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41
GATE ECE 2024 | Question: 41
In the circuit shown below, the transistors $M_{1}$ and $M_{2}$ are biased in saturation. Their small signal transconductances are $g_{m 1}$ and $g_{m 2}$ respectively. Neglect body effect, channel length modulation and intrinsic device capacitances. Assuming that capacitor $C_{1}$ is a ... $\frac{g_{m 2} R_{D}\left(\frac{1}{g_{m 1}}\right)}{\frac{1}{g_{m 1}}+R_{s}}$
In the circuit shown below, the transistors $M_{1}$ and $M_{2}$ are biased in saturation. Their small signal transconductances are $g_{m 1}$ and $g_{m 2}$ respectively. N...
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42
GATE ECE 2024 | Question: 42
Which of the following statements is/are true for a $\text{BJT}$ with respect to its DC current gain $\beta$ ? Under high-level injection condition in forward active mode, $\beta$ will decrease with increase in the magnitude of collector current. ... in active region. A higher value of $\beta$ will lead to a lower value of the collector-to-emitter breakdown voltage.
Which of the following statements is/are true for a $\text{BJT}$ with respect to its DC current gain $\beta$ ?Under high-level injection condition in forward active mode,...
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43
GATE ECE 2024 | Question: 43
Consider a system $S$ represented in state space as \[ \frac{d x}{d t}=\left[\begin{array}{ll} 0 & -2 \\ 1 & -3 \end{array}\right] x+\left[\begin{array}{l} 1 \\ 0 \end{array}\right] r, y=\left[\begin{array}{ll} 2 & -5 \end{array}\ ...
Consider a system $S$ represented in state space as\[\frac{d x}{d t}=\left[\begin{array}{ll}0 & -2 \\1 & -3\end{array}\right] x+\left[\begin{array}{l}1 \\0\end{array}\rig...
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44
GATE ECE 2024 | Question: 44
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, the line integral $\int_{C}\left(F_{1} \mathrm{~d} x+F_{2} \mathrm{~d} y+F_{3} \mathrm{~d} z\right)$ evaluates to ...
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, the line integral $\int_{C}\left(F_{1} \mat...
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45
GATE ECE 2024 | Question: 45
Consider the matrix $\left[\begin{array}{ll}1 & k \\ 2 & 1\end{array}\right]$, where $k$ is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix? $\left[\begin{array}{c}1 \\ -\sqrt{2 / k}\end{array}\right]$ ... $\left[\begin{array}{c}\sqrt{2 k} \\ -1\end{array}\right]$
Consider the matrix $\left[\begin{array}{ll}1 & k \\ 2 & 1\end{array}\right]$, where $k$ is a positive real number. Which of the following vectors is/are e...
260
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46
GATE ECE 2024 | Question: 46
The radian frequency value(s) for which the discrete time sinusoidal signal $x[n]=A \cos (\Omega n+\pi / 3)$ has a period of $40$ is/are $\_\_\_\_\_\_$. $0.15 \pi$ $0.225 \pi$ $0.3 \pi$ $0.45 \pi$
The radian frequency value(s) for which the discrete time sinusoidal signal $x[n]=A \cos (\Omega n+\pi / 3)$ has a period of $40$ is/are $\_\_\_\_\_\_$.$0....
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47
GATE ECE 2024 | Question: 47
Let $X(t)=A \cos \left(2 \pi f_{0} t+\theta\right)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0,2 \pi]$, respectively. $X(t)$ is ... quantization noise ratio (in $\mathrm{dB}$, rounded off to two decimal places) at the output of the quantizer is $\_\_\_\_\_\_$.
Let $X(t)=A \cos \left(2 \pi f_{0} t+\theta\right)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distribut...
124
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numerical-answers
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48
GATE ECE 2024 | Question: 48
A lossless transmission line with characteristic impedance $\mathrm{Z}_{0}=50 \Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma|=0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$ ) is $\_\_\_\_\_\_.$
A lossless transmission line with characteristic impedance $\mathrm{Z}_{0}=50 \Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is ...
140
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49
GATE ECE 2024 | Question: 49
The relationship between any N-length sequence $x[n]$ and its corresponding $\mathrm{N}$-point discrete Fourier transform $X[k]$ is defined as \[ X[k]=\mathcal{F}\{x[n]\} . \] Another sequence $y[n]$ is formed as below \[ y[n]=\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{ ... } . \] For the sequence $x[n]=\{1,2,1,3\}$, the value of $Y[0]$ is $\_\_\_\_\_\_\_\_\_$.
The relationship between any N-length sequence $x[n]$ and its corresponding $\mathrm{N}$-point discrete Fourier transform $X[k]$ is defined as\[X[k]=\mathcal{F}\{x[n]\} ....
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50
GATE ECE 2024 | Question: 50
For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is $\_\_\_\_\_\_$.
For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is $\_\_\_\_\_\_$.
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51
GATE ECE 2024 | Question: 51
Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of $100 \mathrm{~nm}$, a fixed positive oxide charge of $10^{-8} \mathrm{C} / \mathrm{cm}^{2}$ at the oxide-silicon interface, and a metal work function of $4.6 \mathrm{eV}$. ... the work function of the p-type silicon (in $\mathrm{eV}$, rounded off to two decimal places) is $\_\_\_\_\_\_$.
Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of $100 \mathrm{~nm}$, a fixed positive oxide charge of $10^{-8} \mathrm{C} / \mathrm{cm}^{2}...
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52
GATE ECE 2024 | Question: 52
In the network shown below, maximum power is to be transferred to the load $R_{L}$. The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.
In the network shown below, maximum power is to be transferred to the load $R_{L}$.The value of $R_{L}$ (in $\Omega$ ) is $\_\_\_\_\_\_\_$.
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53
GATE ECE 2024 | Question: 53
A non-degenerate n-type semiconductor has $5 \%$ neutral dopant atoms. Its Fermi level is located at $0.25 \mathrm{eV}$ below the conduction band $\left(E_{C}\right)$ and the donor energy level $\left(E_{D}\right)$ has a degeneracy of $2$. Assuming the thermal voltage to ... $E_{C}$ and $E_{D}$ (in $\mathrm{eV}$, rounded off to two decimal places) is $\_\_\_\_\_\_\_$.
A non-degenerate n-type semiconductor has $5 \%$ neutral dopant atoms. Its Fermi level is located at $0.25 \mathrm{eV}$ below the conduction band $\left(E_{C}\right)$ and...
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54
GATE ECE 2024 | Question: 54
An $\text{NMOS}$ transistor operating in the linear region has $I_{D S}$ of $5 \mu \mathrm{A}$ at $V_{D S}$ of $0.1 \mathrm{~V}$. Keeping $V_{G S}$ constant, the $V_{D S}$ is increased to $1.5 \mathrm{~V}$ ... transconductance at the new operating point (in $\mu \mathrm{A} / \mathrm{V}$, rounded off to two decimal places) is $\_\_\_\_\_\_\_$.
An $\text{NMOS}$ transistor operating in the linear region has $I_{D S}$ of $5 \mu \mathrm{A}$ at $V_{D S}$ of $0.1 \mathrm{~V}$. Keeping $V_{G S}$ constant, the $V_{D S}...
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55
GATE ECE 2024 | Question: 55
The photocurrent of a $\text{PN}$ junction diode solar cell is $1 \mathrm{~mA}$. The voltage corresponding to its maximum power point is $0.3 \mathrm{~V}$. If the thermal voltage is $30 \mathrm{mV}$, the reverse saturation current of the diode (in $\mathrm{nA}$, rounded off to two decimal places) is $\_\_\_\_\_\_$.
The photocurrent of a $\text{PN}$ junction diode solar cell is $1 \mathrm{~mA}$. The voltage corresponding to its maximum power point is $0.3 \mathrm{~V}$. If the thermal...
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56
GATE ECE 2023 | GA Question: 1
“I cannot support this proposal. My _________ will not permit it.” conscious consensus conscience consent
“I cannot support this proposal. My _________ will not permit it.”consciousconsensusconscienceconsent
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May 20, 2023
Verbal Aptitude
gateece-2023
verbal-aptitude
english-grammar
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GATE ECE 2023 | GA Question: 2
Courts : _________: : Parliament : Legislature (By word meaning) Judiciary Executive Governmental Legal
Courts : _________: : Parliament : Legislature(By word meaning)JudiciaryExecutiveGovernmentalLegal
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May 20, 2023
Verbal Aptitude
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verbal-aptitude
word-pairs
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GATE ECE 2023 | GA Question: 3
What is the smallest number with distinct digits whose digits add up to $45?$ $123555789$ $123457869$ $123456789$ $99999$
What is the smallest number with distinct digits whose digits add up to $45?$$123555789$$123457869$$123456789$$99999$
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May 20, 2023
Quantitative Aptitude
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quantitative-aptitude
number-theory
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GATE ECE 2023 | GA Question: 4
In a class of $100$ students, there are $30$ students who neither like romantic movies nor comedy movies, the number of students who like romantic movies is twice the number of students who like comedy movies, and the number of students who like both romantic movies and comedy movies is $20$. How many students in the class like romantic movies? $40$ $20$ $60$ $30$
In a class of $100$ students,there are $30$ students who neither like romantic movies nor comedy movies,the number of students who like romantic movies is twice the numbe...
695
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May 20, 2023
Quantitative Aptitude
gateece-2023
quantitative-aptitude
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60
GATE ECE 2023 | GA Question: 5
How many rectangles are present in the given figure? $8$ $9$ $10$ $12$
How many rectangles are present in the given figure? $8$$9$$10$$12$
548
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May 20, 2023
Spatial Aptitude
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spatial-aptitude
counting-figure
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GATE ECE 2023 | GA Question: 6
Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws and some that do not. All creatures that have ... creatures with claws are non-ferocious. Some non-ferocious creatures have claws. Some ferocious creatures are creatures with claws.
Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures th...
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Analytical Aptitude
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analytical-aptitude
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GATE ECE 2023 | GA Question: 7
Which one of the following options represents the given graph? $f(x)=x^{2} 2^{-|x|}$ $f(x)=x 2^{-|x|}$ $f(x)=|x| 2^{-x}$ $f(x)=x 2^{-x}$
Which one of the following options represents the given graph? $f(x)=x^{2} 2^{-|x|}$$f(x)=x 2^{-|x|}$$f(x)=|x| 2^{-x}$$f(x)=x 2^{-x}$
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May 20, 2023
Quantitative Aptitude
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quantitative-aptitude
functions
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GATE ECE 2023 | GA Question: 8
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 ... The child in the passage read stories about interplanetary travel only in parts. It teaches us that stories are good for children.
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...
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May 20, 2023
Verbal Aptitude
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verbal-aptitude
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GATE ECE 2023 | GA Question: 9
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: ... identify all the $100$ covid positive individuals irrespective of how they are grouped. $700$ $600$ $800$ $1000$
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 dev...
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May 20, 2023
Analytical Aptitude
gateece-2023
analytical-aptitude
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GATE ECE 2023 | GA Question: 10
A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ 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 $100 \mathrm{~cm} \times 1 \mathrm{~cm}$. The total number of creases visible when the sheet is unfolded is ___________. $32$ $5$ $31$ $63$
A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ rectangular sheet is folded $5$ times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually,...
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May 20, 2023
Quantitative Aptitude
gateece-2023
quantitative-aptitude
mensuration
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GATE ECE 2023 | Question: 1
Let $v_1=\left[\begin{array}{l}1 \\ 2 \\ 0\end{array}\right]$ and $v_2=\left[\begin{array}{l}2 \\ 1 \\ 3\end{array}\right]$ 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 $\frac{7}{2}$ $\frac{-2}{7}$ $\frac{2}{7}$ $\frac{-7}{2}$
Let $v_1=\left[\begin{array}{l}1 \\ 2 \\ 0\end{array}\right]$ and $v_2=\left[\begin{array}{l}2 \\ 1 \\ 3\end{array}\right]$ be two vectors. The value of the coefficient $...
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GATE ECE 2023 | Question: 2
The rate of increase, of a scalar field $f(x, y, z)=x y z$, in the direction $v=(2,1,2)$ at a point $(0,2,1)$ is $\frac{2}{3}$ $\frac{4}{3}$ $2$ $4$
The rate of increase, of a scalar field $f(x, y, z)=x y z$, in the direction $v=(2,1,2)$ at a point $(0,2,1)$ is$\frac{2}{3}$$\frac{4}{3}$$2$$4$
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GATE ECE 2023 | Question: 3
Let $w^4=16 j$. Which of the following cannot be a value of $w$ ? $2 e^{\frac{j 2 \pi}{8}}$ $2 e^{\frac{j \pi}{8}}$ $2 e^{\frac{j5 \pi}{8}}$ $2 e^{\frac{j9 \pi}{8}}$
Let $w^4=16 j$. Which of the following cannot be a value of $w$ ?$2 e^{\frac{j 2 \pi}{8}}$$2 e^{\frac{j \pi}{8}}$$2 e^{\frac{j5 \pi}{8}}$$2 e^{\frac{j9 \pi}{8}}$
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GATE ECE 2023 | Question: 4
The value of the contour integral, $\oint_C\left(\frac{z+2}{z^2+2 z+2}\right) d z$, where the contour $\mathrm{C}$ is $\left\{z:\left|z+1-\frac{3}{2} j\right|=1\right\}$, taken in the counter clockwise direction, is $-\pi(1+j)$ $\pi(1+j)$ $\pi(1-j)$ $-\pi(1-j)$
The value of the contour integral, $\oint_C\left(\frac{z+2}{z^2+2 z+2}\right) d z$, where the contour $\mathrm{C}$ is $\left\{z:\left|z+1-\frac{3}{2} j\right|=1\right\}$,...
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GATE ECE 2023 | Question: 5
Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\left\{\lambda_k \mid 1 \leq k \leq n\right\}$ and $\left\{v_k \mid 1 \leq k \leq n\right\}$, respectively. For any invertible matrix $P$, the sets of eigenvalues and eigenvectors of the matrix $A$, where ... $\left\{P^{-1} v_k \mid 1 \leq k \leq n\right\}$
Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\left\{\lambda_k \mid 1 \leq k \leq n\right\}$ and $\left\{v_k \mid 1 \leq k \leq n\right\}$, respectivel...
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GATE ECE 2023 | Question: 6
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as degenerate $\text{n}$-type. degenerate $\text{p}$-type. non-degenerate $\text{n}$-type. non-degenerate $\text{p}$-type.
In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known asdegenerate $\text{n}$-type.degenerate $\text{p}$-type.non-deg...
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GATE ECE 2023 | Question: 7
For an intrinsic semiconductor at temperature $\text{T}=0 \; \text{K}$, which of the following statement is true? All energy states in the valence band are filled with electrons and all energy states in the conduction band are empty ... the valence and conduction band are filled with holes. All energy states in the valence and conduction band are filled with electrons.
For an intrinsic semiconductor at temperature $\text{T}=0 \; \text{K}$, which of the following statement is true?All energy states in the valence band are filled with ele...
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GATE ECE 2023 | Question: 8
A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R, L}$ and $\text{C}$ are $R=1 \; \Omega, L=1 \; \mu H$ and $C=1 \; \mu F$ ... $C=1 \; \mu F$ $R=0.001 \; \Omega, L=1 \; \mu H$ and $C=1 \; \mu F$
A series $\text{RLC}$ circuit has a quality factor $\text{Q}$ of $1000$ at a center frequency of $10^{6} \; \mathrm{rad} / \mathrm{s}$. The possible values of $\text{R,...
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GATE ECE 2023 | Question: 9
For a $\text{MOS}$ capacitor, $\text{V}_{\mathrm{fb}}$ and $\text{V}_{\mathrm{t}}$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width $\left(\mathrm{W}_{\mathrm{dep}}\right)$ for varying gate voltage $\left(\text{V}_g\right)$ is best represented by
For a $\text{MOS}$ capacitor, $\text{V}_{\mathrm{fb}}$ and $\text{V}_{\mathrm{t}}$ are the flat-band voltage and the threshold voltage, respectively. The variation of the...
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GATE ECE 2023 | Question: 10
Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_{g}$. Which of the following statement is true? ($c$ ... $v_{p} > c, v_{g} < c$ $v_{p} < c, v_{g} < c$
Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_...
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GATE ECE 2023 | Question: 11
In the circuit shown below, $\text{V}_1$ and $\text{V}_2$ are bias voltages. Based on input and output impedances, the circuit behaves as a voltage controlled voltage source. voltage controlled current source. current controlled voltage source. current controlled current source.
In the circuit shown below, $\text{V}_1$ and $\text{V}_2$ are bias voltages. Based on input and output impedances, the circuit behaves as avoltage controlled voltage sour...
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GATE ECE 2023 | Question: 12
A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when the closed loop gain is less than $1$ and the phase shift is less than $180^{\circ}$. the closed loop gain is greater than $1$ ... $180^{\circ}$. the closed loop gain is greater than $1$ and the phase shift is greater than $180^{\circ}$.
A cascade of common-source amplifiers in a unity gain feedback configuration oscillates whenthe closed loop gain is less than $1$ and the phase shift is less than $180^{\...
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GATE ECE 2023 | Question: 13
In the circuit shown below, $\mathrm{P}$ and $\mathrm{Q}$ are the inputs. The logical function realized by the circuit shown below is $\mathrm{Y}=\mathrm{PQ}$ $\mathrm{Y}=\mathrm{P}+\mathrm{Q}$ $\mathrm{Y}=\overline{\mathrm{PQ}}$ $\mathrm{Y}=\overline{\mathrm{P}+\mathrm{Q}}$
In the circuit shown below, $\mathrm{P}$ and $\mathrm{Q}$ are the inputs. The logical function realized by the circuit shown below is$\mathrm{Y}=\mathrm{PQ}$$\mathrm{Y}=\...
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May 20, 2023
Others
gateece-2023
multiplexers
digital-circuits
combinational-circuits
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GATE ECE 2023 | Question: 14
The synchronous sequential circuit shown below works at a clock frequency $1 \; \mathrm{GHz}$. The throughput, in $\text{Mbits/s,}$ and the latency, in $\text{ns,}$ respectively, are $1000,3$ $333.33,1$ $2000,3$ $333.33,3$
The synchronous sequential circuit shown below works at a clock frequency $1 \; \mathrm{GHz}$. The throughput, in $\text{Mbits/s,}$ and the latency, in $\text{ns,}$ respe...
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GATE ECE 2023 | Question: 15
The open loop transfer function of a unity negative feedback system is $G(s)=\frac{k}{s\left(1+s T_1\right)\left(1+s T_2\right)}$, where $k, T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in $\text{rad/s,}$ is $\frac{1}{\sqrt{T_1 T_2}}$ $\frac{1}{T_1 T_2}$ $\frac{1}{T_1 \sqrt{T_2}}$ $\frac{1}{T_2 \sqrt{T_1}}$
The open loop transfer function of a unity negative feedback system is $G(s)=\frac{k}{s\left(1+s T_1\right)\left(1+s T_2\right)}$, where $k, T_1$ and $T_2$ are positive c...
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May 20, 2023
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