GATE ECE 2022

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Sun, Feb 6, 2022 3:30 AM

## 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

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A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal

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Consider the circuit shown with an ideal long channel nMOSFET (enhancement mode, substrate is connected to the source).

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The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.
Statement I : The sy

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Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the followi

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A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1

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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) = {

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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

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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

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Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR o

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Select the correct statement(s) regarding CMOS implementation of NOT gates.

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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

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A state transition diagram with states A, B, and C, and transition probabilities p1, p2, .....,
p7 is shown in the fig

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Consider a Boolean gate (D) where the output Y is related to the inputs A and b as, Y = A + $$\overline B $$, where + de

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Consider the circuit shown with an ideal OPAMP. The output voltage V0 is __________ V (rounded off to two decimal places

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In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amper

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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

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Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 1017 cm$$-$$3 an

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In a non-degenerate bulk semiconductor with electron density n = 1016 cm$$-$$3, the value of EC $$-$$ EFn = 200 meV, whe

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An ideal MOS capacitor (p-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with V

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Select the CORRECT statements regarding semiconductor devices

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A p-type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. E

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Consider the two-dimensional vector field $$\overrightarrow F (x,y) - x\overrightarrow i + y\overrightarrow j $$, where

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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

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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

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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 $$

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## General Aptitude

Mr. X speaks ____________ Japanese ___________ Chinese.

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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

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A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Furt

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The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

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An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents t

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Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Flo

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Consider the following inequalities.
(i) 2x $$-$$ 1 > 7
(ii) 2x $$-$$ 9
Which one of the following expressions below sa

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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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