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1881
GATE ECE 2022 | Question: 6
Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10} \; \text{cm}^{-3}.$ Electron and hole diffusion lengths are $2 \; \mu\text{m}$ ... $3.7 \times 10^{14} \; \text{cm}^{-3}$ $10^{3} \; \text{cm}^{-3}$
Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentrat...
Arjun
6.6k
points
236
views
Arjun
asked
Feb 15, 2022
Others
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1882
GATE ECE 2022 | Question: 7
In a non-degenerate bulk semiconductor with electron density $n = 10^{16} \; \text{cm}^{-3},$ the value of $E_{c} - E_{Fn} = 200 \; \text{meV},$ where $E_{c}$ and $E_{Fn}$ denote the bottom of the conduction band energy and electron Fermi level energy, ... given options, is ____________. $226 \; \text{meV}$ $174 \; \text{meV}$ $218 \; \text{meV}$ $182 \; \text{meV}$
In a non-degenerate bulk semiconductor with electron density $n = 10^{16} \; \text{cm}^{-3},$ the value of $E_{c} – E_{Fn} = 200 \; \text{meV},$ where $E_{c}$ and $E_{F...
Arjun
6.6k
points
306
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Arjun
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Feb 15, 2022
Others
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1883
GATE ECE 2022 | Question: 8
Consider the $\text{CMOS}$ circuit shown in the figure (substrates are connected to their respective sources). The gate width $(W)$ to gate length $(L)$ ratios $\left( \frac{W}{L} \right)$ of the transistors are as shown. Both the transistors have the same gate oxide capacitance ... $2\; \text{V}$ less than $2 \; \text{V}$ equal to $2 \; \text{V}$
Consider the $\text{CMOS}$ circuit shown in the figure (substrates are connected to their respective sources). The gate width $(W)$ to gate length $(L)$ ratios $\left( \f...
Arjun
6.6k
points
258
views
Arjun
asked
Feb 15, 2022
Others
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1884
GATE ECE 2022 | Question: 9
Consider the $ \text{2-bit}$ multiplexer $\text{(MUX)}$ shown in the figure. For $\text{OUTPUT}$ to be the $\text{XOR}$ of $\text{C}$ and $\text{D},$ the values for $A_{0}, A_{1}, A_{2},$ and $A_{3}$ are _______________. $A_{0} = 0, A_{1} = 0, A_{2} = 1, A_{3} = 1$ ... $A_{0} = 0, A_{1} = 1, A_{2} = 1, A_{3} = 0$ $A_{0} = 1, A_{1} = 1, A_{2} = 0, A_{3} = 0$
Consider the $ \text{2–bit}$ multiplexer $\text{(MUX)}$ shown in the figure. For $\text{OUTPUT}$ to be the $\text{XOR}$ of $\text{C}$ and $\text{D},$ the values for $A_...
Arjun
6.6k
points
396
views
Arjun
asked
Feb 15, 2022
Others
gateece-2022
multiplexers
combinational-circuits
digital-circuits
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1885
GATE ECE 2022 | Question: 10
The ideal long channel $n\text{MOSFET}$ and $p\text{MOSFET}$ devices shown in the circuits have threshold voltages of $1 \; \text{V}$ and $ - 1 \; \text{V},$ respectively. The $\text{MOSFET}$ substrates are connected to their respective sources. Ignore leakage currents and assume that the ... $V_{1} = 4 \; \text{V}, \quad V_{2} = - 5 \; \text{V}$
The ideal long channel $n\text{MOSFET}$ and $p\text{MOSFET}$ devices shown in the circuits have threshold voltages of $1 \; \text{V}$ and $ – 1 \; \text{V},$ respective...
Arjun
6.6k
points
305
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Arjun
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Feb 15, 2022
Others
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1886
GATE ECE 2022 | Question: 11
Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure. Note that the Nyquist contour has been ... of the closed-loop transfer function in the closed right-half of the complex plane is ________________. $0$ $1$ $2$ $3$
Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer func...
Arjun
6.6k
points
229
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Arjun
asked
Feb 15, 2022
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1887
GATE ECE 2022 | Question: 12
The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Note that $K$ is varied from $0$ to $\infty.$ Select the transfer function $G(s)$ that results in the root-locus plot of the closed-loop system as ... $G(s) = \frac{s - 1}{(s+1)^{6}}$ $G(s) = \frac{s + 1}{s^{6}+1}$
The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Note that $K$ is varied...
Arjun
6.6k
points
195
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Arjun
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Feb 15, 2022
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1888
GATE ECE 2022 | Question: 13
The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure. Statement $\text{I}:$ The system is necessarily a pure delay system for inputs which are bandlimited to $ - \alpha \leq f \leq \alpha.$ Statement ... $\text{II}$ is correct Statement $\text{I}$ is incorrect, Statement $\text{II}$ is incorrect
The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure.Statement $\text{I}:$ The system is necessarily a pure delay system f...
Arjun
6.6k
points
214
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Arjun
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Feb 15, 2022
Others
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1889
GATE ECE 2022 | Question: 14
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current $\text{(in Amperes)}$ through the resistor is $2\sin (t+\pi/2).$ The displacement current $\text{(in Amperes)}$ through the capacitor is ______________. $2 \sin (t)$ $2 \sin (t + \pi)$ $2 \sin(t + \pi/2)$ $0$
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current $\text{(in Amperes)}$ through the resistor is $2\sin (t+\pi...
Arjun
6.6k
points
241
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Arjun
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Feb 15, 2022
Others
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1890
GATE ECE 2022 | Question: 15
Consider the following partial differential equation $\text{(PDE)}$ $a \frac{ \partial^{2} f(x ,y)}{\partial x^{2}} + b \frac{ \partial^{2} f(x ,y)}{\partial y^{2}} = f(x, y),$ where $a$ and $b$ are distinct positive real numbers. Select the combination(s) of values of the ... $\xi = 0, \eta = 0$ $\xi = \frac{1}{\sqrt{a}}, \eta = \frac{1}{\sqrt{b}}$
Consider the following partial differential equation $\text{(PDE)}$$$a \frac{ \partial^{2} f(x ,y)}{\partial x^{2}} + b \frac{ \partial^{2} f(x ,y)}{\partial y^{2}} = f(x...
Arjun
6.6k
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149
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Arjun
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Feb 15, 2022
Others
gateece-2022
multiple-selects
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1891
GATE ECE 2022 | Question: 16
An ideal $\text{OPAMP}$ circuit with a sinusoidal input is shown in the figure. The $3 \; \text{dB}$ frequency is the frequency at which the magnitude of the voltage gain decreases by $3 \; \text{dB}$ from the maximum value. Which of the options is/are correct? The circuit ... $1000 \; \text{rad/s}.$ The $3 \; \text{dB}$ frequency is $\frac{1000}{3} \; \text{rad/s}.$
An ideal $\text{OPAMP}$ circuit with a sinusoidal input is shown in the figure. The $3 \; \text{dB}$ frequency is the frequency at which the magnitude of the voltage gain...
Arjun
6.6k
points
187
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Arjun
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Feb 15, 2022
Others
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1892
GATE ECE 2022 | Question: 17
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation. $x + z + xy$ $(x + y)(x + z)$ $x + xy + yz$ $x + xz + xy$
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation.$x + z + xy$$(x + y)(x + z...
Arjun
6.6k
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583
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Arjun
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multiple-selects
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1893
GATE ECE 2022 | Question: 18
Select the correct statement(s) regarding $\text{CMOS}$ implementation of $\text{NOT}$ gates. Noise Margin High $(NM_{H})$ is always equal to the Noise Margin Low $(NM_{L}),$ irrespective of the sizing of transistors. Dynamic power consumption ... $\text{NOT}$ gate.
Select the correct statement(s) regarding $\text{CMOS}$ implementation of $\text{NOT}$ gates.Noise Margin High $(NM_{H})$ is always equal to the Noise Margin Low $(NM_{L}...
Arjun
6.6k
points
145
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Feb 15, 2022
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1894
GATE ECE 2022 | Question: 19
Let $H(X)$ denote the entropy of a discrete random variable $X$ taking $K$ possible distinct real values. Which of the following statements is/are necessarily true? $H(X) \leq \log_{2} K \; \text{bits}$ $H(X) \leq H (2X)$ $H(X) \leq H (X^{2})$ $H(X) \leq H (2^{X})$
Let $H(X)$ denote the entropy of a discrete random variable $X$ taking $K$ possible distinct real values. Which of the following statements is/are necessarily true?$H(X) ...
Arjun
6.6k
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185
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Arjun
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1895
GATE ECE 2022 | Question: 20
Consider the following wave equation, $\frac{\partial^{2}f(x, t)}{\partial t^{2}} = 10000 \frac{\partial^{2}f(x, t)}{\partial x^{2}} $ Which of the given options is/are solution(s) to the given wave equation? $f(x, t) = e^{ - (x-100t)^{2}} + e^{ - (x+100t)^{2}}$ ... $f(x, t) = e^{ j 100 \pi (- 100x + t)} + e^{ j 100 \pi (100x + t)}$
Consider the following wave equation,$$\frac{\partial^{2}f(x, t)}{\partial t^{2}} = 10000 \frac{\partial^{2}f(x, t)}{\partial x^{2}} $$Which of the given options is/are s...
Arjun
6.6k
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186
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Arjun
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Feb 15, 2022
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1896
GATE ECE 2022 | Question: 21
The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in $17$ of her matches, the bowler has taken $5$ wickets each. The median number of wickets taken by the bowler in a match is _______________ (rounded off to one decimal place).
The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in $17$ of her matches, the bowler has taken $5$ wicke...
Arjun
6.6k
points
727
views
Arjun
asked
Feb 15, 2022
Analytical Aptitude
gateece-2022
numerical-answers
bar-graph
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1897
GATE ECE 2022 | Question: 22
A simple closed path $C$ in the complex plane is shown in the figure. If $\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$ where $i = \sqrt{-1},$ then the value of $A$ is _________ (rounded off to two decimal places).
A simple closed path $C$ in the complex plane is shown in the figure. If$$\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$$where $i = \sqrt{-1},$ then the value of $...
Arjun
6.6k
points
211
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Arjun
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Feb 15, 2022
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numerical-answers
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1898
GATE ECE 2022 | Question: 23
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}(t),$ then $\displaystyle \lim_{t \rightarrow \infty} y(t) =$ ______________ (rounded off to one decimal place).
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function.If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x...
Arjun
6.6k
points
165
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Arjun
asked
Feb 15, 2022
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numerical-answers
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1899
GATE ECE 2022 | Question: 24
An ideal $\text{MOS}$ capacitor (p-type semiconductor) is shown in the figure. The $\text{MOS}$ capacitor is under strong inversion with $V_{G} = 2 \; \text{V}.$ The corresponding inversion charge density $(Q_{IN})$ is $2.2 \; \mu \text{C /cm}^{2}.$ ... $Q_{IN}$ is ______________ $\mu \text{C/cm}^{2}$ (rounded off to one decimal place).
An ideal $\text{MOS}$ capacitor (p-type semiconductor) is shown in the figure. The $\text{MOS}$ capacitor is under strong inversion with $V_{G} = 2 \; \text{V}.$ The corr...
Arjun
6.6k
points
206
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Arjun
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Feb 15, 2022
Others
gateece-2022
numerical-answers
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1900
GATE ECE 2022 | Question: 25
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the raw (uncoded) data rate is ____________ mega-bits per second (rounded off to one decimal place).
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the ...
Arjun
6.6k
points
236
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Arjun
asked
Feb 15, 2022
Others
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numerical-answers
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1901
GATE ECE 2022 | Question: 26
The function $f(x) = 8 \log_{e} x – x^{2} + 3$ attains its minimum over the interval $[1, e]$ at $x = $____________. (Here $\log_{e}x$ is the natural logarithm of $x$.) $2$ $1$ $e$ $\frac{1+e}{2}$
The function $f(x) = 8 \log_{e} x – x^{2} + 3$ attains its minimum over the interval $[1, e]$ at $x = $____________.(Here $\log_{e}x$ is the natural logarithm of $x$.)$...
Arjun
6.6k
points
131
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Arjun
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Others
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1902
GATE ECE 2022 | Question: 27
Let $\alpha, \beta$ be two non-zero real numbers and $v_{1}, v_{2}$ be two non-zero real vectors of size $3 \times 1.$ Suppose that $v_{1}$ and $v_{2}$ satisfy $v_{1}^{T} v_{2} = 0, v_{1}^{T} v_{1} = 1,$ and $v_{2}^{T} v_{2} = 1.$ Let $A$ be ... $0, \alpha+\beta, \alpha-\beta$ $0, \frac{\alpha+\beta}{2}, \sqrt{\alpha \beta}$ $0, 0, \sqrt{\alpha^{2} + \beta^{2}}$
Let $\alpha, \beta$ be two non-zero real numbers and $v_{1}, v_{2}$ be two non-zero real vectors of size $3 \times 1.$ Suppose that $v_{1}$ and $v_{2}$ satisfy $v_{1}^{T}...
Arjun
6.6k
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143
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Arjun
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Feb 15, 2022
Others
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1903
GATE ECE 2022 | Question: 28
For the circuit shown, the locus of the impedance $Z (j \omega)$ is plotted as $\omega$ increases from zero to infinity. The values of $R_{1}$ and $R_{2}$ are: $R_{1} = 2 \; \text{k} \Omega, R_{2} = 3 \; \text{k} \Omega$ ... $R_{1} = 2 \; \text{k} \Omega, R_{2} = 5 \; \text{k} \Omega$
For the circuit shown, the locus of the impedance $Z (j \omega)$ is plotted as $\omega$ increases from zero to infinity. The values of $R_{1}$ and $R_{2}$ are:$R_{1} = 2 ...
Arjun
6.6k
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149
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Arjun
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Feb 15, 2022
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1904
GATE ECE 2022 | Question: 29
Consider the circuit shown in the figure with input $V(t)$ in volts. The sinusoidal steady state current $I(t)$ flowing through the circuit is shown graphically (where $t$ is in seconds). The circuit element $Z$ can be ____________. a capacitor of $1 \; \text{F}$ an inductor of $1 \; \text{H}$ a capacitor of $\sqrt{3} \; \text{F}$ an inductor of $\sqrt{3} \; \text{H}$
Consider the circuit shown in the figure with input $V(t)$ in volts. The sinusoidal steady state current $I(t)$ flowing through the circuit is shown graphically (where $t...
Arjun
6.6k
points
130
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Arjun
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Feb 15, 2022
Others
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1905
GATE ECE 2022 | Question: 30
Consider an ideal long channel $n \text{MOSFET}$ (enhancement-mode) with gate length $10 \; \mu \text{m}$ and width $100 \; \mu \text{m}.$ The product of electron mobility $(\mu_{n})$ and oxide capacitance per unit area $(C_{\text{ox}})$ ... -to-source current is _____________. $40 \; \text{mA}$ $20 \; \text{mA}$ $15 \; \text{mA}$ $5 \; \text{mA}$
Consider an ideal long channel $n \text{MOSFET}$ (enhancement-mode) with gate length $10 \; \mu \text{m}$ and width $100 \; \mu \text{m}.$ The product of electron mobilit...
Arjun
6.6k
points
112
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Arjun
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Feb 15, 2022
Others
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1906
GATE ECE 2022 | Question: 31
For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________. $15 \; \text{V}$ $27 \; \text{V}$ $13 \; \text{V}$ $14 \; \text{V}$
For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________.$15 \...
Arjun
6.6k
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73
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Arjun
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Feb 15, 2022
Others
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1907
GATE ECE 2022 | Question: 32
A circuit with an ideal $\text{OPAMP}$ is shown. The Bode plot for the magnitude $\text{(in dB)}$ of the gain transfer function $(A_{V} (j \omega) = V_{\text{out}} (j \omega) / V_{\text{in}} (j \omega))$ of the circuuit is also provided (here, $\omega$ is the angular frequency ... $R = 3 \; \text{k} \Omega, C = 2 \; \mu \text{F}$
A circuit with an ideal $\text{OPAMP}$ is shown. The Bode plot for the magnitude $\text{(in dB)}$ of the gain transfer function $(A_{V} (j \omega) = V_{\text{out}} (j \om...
Arjun
6.6k
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69
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Arjun
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1908
GATE ECE 2022 | Question: 33
For the circuit shown, the clock frequency is $f_{0}$ and the duty cycle is $25 \%.$ For the signal at the $\text{Q}$ output of the Flip-Flop, _______________. frequency is $f_{0}/4$ and duty cycle is $50 \%$ frequency is $f_{0}/4$ and duty cycle is $25 \%$ frequency is $f_{0}/2$ and duty cycle is $50 \%$ frequency is $f_{0}$ and duty cycle is $25 \%$
For the circuit shown, the clock frequency is $f_{0}$ and the duty cycle is $25 \%.$ For the signal at the $\text{Q}$ output of the Flip-Flop, _______________.frequency i...
Arjun
6.6k
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62
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Arjun
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Feb 15, 2022
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1909
GATE ECE 2022 | Question: 34
Consider an even polynomial $p(s)$ given by $p(s) = s^{4} + 5s^{2} + 4 + K,$ where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all its roots on the imaginary axis is _____________. $ – 4 \leq K \leq \frac{9}{4}$ $ – 3 \leq K \leq \frac{9}{2}$ $ – 6 \leq K \leq \frac{5}{4}$ $ – 5 \leq K \leq 0$
Consider an even polynomial $p(s)$ given by$$p(s) = s^{4} + 5s^{2} + 4 + K,$$where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all it...
Arjun
6.6k
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81
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Feb 15, 2022
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1910
GATE ECE 2022 | Question: 35
Consider the following series: $ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$ For which of the following combinations of $c, d$ values does this series converge? $ c= 1, d = – 1$ $ c= 2, d = 1$ $ c= 0.5, d = – 10$ $ c= 1, d = – 2$
Consider the following series:$$ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$$For which of the following combinations of $c, d$ values does this series converge?$ c= 1, d = �...
Arjun
6.6k
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73
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Arjun
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1911
GATE ECE 2022 | Question: 36
The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure. Based on the given information, which of the four systems is/are definitely $\text{NOT LTI}$ (linear and time-invariant)? $S_{1}$ $S_{2}$ $S_{3}$ $S_{4}$
The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure.Based on th...
Arjun
6.6k
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81
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Arjun
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1912
GATE ECE 2022 | Question: 37
Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices. Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium. Collector region is generally more heavily doped than Base region in a $\text{BJT}.$ ... under steady state condition. Mobility of electrons always increases with temperature in Silicon beyond $300 \; \text{K}.$
Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices.Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.Collector r...
Arjun
6.6k
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77
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1913
GATE ECE 2022 | Question: 38
A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the probability of transition from state $A$ to $B$). For this state diagram, select the statement(s) which is/are ... $p_{1} + p_{4} + p_{7} = 1$ $p_{2} + p_{5} + p_{7} = 1$
A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the...
Arjun
6.6k
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66
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Arjun
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1914
GATE ECE 2022 | Question: 39
Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation. The Boolean inputs $'0'$ and $'1'$ are also ... $\text{OR}$ logic cannot be implemented $\text{NOR}$ logic can be implemented $\text{AND}$ logic cannot be implemented
Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation...
Arjun
6.6k
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536
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Arjun
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Feb 15, 2022
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gateece-2022
multiple-selects
functional-completeness
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1915
GATE ECE 2022 | Question: 40
Two linear time-invariant systems with transfer functions $G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$ have unit step responses $y_{1}(t)$ and $y_{2}(t),$ respectively. Which of the following ... and $y_{2}(t)$ have the same damped frequency of oscillation. $y_{1}(t)$ and $y_{2}(t)$ have the same $2\%$ settling time.
Two linear time-invariant systems with transfer functions$$G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$$have unit step resp...
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1916
GATE ECE 2022 | Question: 41
Consider an $\text{FM}$ broadcast that employs the pre-emphasis filter with frequency response $H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}},$ where $\omega_{0} = 10^{4} \; \text{rad/sec}.$ For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate ... $R = 1 \; k \Omega, C = 2 \; \mu F$ $R = 2 \; k \Omega, C = 0.5 \; \mu F$
Consider an $\text{FM}$ broadcast that employs the pre-emphasis filter with frequency response$$H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}},$$where $\omega_{0} = 10^...
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1917
GATE ECE 2022 | Question: 42
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light in air to be $3 \times 10^{8} \; \text{m/s}.$ The frequency/frequencies of $\text{TM}$ waves which can ... $8 \times 10^{14} \; \text{Hz}$ $1 \times 10^{13} \; \text{Hz}$
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light...
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1918
GATE ECE 2022 | Question: 43
The value of the integral $ \iint_{D} 3(x^{2} + y^{2})dxdy,$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).
The value of the integral$$ \iint_{D} 3(x^{2} + y^{2})dxdy,$$where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest in...
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1919
GATE ECE 2022 | Question: 44
A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance $R$ is connected across Port $2.$ As $R$ is varied, the measured voltage ... by the load shown in $\text{Fig.(c)},$ the current $I_{2}$ is ___________ $\text{mA}$ (rounded off to one decimal place).
A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance...
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1920
GATE ECE 2022 | Question: 45
For a vector $\overline{x} = \left[ x [0], x[1], \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\overline{x}) = \left[ X [0], X[1], \dots, X[7] \right],$ ... $\overline{y} = DFT (DFT(\overline{x})),$ then the value of $y[0]$ is _____________ (rounded off to one decimal place).
For a vector $\overline{x} = \left[ x [0], x , \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\ov...
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