilibrium is shown in the figure, where the
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Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of 100 nm, a fixed positive oxide charge of
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A non-degenerate n-type semiconductor has 5 % neutral dopant atoms. Its Fermi level is located at 0.25 eV below the cond
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The photocurrent of a PN junction diode solar cell is 1 mA. The voltage corresponding to its maximum power point is 0.3
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The general form of the complementary function of a differential equation is given by $y(t) = (At + B)e^{-2t}$, where $A
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Let $\rho(x, y, z, t)$ and $u(x, y, z, t)$ represent density and velocity, respectively, at a point $(x, y, z)$ and time
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Let $\mathbb{R}$ and $\mathbb{R}^3$ denote the set of real numbers and the three dimensional vector space over it, respe
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Suppose $X$ and $Y$ are independent and identically distributed random variables that are distributed uniformly in the i
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Consider the Earth to be a perfect sphere of radius $R$. Then the surface area of the region, enclosed by the 60°N latit
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Let $z$ be a complex variable. If $f(z)=\frac{\sin(\pi z)}{z^{7}(z-2)}$ and $C$ is the circle in the complex plane with
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Let $F_1$, $F_2$, and $F_3$ be functions of $(x, y, z)$. Suppose that for every given pair of points A and B in space, t
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Consider the matrix $\begin{bmatrix}1 & k \\ 2 & 1\end{bmatrix}$, where $k$ is a positive real number. Which of the foll
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In the given circuit, the current $I_x$ (in mA) is _______ .
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In the circuit given below, the switch $S$ was kept open for a sufficiently long time and is closed at time $t = 0$. The
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For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is ______.
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In the network shown below, maximum power is to be transferred to the load $R_L$.The value of $R_L$ (in Ω) is ______.
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A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0
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For a causal discrete-time LTI system with transfer function$H(z) = \frac{2z^2 + 3}{\left(z + \frac{1}{3}\right)\left(z
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Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$
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A continuous time signal $x(t) = 2 \cos(8 \pi t + \frac{\pi}{3})$ is sampled at a rate of 15 Hz. The sampled signal $x_s
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The radian frequency value(s) for which the discrete time sinusoidal signal $x[n] = A \cos(\Omega n + \pi/3)$ has a peri
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The relationship between any N-length sequence $x[n]$ and its corresponding N-point discrete Fourier transform $X[k]$ is
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General Aptitude

If ‘→’ denotes increasing order of intensity, then the meaning of the words [charm → enamor → bewitch] is analogous to [
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P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms.
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Five years ago, the ratio of Aman’s age to his father’s age was 1:4, and five years from now, the ratio will be 2:5. Wha
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For a real number $x > 1$ , $$ \frac{1}{\log_{2}x} + \frac{1}{\log_{3}x} + \frac{1}{\log_{4}x} = 1$$ The value of $x$ is
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The greatest prime factor of $(3^{199} - 3^{196})$ is
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Sequence the following sentences (P, Q, R, S) in a coherent passage:P: Shifu’s student exclaimed, “Why do you run since
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Four identical cylindrical chalk-sticks, each of radius $r = 0.5$ cm and length $l = 10$ cm, are bound tightly together
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The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index
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Examples of mirror and water reflections are shown in the figures below:An object appears as the following image after f
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Two identical sheets A and B, of dimensions 24 cm × 16 cm, can be folded into half using two distinct operations, FO1 or
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