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 $R_ View Question In the circuit shown below, the transistors$M_1$and$M_2$are biased in saturation. Their small signal transconductanc View Question Which of the following statements is/are true for a BJT with respect to its DC current gain$\beta$? View Question An NMOS transistor operating in the linear region has$I_{D}$of 5$\mu$A at$V_{DS}$of 0.1 V. Keeping$V_{GS}$constan View Question A digital communication system transmits through a noiseless bandlimited channel$[-W, W]$. The received signal$z(t)$a View Question A white Gaussian noise$w(t)$with zero mean and power spectral density$\frac{N_0}{2}$, when applied to a first-order R View Question 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 View Question A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _______ . View Question A source transmits a symbol$s$, taken from$\\{-4, 0, 4\\}$with equal probability, over an additive white Gaussian noi View Question 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) View Question 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 View Question In the context of Bode magnitude plots, 40 dB/decade is the same as ______. View Question 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 View Question Consider a unity negative feedback control system with forward path gain$G(s) = \frac{K}{(s + 1)(s + 2)(s + 3)}$as sho View Question A satellite attitude control system, as shown below, has a plant with transfer function$G(s) = \frac{1}{s^2}$cascaded View Question Consider a system$S$represented in state space as$$\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \ View Question 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 ________ View Question A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set o View Question 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 View Question 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 View Question The propagation delay of the 2 x 1 MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as View Question The sequence of states (Q_1 Q_0) of the given synchronous sequential circuit is ________. View Question A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a norm View Question Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards View Question Let \hat{i} and \hat{j} be the unit vectors along x and y axes, respectively and let A be a positive constant. View Question 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 View Question A lossless transmission line with characteristic impedance Z_0 = 50 \Omega is terminated with an unknown load. The mag View Question For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (T) dependence View Question The free electron concentration profile n(x) in a doped semiconductor at equilibrium is shown in the figure, where the View Question Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of 100 nm, a fixed positive oxide charge of View Question A non-degenerate n-type semiconductor has 5 % neutral dopant atoms. Its Fermi level is located at 0.25 eV below the cond View Question The photocurrent of a PN junction diode solar cell is 1 mA. The voltage corresponding to its maximum power point is 0.3 View Question The general form of the complementary function of a differential equation is given by y(t) = (At + B)e^{-2t}, where A View Question 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 View Question Let \mathbb{R} and \mathbb{R}^3 denote the set of real numbers and the three dimensional vector space over it, respe View Question Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the i View Question Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the 60°N latit View Question 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 View Question 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 View Question Consider the matrix \begin{bmatrix}1 & k \\ 2 & 1\end{bmatrix}, where k is a positive real number. Which of the foll View Question In the given circuit, the current I_x (in mA) is _______ . View Question In the circuit given below, the switch S was kept open for a sufficiently long time and is closed at time t = 0. The View Question For the two port network shown below, the value of the Y_{21} parameter (in Siemens) is ______. View Question In the network shown below, maximum power is to be transferred to the load R_L.The value of R_L (in Ω) is ______. View Question 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 View Question For a causal discrete-time LTI system with transfer functionH(z) = \frac{2z^2 + 3}{\left(z + \frac{1}{3}\right)\left(z View Question Consider two continuous time signals x(t) and y(t) as shown below If X(f) denotes the Fourier transform of x(t) View Question 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 View Question The radian frequency value(s) for which the discrete time sinusoidal signal x[n] = A \cos(\Omega n + \pi/3) has a peri View Question The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is View Question ## General Aptitude If ‘→’ denotes increasing order of intensity, then the meaning of the words [charm → enamor → bewitch] is analogous to [ View Question 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. View Question 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 View Question 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 View Question The greatest prime factor of$(3^{199} - 3^{196})$is View Question Sequence the following sentences (P, Q, R, S) in a coherent passage:P: Shifu’s student exclaimed, “Why do you run since View Question 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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