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41
GATE ECE 2024 | Question: 31
The propagation delay of the $2 \times 1$ MUX shown in the circuit is $10 \mathrm{~ns}$. Consider the propagation delay of the inverter as $0 \mathrm{~ns}$. If $\text{S}$ is set to $1$ then the output $\text{Y}$ is $\_\_\_\_\_\_$. a square wave of frequency $100 \mathrm{MHz}$ a square wave of frequency $50 \mathrm{MHz}$ constant at $0$ constant at $1$
The propagation delay of the $2 \times 1$ MUX shown in the circuit is $10 \mathrm{~ns}$. Consider the propagation delay of the inverter as $0 \mathrm{~ns}$...
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42
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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43
GATE ECE 2024 | Question: 32
The sequence of states $\left(Q_{1} Q_{0}\right)$ of the given synchronous sequential circuit is - $\_\_\_\_\_\_\_$. $00 \rightarrow 10 \rightarrow 11 \rightarrow 00$ $11 \rightarrow 00 \rightarrow 10 \rightarrow 01 \rightarrow 00$ $01 \rightarrow 10 \rightarrow 11 \rightarrow 00 \rightarrow 01$ $00 \rightarrow 01 \rightarrow 10 \rightarrow 00$
The sequence of states $\left(Q_{1} Q_{0}\right)$ of the given synchronous sequential circuit is - $\_\_\_\_\_\_\_$.$00 \rightarrow 10 \rightarrow 11 \righ...
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44
GATE ECE 2024 | Question: 30
A $4$-bit priority encoder has inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$ in descending order of priority. The two-bit output $A B$ is generated as $00,01,10$, and 11 corresponding to inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$, respectively. The ... $D_{3} \overline{D_{2}}+\overline{D_{3}} D_{1}$ $\overline{D_{3}} \overline{D_{1}}$
A $4$-bit priority encoder has inputs $D_{3}, D_{2}, D_{1}$, and $D_{0}$ in descending order of priority. The two-bit output $A B$ is generated as $00,01,1...
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45
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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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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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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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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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...
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GATE ECE 2024 | Question: 38
A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI system with impulse response \[ h(t)=\left(\frac{\sin 2 \pi t}{\pi t}\right) \cos (38 \pi t-\pi / 2) \] ... $15 \sin (38 \pi t-\pi / 3)$ $15 \cos (38 \pi t-\pi / 6)$ $15 \cos (38 \pi t+\pi / 6)$
A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI s...
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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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GATE ECE 2024 | Question: 33
Let $z$ be a complex variable. If $f(z)=\frac{\sin (\pi z)}{z^{2}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint_{C} f(z) d z$ is $\_\_\_\_\_\_$. $\pi^{2} j$ $j \pi\left(\frac{1}{2}-\pi\right)$ $j \pi\left(\frac{1}{2}+\pi\right)$ $-\pi^{2} j$
Let $z$ be a complex variable. If $f(z)=\frac{\sin (\pi z)}{z^{2}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint_{C} f(z) d z$ ...
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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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GATE ECE 2024 | Question: 40
In the circuit below, the opamp is ideal. If the circuit is to show sustained oscillations, the respective values of $R_{1}$ and the corresponding frequency of oscillation are $29 R$ and $1 /(2 \pi \sqrt{6} R C)$ $2 R$ and $1 /(2 \pi R C)$ $29 R$ and $1 /(2 \pi R C)$ $2 R$ and $1 /(2 \pi \sqrt{6} R C)$
In the circuit below, the opamp is ideal.If the circuit is to show sustained oscillations, the respective values of $R_{1}$ and the corresponding frequency of oscillation...
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GATE ECE 2024 | Question: 29
A uniform plane wave with electric field $\vec{E}(x)=A_{y} \hat{a}_{y} e^{-j \frac{2 \pi x}{3}} \mathrm{~V} / \mathrm{m}$ is travelling in the air (relative permittivity, $\epsilon_{r}=1$ and relative permeability, $\mu_{r}=1$ ) in the $+x$ direction ( $A_{y}$ is a ... air (measured from $x=0$, in metres) is $\_\_\_\_\_\_\_$. $-\frac{3}{4}$ $-\frac{3}{2}$ $-6$ $-3$
A uniform plane wave with electric field $\vec{E}(x)=A_{y} \hat{a}_{y} e^{-j \frac{2 \pi x}{3}} \mathrm{~V} / \mathrm{m}$ is travelling in the air (relative permittivity,...
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GATE ECE 2024 | Question: 37
The information bit sequence $\{111010101\}$ is to be transmitted by encoding with Cyclic Redundancy Check $4$ (CRC-$4$) code, for which the generator polynomial is $C(x)=x^{4}+x+1$. The encoded sequence of bits is $\_\_\_\_\_\_\_$. $\{1110101011100\}$ $\{1110101011101\}$ $\{1110101011110\}$ $\{1110101010100\}$
The information bit sequence $\{111010101\}$ is to be transmitted by encoding with Cyclic Redundancy Check $4$ (CRC-$4$) code, for which the generator poly...
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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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GATE ECE 2024 | Question: 36
A full scale sinusoidal signal is applied to a $10$ -bit $\mathrm{ADC}$. The fundamental signal component in the $\mathrm{ADC}$ output has a normalized power of $1 \mathrm{~W}$, and the total noise and distortion normalized power is $10 \mu \mathrm{W}$. The effective ... off to the nearest integer) of the $\mathrm{ADC}$ is $\_\_\_\_\_\_\_$. $7$ $8$ $9$ $10$
A full scale sinusoidal signal is applied to a $10$ -bit $\mathrm{ADC}$. The fundamental signal component in the $\mathrm{ADC}$ output has a normalized pow...
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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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GATE ECE 2024 | Question: 35
A source transmits a symbol $s$, taken from $\{-4,0,4\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r=s+w$, where the noise $w$ is zero mean with variance 4 and is independent of $s$ ... $\frac{2}{3} Q(2)$ $\frac{4}{3} Q(1)$ $\frac{2}{3} Q(1)$ $\frac{4}{3} Q(2)$
A source transmits a symbol $s$, taken from $\{-4,0,4\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $...
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GATE ECE 2024 | Question: 39
The opamps in the circuit shown are ideal, but have saturation voltages of $\pm 10 \mathrm{~V}$. Assume that the initial inductor current is $0 \mathrm{~A}$. The input voltage $\left(\mathrm{V}_{\mathrm{i}}\right)$ is a triangular signal with peak ... delayed by $1 \mu$ s relative to $\mathrm{V}_{\mathrm{i}}$, and $\mathrm{V}_{02}$ is a trapezoidal waveform.
The opamps in the circuit shown are ideal, but have saturation voltages of $\pm 10 \mathrm{~V}$.Assume that the initial inductor current is $0 \mathrm{~A}$...
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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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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 ...
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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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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...
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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...
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46.4k
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May 20, 2023
Quantitative Aptitude
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quantitative-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}$$f(x)=x 2^{-x}$
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Quantitative Aptitude
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quantitative-aptitude
functions
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GATE ECE 2023 | GA Question: 10
A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ rectangular sheet is folded $5$ times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions $100 \mathrm{~cm} \times 1 \mathrm{~cm}$. The total number of creases visible when the sheet is unfolded is ___________. $32$ $5$ $31$ $63$
A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ rectangular sheet is folded $5$ times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually,...
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May 20, 2023
Quantitative Aptitude
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quantitative-aptitude
mensuration
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GATE ECE 2023 | Question: 28
Let $\boldsymbol{x}$ be an $n \times 1$ real column vector with length $l=\sqrt{\boldsymbol{x}^{T} \boldsymbol{x}}$ The trace of the matrix $P=\boldsymbol{x} \boldsymbol{x}^{T}$ is $l^{2}$ $\frac{l^{2}}{4}$ $l$ $\frac{l^{2}}{2}$
Let $\boldsymbol{x}$ be an $n \times 1$ real column vector with length $l=\sqrt{\boldsymbol{x}^{T} \boldsymbol{x}}$ The trace of the matrix $P=\boldsymbol{x} \boldsymbol{...
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46.4k
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GATE ECE 2023 | Question: 3
Let $w^4=16 j$. Which of the following cannot be a value of $w$ ? $2 e^{\frac{j 2 \pi}{8}}$ $2 e^{\frac{j \pi}{8}}$ $2 e^{\frac{j5 \pi}{8}}$ $2 e^{\frac{j9 \pi}{8}}$
Let $w^4=16 j$. Which of the following cannot be a value of $w$ ?$2 e^{\frac{j 2 \pi}{8}}$$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: 53
In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of $1 \; \mathrm{MHz}$, the frequency of signal $\mathrm{Q}_2$ in $\mathrm{kHz}$, is __________ (rounded off to the nearest integer).
In a given sequential circuit, initial states are $Q_1=1$ and $Q_2=0$. For a clock frequency of $1 \; \mathrm{MHz}$, the frequency of signal $\mathrm{Q}_2$ in $\mathrm{kH...
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GATE ECE 2023 | Question: 45
The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).
The value of the integral $\iint_R \text{xy dx dy}$ over the region $R$, given in the figure, __________ is (rounded off to the nearest integer).
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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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multiplexers
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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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Analytical Aptitude
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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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46.4k
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May 20, 2023
Verbal Aptitude
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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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May 20, 2023
Analytical Aptitude
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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$
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Spatial Aptitude
gateece-2023
spatial-aptitude
counting-figure
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1
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78
GATE ECE 2009 | Question: 58
Consider the CMOS circuit shown, where the gate voltage $V_{G}$ of the $\text{n-MOSFET}$ is increased from zero, while the gate voltage of the $\text{p-MOSFET}$ is kept constant at $3 \mathrm{~V}$ ... $4-\frac{\sqrt{3}}{2} \mathrm{~V}$ $4+\frac{\sqrt{3}}{2} \mathrm{~V}$
Consider the CMOS circuit shown, where the gate voltage $V_{G}$ of the $\text{n-MOSFET}$ is increased from zero, while the gate voltage of the $\text{p-MOSFET}$ is kept c...
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Others
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79
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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Verbal Aptitude
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2
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80
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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Verbal Aptitude
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