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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 $3 \mathrm{~V}$ ... $4-\frac{\sqrt{3}}{2} \mathrm{~V}$ $4+\frac{\sqrt{3}}{2} \mathrm{~V}$
Vidhya16
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Mar 1
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2
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 $\_\_\_\_\_\_$. $0.15 \pi$ $0.225 \pi$ $0.3 \pi$ $0.45 \pi$
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Feb 19
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GATE ECE 2024 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [ charm $\rightarrow$ enamor $\rightarrow$ bewitch] is analogous to [bored $\rightarrow \_\_\_\_\_\_ \longrightarrow$ weary] Which one of the given options is appropriate to fill the blank? jaded baffled dead worsted
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Feb 17
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4
GATE ECE 2024 | GA Question: 2
$\text{P, Q, R, S}$, and $\text{T}$ have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room. If $\text{S}$ and $\text{Q}$ are single children ... and $\mathrm{T}$ $\mathrm{P}$ and $\mathrm{S}$ $\mathrm{T}$ and $\mathrm{Q}$ $\mathrm{T}$ and $\mathrm{R}$
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Feb 17
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5
GATE ECE 2024 | GA Question: 3
Five years ago, the ratio of Aman's age to his father's age was $1: 4$, and five years from now, the ratio will be $2:5$. What was his father's age when Aman was born? $28$ years $30$ years $35$ years $32$ years
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Feb 17
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Arjun
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376
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6
GATE ECE 2024 | GA Question: 4
For a real number $x>1$, \[ \frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1 \] The value of $x$ is $4$ $12$ $24$ $36$
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Feb 17
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7
GATE ECE 2024 | GA Question: 5
The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is $13$ $17$ $3$ $11$
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Feb 17
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Arjun
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8
GATE ECE 2024 | GA Question: 6
Sequence the following sentences $(\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S})$ in a coherent passage: $\text{P}$: Shifu's student exclaimed, "Why do you run since the bull is an illusion?" $\text{Q}$: Shifu said, "Surely my running ... a bull gave him chase, Shifu began running for his life. $\text{SPRQ}$ $\text{SRPQ}$ $\text{RSPQ}$ $\text{RPQS}$
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Feb 17
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Arjun
6.5k
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438
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9
GATE ECE 2024 | GA Question: 7
Four identical cylindrical chalk-sticks, each of radius $r=0.5 \mathrm{~cm}$ and length $l=10 \mathrm{~cm}$, are bound tightly together using a duct tape as shown in the following figure. The width of the duct tape is equal to the length of the chalk-stick. The area ... to wrap the bundle of chalk-sticks once, is $20(4+\pi)$ $20(8+\pi)$ $10(8+\pi)$ $10(4+\pi)$
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Feb 17
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Arjun
6.5k
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420
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gateece-2024
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10
GATE ECE 2024 | GA Question: 8
The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index $\text{(BMI)}$ in $2003$ and $2023$. Based on the data provided, which one of the following options is INCORRECT? ... normal category has decreased in $20$ years. The percentage of population falling into normal category has decreased in $20$ years.
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Feb 17
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Arjun
6.5k
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502
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11
GATE ECE 2024 | GA Question: 9
Examples of mirror and water reflections are shown in the figures below: An object appears as the following image after first reflecting in a mirror and then reflecting on water. The original object is
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Feb 17
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Arjun
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400
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gateece-2024
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12
GATE ECE 2024 | GA Question: 10
Two identical sheets $\text{A}$ and $\text{B}$, of dimensions $24 \mathrm{~cm} \times 16 \mathrm{~cm}$, can be folded into half using two distinct operations, $\text{FO1}$ or $\text{FO2}$. In $\text{FO1}$, the axis of folding remains parallel to the initial ... of the perimeters of the final shapes of $\text{A}$ and $\text{B}$ is $14:11$ $11: 14$ $18:11$ $11: 18$
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Feb 17
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386
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13
GATE ECE 2024 | Question: 1
The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ ...
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Feb 17
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14
GATE ECE 2024 | Question: 2
In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$ $12 \mathrm{~dB} /$ octave $6 \mathrm{~dB} /$ octave $20 \mathrm{~dB} /$ octave $10 \mathrm{~dB} /$ octave
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Feb 17
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admin
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15
GATE ECE 2024 | Question: 3
In the feedback control system shown in the figure below $G(s)=\frac{6}{s(s+1)(s+2)}$. $\text{R(s), Y(s)}$, and $\text{E(s)}$ are the Laplace transforms of $r(t), y(t)$, and $e(t)$, respectively. If the input $r(t)$ is a unit step function, ... $\lim _{t \rightarrow \infty} e(t)=\frac{1}{4}$ $\lim _{t \rightarrow \infty} e(t)$ does not exist, $e(t)$ is oscillatory
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Feb 17
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16
GATE ECE 2024 | Question: 4
A digital communication system transmits through a noiseless bandlimited channel $[-W W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t)=\sum_{n} b[n] x(t-n T)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a ... $\sum_{m=-\infty}^{\infty} X(f+m T)=T$ $\sum_{m=-\infty}^{\infty} X(f+m T)=\frac{1}{T}$
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Feb 17
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340
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17
GATE ECE 2024 | Question: 5
Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances $z_{\text {inA }}, z_{i n B}, z_{i n C}$, and $z_{i n D}$ ... $z_{i n A}=+0.4 j \Omega, z_{i n B}=\infty, z_{i n C}=-0.4 j \Omega, z_{i n D}=0$
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Feb 17
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270
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18
GATE ECE 2024 | Question: 6
Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following statements is true for the vector fields $\overrightarrow{F_{1}}=A(\hat{i} y+\hat{j} x)$ ... Only $\vec{F}_{2}$ is an electrostatic field. Neither $\vec{F}_{1}$ nor $\vec{F}_{2}$ is an electrostatic field. .
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Feb 17
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19
GATE ECE 2024 | Question: 7
In the circuit below, assume that the long channel $\text{NMOS}$ transistor is biased in saturation. The small signal trans-conductance of the transistor is $g_{m}$ ...
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Feb 17
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admin
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gateece-2024
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20
GATE ECE 2024 | Question: 8
For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is $40$. All the transistors are biased in saturation. The current source $I_{S S}$ is ideal. Neglect body effect, channel length modulation and intrinsic device ... off to three decimal places) is $\_\_\_\_\_\_$. $0.976$ $1.000$ $1.025$ $0.488$
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Feb 17
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admin
46.4k
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222
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gateece-2024
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21
GATE ECE 2024 | Question: 9
For the Boolean function \[ F(A, B, C, D)=\sum m(0,2,5,7,8,10,12,13,14,15) \text {, } \] the essential prime implicants are $\_\_\_\_\_\_$. $B D, \bar{B} \bar{D}$ $B D, A B$ $A B, \bar{B} \bar{D}$ $B D, \bar{B} \bar{D}, A B$
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Feb 17
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22
GATE ECE 2024 | Question: 10
A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_{0}}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t=t_{k}$, the variance of the random variable $n\left(t_{k}\right)$ is $\_\_\_\_\_\_\_$. $\frac{N_{0}}{4 R C}$ $\frac{N_{0}}{2 R C}$ $\frac{N_{0}}{R C}$ $\frac{2 N_{0}}{R C}$
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Feb 17
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302
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23
GATE ECE 2024 | Question: 11
A causal and stable $\text{LTI}$ system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5 t)$ is applied to another causal and stable $\text{LTI}$ system with impulse response $h(0.5 t)$. The resulting output is $\_\_\_\_\_\_\_$. $2 y(0.5 t)$ $4 y(0.5 t)$ $0.25 y(2 t)$ $0.25 y(0.25 t)$
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Feb 17
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24
GATE ECE 2024 | Question: 12
For non-degenerately doped n-type silicon, which one of the following plots represents the temperature $(T)$ dependence of free electron concentration $(n)$ ?
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Feb 17
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25
GATE ECE 2024 | Question: 13
In the circuit shown, the $n: 1$ step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward biased condition. If the input voltage (in Volts) is $V_{s}(t)=10 \sin \omega t$ and the average value of load voltage $V_{L}(t)$ (in Volts) is $2.5 / \pi$, the value of $n$ is $\_\_\_\_\_\_\_$. $4$ $8$ $12$ $16$
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Feb 17
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26
GATE ECE 2024 | Question: 14
For a causal discrete-time LTI system with transfer function \[ H(z)=\frac{2 z^{2}+3}{\left(z+\frac{1}{3}\right)\left(z-\frac{1}{3}\right)} \] which of the following statements is/are true? The system is stable. The system is a minimum phase system. The initial value of the impulse response is $2$. The final value of the impulse response is $0$.
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Feb 17
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27
GATE ECE 2024 | Question: 15
Let $\rho(x, y, z, t)$ and $u(x, y, z, t)$ represent density and velocity, respectively, at a point $(x, y, z)$ and time $t$. Assume $\frac{\partial \rho}{\partial t}$ is continuous. Let $V$ be an arbitrary volume in space enclosed by the closed surface ... $\int_{V} \frac{\partial \rho}{\partial t} d v=\int_{V} \nabla \cdot(\rho u) d v$
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28
GATE ECE 2024 | Question: 16
The free electron concentration profile $n(x)$ in a doped semiconductor at equilibrium is shown in the figure, where the points $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ mark three different positions. Which of the following statements is/are true? For $x$ ... $\mathrm{B}$ and $\mathrm{A}$, the electric field is directed from $\mathrm{A}$ to $\mathrm{B}$.
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Feb 17
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29
GATE ECE 2024 | Question: 17
A machine has a $32$-bit architecture with $1$-word long instructions. It has $24$ registers and supports an instruction set of size $40$. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register ... value. Assuming that the immediate operand is an unsigned integer, its maximum value is $\_\_\_\_\_\_$.
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30
GATE ECE 2024 | Question: 18
An amplitude modulator has output (in Volts) \[ s(t)=A \cos (400 \pi t)+B \cos (360 \pi t)+B \cos (440 \pi t) . \] The carrier power normalized to $1 \Omega$ resistance is $50$ Watts. The ratio of the total sideband power to the total power is $1 / 9$. The value of $\text{B}$ (in Volts, rounded off to two decimal places) is $\_\_\_\_\_\_\_$.
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31
GATE ECE 2024 | Question: 19
In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.
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32
GATE ECE 2024 | Question: 20
Let $\mathbb{R}$ and $\mathbb{R}^{3}$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors \[ \left\{\left[\begin{array}{lll} 2 & -3 & \alpha \end{array}\right], \quad\left ... ; 7 \end{array}\right]\right\} \] does not form a basis of $\mathbb{R}^{3}$ is $\_\_\_\_\_\_\_$.
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33
GATE ECE 2024 | Question: 21
In the given circuit, the current $I_{x}$ (in $m A$ ) is $\_\_\_\_\_\_\_\_$.
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34
GATE ECE 2024 | Question: 22
In the circuit given below, the switch $\text{S}$ was kept open for a sufficiently long time and is closed at time $t=0$. The time constant (in seconds) of the circuit for $t>0$ is $\_\_\_\_\_\_$.
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35
GATE ECE 2024 | Question: 23
Suppose $\text{X}$ and $\text{Y}$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$. The probability that $\text{X} \geq \text{Y}$ is $\_\_\_\_\_\_$.
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36
GATE ECE 2024 | Question: 24
A source transmits symbols from an alphabet of size $16$. The value of maximum achievable entropy (in bits) is $\_\_\_\_\_\_$.
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37
GATE ECE 2024 | Question: 25
As shown in the circuit, the initial voltage across the capacitor is $10 \mathrm{~V}$, with the switch being open. The switch is then closed at $t=0$. The total energy dissipated in the ideal Zener diode $\left(V_{Z}=5 \mathrm{~V}\right)$ after the switch is closed (in $\mathrm{mJ}$, rounded off to three decimal places) is $\_\_\_\_\_\_$.
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38
GATE ECE 2024 | Question: 26
Consider the Earth to be a perfect sphere of radius $\text{R}$. Then the surface area of the region, enclosed by the $60^{\circ} \mathrm{N}$ latitude circle, that contains the north pole in its interior is $\_\_\_\_\_\_$. $(2-\sqrt{3}) \pi R^{2}$ $\frac{(\sqrt{2}-1) \pi R^{2}}{2}$ $\frac{2 \pi R^{2}}{3}$ $\frac{(2+\sqrt{3}) \pi R^{2}}{8 \sqrt{2}}$
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39
GATE ECE 2024 | Question: 27
Consider a unity negative feedback control system with forward path gain $G(s)=\frac{K}{(s+1)(s+2)(s+3)}$ as shown. The impulse response of the closed-loop system decays faster than $e^{-t}$ if $\_\_\_\_\_\_$. $1 \leq K \leq 5$ $7 \leq K \leq 21$ $-4 \leq K \leq-1$ $-24 \leq K \leq-6$
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40
GATE ECE 2024 | Question: 28
A satellite attitude control system, as shown below, has a plant with transfer function $G(s)=\frac{1}{s^{2}}$ cascaded with a compensator $C(s)=\frac{K(s+\alpha)}{s+4}$, where $K$ and $\alpha$ are positive real constants. In order for the closed-loop system to have poles at $-1 \pm j \sqrt{3}$, the value of $\alpha$ must be $\_\_\_\_\_\_$. $0$ $1$ $2$ $3$
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