GATE ECE 2023
GATE 2023 Previous Year
3 hDuration
100Total Marks
64Questions
10Sections
Instructions
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Paper Structure
Electromagnetics
Electromagnetics
Q1.
mcq multi
+2 / 0
The following circuit(s) representing a lumped element equivalent of an infinitesimal sectioin of a transmission line is/are
Q2.
mcq multi
+2 / 0
The standing wave ratio on a 50 $$\Omega$$ lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. $$Z_L$$ can be replaced by an equivalent length $$l_m$$ and terminating resistance $$R_m$$ of the same line. The value of $$R_m$$ and $$l_m$$, respectively, are
Q3.
numerical
+2 / 0
A transparent dielectric coating is applied to glass ($$\varepsilon _r=4,\mu_r=1$$) to eliminate the reflection of red light ($$\lambda_0=0.75~\mu\mathrm{m}$$). The minimum thickness of the dielectric coating, in $$\mu\mathrm{m}$$, that can be used is __________ (rounded off to two decimal places).
Q4.
mcq single
+1 / 0.33
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.)
Q5.
mcq multi
+2 / 0
The electric field of a plane electromagnetic wave is
$$E = {a_x}{C_{1x}}\cos (\omega t - \beta z) + {a_y}{C_{1y}}\cos (\omega t - \beta z + \theta )$$ V/m.
Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?
Analog Circuits
Analog Circuits
Q1.
mcq single
+1 / 0.33
A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when
Q2.
mcq single
+2 / 0.67
The $$\mathrm{{{{V_{OUT}}} \over {{V_{IN}}}}}$$ of the circuit shown below is
Q3.
numerical
+2 / 0
A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 $$\mu$$s. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is ___________ $$\mu$$s (rounded off to two decimal places).
Q4.
mcq single
+2 / 0.67
In the circuit shown below, D$$_1$$ and D$$_2$$ are silicon diodes with cut-in voltage of 0.7 V. $$\mathrm{V_{IN}}$$ and $$\mathrm{V_{OUT}}$$ are input and output voltages in volts. The transfer characteristic is
Q5.
mcq single
+1 / 0.33
In the circuit shown below, $$V_1$$ and $$V_2$$ are bias voltages. Based on input and output impedances, the circuit behaves as a
Signals And Systems
Signals And Systems
Q1.
mcq single
+2 / 0.67
Let an input $$x[n]$$ having discrete time Fourier transform $$x({e^{j\Omega }}) = 1 - {e^{ - j\Omega }} + 2{e^{ - 3j\Omega }}$$ be passed through an LTI system. The frequency response of the LTI system is $$H({e^{j\Omega }}) = 1 - {1 \over 2}{e^{ - j2\Omega }}$$. The output $$y[n]$$ of the system is
Q2.
mcq single
+1 / 0.33
Let $${w^4} = 16j$$. Which of the following cannot be a value of $$w$$?
Q3.
mcq single
+2 / 0.67
Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be $$x[n] = \sum\limits_{k = 0}^4 {{a_k}{e^{{{jk2\pi m} \over 5}}}} $$, where $${a_0} = 1,{a_1} = 3j,{a_2} = 2j,{a_3} = - 2j$$ and $${a_4} = - 3j$$. The value of the sum $$\sum\limits_{n = 0}^4 {x[n]\sin {{4\pi n} \over 5}} $$ is
Q4.
mcq single
+1 / 0.33
Consider a system with input $$x(t)$$ and output $$y(t) = x({e^t})$$. The system is
Q5.
mcq single
+2 / 0.67
Let $$x(t) = 100\cos (10.5Wt)$$ be passed through an LTI system having impulse response $$h(t) = \pi {\left( {{{\sin Wt} \over {\pi t}}} \right)^2}\cos 10Wt$$. The output of the system is
Q6.
mcq single
+1 / 0.33
The Fourier transform $$x(\omega )$$ of $$x(t) = {e^{ - {t^2}}}$$ is
Note : $$\int\limits_{ - \infty }^\infty {{e^{ - {y^2}}}dy = \sqrt \pi } $$
Q7.
mcq single
+1 / 0.33
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
Q8.
mcq single
+1 / 0.33
In the table shown below, match the signal type with its spectral characteristics.
Signal type
Spectral characteristics
(i)
Continuous, aperiodic
(a)
Continuous, aperiodic
(ii)
Continuous, periodic
(b)
Continuous, periodic
(iii)
Discrete, aperiodic
(c)
Discrete, aperiodic
(iv)
Discrete, periodic
(d)
Discrete, periodic
Q9.
numerical
+2 / 0
Let $$\mathrm{x_1(t)=u(t+1.5)-u(t-1.5)}$$ and $$\mathrm{x_2(t)}$$ is shown in the figure below. For $$\mathrm{y(t)=x_1(t)~*~x_2(t)}$$, the $$\int_{ - \infty }^\infty {y(t)dt} $$ is ____________ (rounded off to the nearest integer).
Network Theory
Network Theory
Q1.
mcq single
+2 / 0.67
The S-parameters of a two port network is given as
$$[S] = \left[ {\matrix{
{{S_{11}}} & {{S_{12}}} \cr
{{S_{21}}} & {{S_{22}}} \cr
} } \right]$$
with reference to $${Z_0}$$. Two lossless transmission line sections of electrical lengths $${\theta _1} = \beta {l_1}$$ and $${\theta _2} = \beta {l_2}$$ are added to the input and output ports for measurement purposes, respectively. The S-parameters $$[S']$$ of the resultant two port network is
Q2.
numerical
+1 / 0
For the two port network shown below, the [Y]-parameters is given as
$$[Y] = {1 \over {100}}\left[ {\matrix{
2 & { - 1} \cr
{ - 1} & {4/3} \cr
} } \right]S$$
The value of load impedance $$\mathrm{Z_L}$$, in $$\Omega$$, for maximum power transfer will be ___________ (rounded off to the nearest integer).
Q3.
mcq single
+2 / 0.67
The switch S$$_1$$ was closed and S$$_2$$ was open for a long time. At t = 0, switch S$$_1$$ is opened and S$$_2$$ is closed, simultaneously. The value of i$$_\mathrm{c}$$(0$$^+$$), in amperes, is
Q4.
numerical
+1 / 0
In the circuit shown below, switch S was closed for a long time. If the switch is opened at t = 0, the maximum magnitude of the voltage $$\mathrm{V_R}$$, in volts, is __________ (rounded off to the nearest integer).
Q5.
numerical
+1 / 0
In the circuit shown below, the current i flowing through 200 $$\Omega$$ resistor is __________ mA (rounded off to two decimal places).
Q6.
mcq single
+1 / 0.33
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
Engineering Mathematics
Engineering Mathematics
Q1.
mcq single
+1 / 0.33
The value of the contour integral, $$\oint\limits_C {\left( {{{z + 2} \over {{z^2} + 2z + 2}}} \right)dz} $$, where the contour C is $$\left\{ {z:\left| {z + 1 - {3 \over 2}j} \right| = 1} \right\}$$, taken in the counter clockwise direction, is
Q2.
mcq single
+1 / 0.33
The rate of increase, of a scalar field $$f(x,y,z) = xyz$$, in the direction $$v = (2,1,2)$$ at a point (0,2,1) is
Q3.
mcq single
+1 / 0.33
Let $${v_1} = \left[ {\matrix{
1 \cr
2 \cr
0 \cr
} } \right]$$ and $${v_2} = \left[ {\matrix{
2 \cr
1 \cr
3 \cr
} } \right]$$ be two vectors. The value of the coefficient $$\alpha$$ in the expression $${v_1} = \alpha {v_2} + e$$, which minimizes the length of the error vector e, is
Q4.
mcq single
+2 / 0.67
Let $$x$$ be an $$n \times 1$$ real column vector with length $$l = \sqrt {{x^T}x} $$. The trace of the matrix $$P = x{x^T}$$ is
Q5.
mcq single
+2 / 0.67
The state equation of a second order system is
$$x(t) = Ax(t),\,\,\,\,x(0)$$ is the initial condition.
Suppose $$\lambda_1$$ and $$\lambda_2$$ are two distinct eigenvalues of A and $$v_1$$ and $$v_2$$ are the corresponding eigenvectors. For constants $$\alpha_1$$ and $$\alpha_2$$, the solution, $$x(t)$$, of the state equation is
Q6.
mcq single
+1 / 0.33
Let the sets of eigenvalues and eigenvectors of a matrix B be $$\{ {\lambda _k}|1 \le k \le n\} $$ and $$\{ {v_k}|1 \le k \le n\} $$, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where $$B = {P^{ - 1}}AP$$, respectively, are
Q7.
mcq single
+2 / 0.67
The value of the line integral $$\int_P^Q {({z^2}dx + 3{y^2}dy + 2xz\,dz)} $$ along the straight line joining the points $$P(1,1,2)$$ and $$Q(2,3,1)$$ is
Q8.
numerical
+2 / 0
The value of the integral $$\int\limits\!\!\!\int_R {xy\,dx\,dy} $$ over the regioin R, given in the figure, is _________ (rounded off to the nearest integer).
Control Systems
Control Systems
Q1.
mcq single
+2 / 0.67
In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as Y(s) = G$$_1$$(s)R(s) + G$$_2$$(s)D(s).
G$$_1$$(s) and G$$_2$$(s) are given by
Q2.
mcq single
+2 / 0.67
A closed loop system is shown in the figure where $$k>0$$ and $$\alpha > 0$$. The steady state error due to a ramp input $$(R(s) = \alpha /{s^2})$$ is given by
Q3.
numerical
+2 / 0
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $$(s) = {{k{{(s + z)}^a}} \over {{s^b}{{(s + p)}^c}}}$$, where $$k,z,p,z,b$$ and $$c$$ are positive constants. The value of $$(a + b + c)$$ is ___________ (rounded off to the nearest integer)
Q4.
mcq single
+1 / 0.33
The open loop transfer function of a unity negative feedback system is $$G(s) = {k \over {s(1 + s{T_1})(1 + s{T_2})}}$$, where $$k,T_1$$ and $$T_2$$ are positive constants. The phase cross-over frequency, in rad/s, is
General Aptitude
General Aptitude
Q1.
mcq single
+1 / 0.33
"I cannot support this proposal. My __________ will not permit it."
Q2.
mcq single
+2 / 0.67
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]
Q3.
mcq single
+1 / 0.33
Courts : __________ : : Parliament : Legislature
(By word meaning)
Q4.
mcq single
+2 / 0.67
Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.
Based only on the information provided above, which one of the following options can be logically inferred with certainty?
Q5.
mcq single
+1 / 0.33
How many rectangles are present in the given figure?
Q6.
mcq single
+2 / 0.67
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 __________.
Q7.
mcq single
+1 / 0.33
In a class of 100 students,
(i) there are 30 students who neither like romantic movies nor comedy movies,
(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and
(iii) the number of students who like both romantic movies and comedy movies is 20.
How many students in the class like romantic movies?
Q8.
mcq single
+2 / 0.67
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.
Q9.
mcq single
+1 / 0.33
What is the smallest number with distinct digits whose digits add up to 45?
Q10.
mcq single
+2 / 0.67
Which one of the following options represents the given graph?
Electronic Devices And Vlsi
Electronic Devices And Vlsi
Q1.
numerical
+2 / 0
In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is 1 $$\times$$ 10$$^{19}$$ cm$$^{-3}$$. The thermal equilibrium hole concentration in silicon at 400 K is _____________ $$\times$$ 10$$^{13}$$ cm$$^{-3}$$ (rounded off to two decimal places).
Given kT at 300 K is 0.026 eV.
Q2.
numerical
+2 / 0
In an extrinsic semiconductor, the hole concentration is given to be 1.5$$n_i$$ where $$n_i$$ is the intrinsic carrier concentration of 1 $$\times$$ 10$$^{10}$$ $$cm^{-3}$$. The ratio of electron to hole mobility for equal hole and electron drift current is given as ___________ (rounded off to two decimal places).
Q3.
mcq single
+1 / 0.33
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as
Q4.
mcq single
+1 / 0.33
For an intrinsic semiconductor at temperature $$T=0K$$, which of the following statement is true?
Q5.
numerical
+2 / 0
In the circuit below, the voltage V$$_{\mathrm{L}}$$ is _____________ V (rounded off to two decimal places).
Q6.
mcq single
+1 / 0.33
For a MOS capacitor, $$\mathrm{V_{fb}}$$ and $$\mathrm{V_{t}}$$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width ($$\mathrm{W_{dep}}$$) for varying gate voltage ($$\mathrm{V_{g}}$$) is best represented by
Digital Circuits
Digital Circuits
Q1.
mcq single
+1 / 0.33
In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is
Q2.
numerical
+2 / 0
In a given sequential circuit, initial states are Q$$_1$$ = 1 and Q$$_2$$ = 0. For a clock frequency of 1 MHz, the frequency of signal Q$$_2$$ in kHz, is ___________ (rounded off to the nearest integer).
Q3.
mcq single
+1 / 0.33
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
Q4.
numerical
+1 / 0
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).
Q5.
numerical
+1 / 0
For the circuit shown below, the propagation delay of each NAND gate is 1 ns. The critical path delay, in ns, is __________ (rounded off to the nearest integer).
Communications
Communications
Q1.
numerical
+2 / 0
The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of "yes/no" questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _____________ (rounded off to two decimal places).
Symbols
a
b
c
d
e
f
g
h
Frequency of occurrence
$$\frac{1}{2}$$
$${1 \over 4}$$
$${1 \over 8}$$
$${1 \over {16}}$$
$${1 \over {32}}$$
$${1 \over {64}}$$
$${1 \over {128}}$$
$${1 \over {128}}$$
Q2.
mcq multi
+1 / 0
For a real signal, which of the following is/are valid power spectral density/densities?
Q3.
mcq single
+2 / 0.67
A random variable X, distributed normally as N(0, 1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is
(In the options given below, a, b, c are non-zero constants and g(y) is piece-wise continuous function)
Q4.
numerical
+2 / 0
Let X(t) be a white Gaussian noise with power spectral density $$\frac{1}{2}$$W/Hz. If X(t) is input to an LTI system with impulse response $$e^{-t}u(t)$$. The average power of the system output is ____________ W (rounded off to two decimal places).
Q5.
mcq single
+2 / 0.67
Let a frequency modulated (FM) signal $$x(t) = A\cos ({\omega _c}t + {k_f}\int_{ - \infty }^t {m(\lambda )d\lambda )} $$, where $$m(t)$$ is a message signal of bandwidth W. It is passed through a non-linear system with output $$y(t) = 2x(t) + 5{(x(t))^2}$$. Let $${B^T}$$ denote the FM bandwidth. The minimum value of $${\omega _c}$$ required to recover $$x(t)$$ from $$y(t)$$ is
Q6.
mcq single
+2 / 0.67
Let x$$_1$$(t) and x$$_2$$(t) be two band-limited signals having bandwidth $$B=4\pi\times10^3$$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is
