GATE ECE 2022
Paper was held on Sun, Feb 6, 2022 3:30 AM
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## GATE ECE

Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width (W)
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The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and $$-$$1 V, re
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An ideal OPAMP circuit with a sinusoidal input is shown in the figure. The 3 dB frequency is the frequency at which the
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Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 $$\mu$$m and width 100 $$\mu$$m. The produ
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For the following circuit with an ideal OPAMP, the difference between the maximum and the minimum values of the capacito
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A circuit with an ideal OPAMP is shown. The Bode plot for the magnitude (in dB) of the gain transfer function (Av(j$$\om View Question A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal View Question Consider the circuit shown with an ideal long channel nMOSFET (enhancement mode, substrate is connected to the source). View Question The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure. Statement I : The sy View Question Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the followi View Question A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 View Question Consider an FM broadcast that employs the pre-emphasis filter with frequency response$${H_{pe}}(\omega ) = 1 + {{j\omeg
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The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in th
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Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is r
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Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel Y be the inpu
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Consider a real valued source whose samples are independent and identically distributed random variables with the probab
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Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2.
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The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path
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Consider an even polynomial p(s) given by $$p(s) = {s^4} + 5{s^2} + 4 + K$$ where K is an unknown real parameter. The co
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Two linear time-invariant systems with transfer functions $${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = { View Question The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transform View Question Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A0, A1, A2 View Question Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR o View Question Select the correct statement(s) regarding CMOS implementation of NOT gates. View Question for the circuit shown, the clock frequency is f0 and the duty cycle is 25%. For the signal at the Q output of the Flip-F View Question A state transition diagram with states A, B, and C, and transition probabilities p1, p2, ....., p7 is shown in the fig View Question Consider a Boolean gate (D) where the output Y is related to the inputs A and b as, Y = A +$$\overline B $$, where + de View Question Consider the circuit shown with an ideal OPAMP. The output voltage V0 is __________ V (rounded off to two decimal places View Question In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amper View Question Consider the following wave equation,$${{{\partial ^2}f(x,t)} \over {\partial {t^2}}} = 10000{{{\partial ^2}f(x,t)} \ov
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A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10$$-$$4 cm, with air as th
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In an electrostatic field, the electric displacement density vector, $$\overrightarrow D$$, is given by $$\overrightarr View Question Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 1017 cm$$-$$3 an View Question In a non-degenerate bulk semiconductor with electron density n = 1016 cm$$-$$3, the value of EC$$-$$EFn = 200 meV, whe View Question An ideal MOS capacitor (p-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with V View Question Select the CORRECT statements regarding semiconductor devices View Question A p-type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. E View Question Consider the two-dimensional vector field$$\overrightarrow F (x,y) - x\overrightarrow i + y\overrightarrow j $$, where View Question Consider a system of linear equations Ax = b, where$$A = \left[ {\matrix{ 1 \hfill & { - \sqrt 2 } \hfill & 3 \hfill
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Consider the following partial differential equation (PDE) $$a{{{\partial ^2}f(x,y)} \over {\partial {x^2}}} + b{{{\part View Question The bar graph shown the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 1 View Question A simple closed path C in the complex plane is shown in the figure. If$$\oint\limits_c {{{{2^z}} \over {{z^2} - 1}}dz =
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The function f(x) = 8loge x $$-$$ x2 + 3 attains its minimum over the interval [1, e] at x = __________. (Here loge x is
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Let $$\alpha$$, $$\beta$$ two non-zero real numbers and v1, v2 be two non-zero real vectors of size 3 $$\times$$ 1. Supp
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Consider the following series: $$\sum\limits_{n = 1}^\infty {{{{n^d}} \over {{c^n}}}}$$ For which of the following com
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The value of the integral $$\int\!\!\!\int\limits_D {3({x^2} + {y^2})dx\,dy}$$, where D is the shaded triangular region
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The current I in the circuit shown is _________.
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Consider the circuit shown in the figure. The current I flowing through the 10 $$\Omega$$ resister is ___________.
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For the circuit shown, the locus of the impedance Z(j$$\omega$$) is plotted as $$\omega$$ increases from zero to infinit
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Consider the circuit shown in the figure with input V(t) in volts. The sinusoidal steady state current I(t) flowing thro
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A linear 2-port network is shown in Fig. (a). An ideal DC voltage source of 10 V is connected across Port 1. A variable
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The Fourier transform X(j$$\omega$$) of the signal $$x(t) = {t \over {{{(1 + {t^2})}^2}}}$$ is ____________.
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Let x1(t) = e$$-$$t u(t) and x2(t) = u(t) $$-$$ u(t $$-$$ 2), where u( . ) denotes the unit step function. If y(t) denot
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The outputs of four systems (S1, S2, S3 and S4) corresponding to the input signal sin(t), for all time t, are shown in t
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For a vector $$\overline x$$ = [x[0], x[1], ....., x[7]], the 8-point discrete Fourier transform (DFT) is denoted by $$View Question ## General Aptitude Mr. X speaks ____________ Japanese ___________ Chinese. View Question A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively. If R gets Rs. 10 View Question A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Furt View Question The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. View Question An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents t View Question Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Flo View Question Consider the following inequalities. (i) 2x$$-$$1 > 7 (ii) 2x$$-$$9 Which one of the following expressions below sa View Question Four points P(0, 1), Q(0,$$-$$3), R($$-$$2,$$-$$1), and S(2,$$-1) represent the vertices of a quadrilateral. What i
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In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary com
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Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively. Let X, Y an
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