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385
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GATE ECE 2025 | Question: 55
Two resistors are connected in a circuit loop of area $5 \mathrm{~m}^{2}$, as shown in the figure below. The circuit loop is placed on the $x-y$ plane.When a time-varying...
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343
343 views
GATE ECE 2025 | Question: 54
A $50 \Omega$ lossless transmission line is terminated with a load $\mathrm{Z}_{\mathrm{L}}$ of $(50-\mathrm{j} 75) \Omega$.If the average incident power on the line is $...
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585
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GATE ECE 2025 | Question: 53
An ideal p-n junction germanium diode has a reverse saturation current of $10 \mu \mathrm{~A}$ at $300 \: \mathrm{ K}$.The voltage (in Volts, rounded off to two decimal p...
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547
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GATE ECE 2025 | Question: 52
In the circuit shown below, the $\mathrm{AND}$ gate has a propagation delay of $1 \: \mathrm{ ns}$. The edge-triggered flip-flops have a set-up time of $2 \: \mathrm{ ns}...
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GATE ECE 2025 | Question: 51
The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by $V_{I}=10 \sin 100 \pi t$, where time $t$ is in seconds.The time duration (in $\ma...
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433
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GATE ECE 2025 | Question: 50
$X$ and $Y$ are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by:$$ \begin{array}{l} P(X=0, ...
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GATE ECE 2025 | Question: 49
Consider the vectors $$ \boldsymbol{a}=\left[\begin{array}{l} 1 \\ 1 \end{array}\right], \quad \boldsymbol{b}=\left[\begin{array}{c} 0 \\ 3 \sqrt{2} \end{array}\right] ...
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GATE ECE 2025 | Question: 48
Two fair dice (with faces labeled $1,2,3,4,5$, and $6$) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained.The expectation of $X$ is ________...
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GATE ECE 2025 | Question: 47
All the diodes in the circuit given below are ideal.Which of the following plots is/are correct when $V_{I}$ (in Volts) is swept from $-M$ to $M$?
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GATE ECE 2025 | Question: 46
Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).
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GATE ECE 2025 | Question: 45
Let $f(t)$ be a periodic signal with fundamental period $T_{0}>0$. Consider the signal $y(t)=f(\alpha t)$, where $\alpha>1$.The Fourier series expansions of $f(t)$ and $y...
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GATE ECE 2025 | Question: 44
The random variable $X$ takes values in $\{-1,0,1\}$ with probabilities $P(X=-1)=P(X=1)=\alpha$ and $P(X=0)=1-2 \alpha$, where $0<\alpha<1 / 2$.Let $g(\alpha)$ denote the...
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572
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GATE ECE 2025 | Question: 43
Consider a system where $x_{1}(t), x_{2}(t)$, and $x_{3}(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the sys...
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GATE ECE 2025 | Question: 42
Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle $C$ in the complex plane is/are TRUE?$\oint_{C} e^{z} \: d ...
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746 views
GATE ECE 2025 | Question: 41
Consider a non-negative function $f(x)$ which is continuous and bounded over the interval $[2,8]$. Let $M$ and $m$ denote, respectively, the maximum and the minimum value...
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GATE ECE 2025 | Question: 38
The electron mobility $\mu_{\mathrm{n}}$ in a non-degenerate germanium semiconductor at $300 \: \mathrm{K}$ is $0.38 \mathrm{~m}^{2} / \mathrm{Vs}$.The electron diffusivi...
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511
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GATE ECE 2025 | Question: 37
In the circuit shown, the identical transistors $\text{Q1}$ and $\text{Q2}$ are biased in the active region with $\beta=120$. The Zener diode is in the breakdown region w...
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GATE ECE 2025 | Question: 36
The intrinsic carrier concentration of a semiconductor is $2.5 \times 10^{16} / \mathrm{m}^{3}$ at $300 \: \mathrm{K}$.If the electron and hole mobilities are $0.15 \math...
1 1 answer
1.6k
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GATE ECE 2025 | Question: 35
A positive-edge-triggered sequential circuit is shown below. There are no timing violations in the circuit. Input $P 0$ is set to logic '$0$ ' and $P 1$ is set to logic '...
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GATE ECE 2025 | Question: 34
A $10$-bit analog-to-digital converter (ADC) has a sampling frequency of $1\: \mathrm{MHz}$ and a full scale voltage of $3.3 \: \mathrm{V}$.For an input sinusoidal signal...
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GATE ECE 2025 | Question: 33
The identical MOSFETs $M_{1}$ and $M_{2}$ in the circuit given below are ideal and biased in the saturation region. $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ have a transcond...
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GATE ECE 2025 | Question: 32
Consider a real-valued random process$$f(t)=\sum_{n=1}^{N} a_{n} \: p(t-n T),$$where $T>0$ and $N$ is a positive integer. Here, $p(t)=1$ for $t \in[0,0.5 T]$ and $0$ othe...
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GATE ECE 2025 | Question: 31
A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$. The receiver obtains $Y=S+N$, where $N$ is a zero-mean Gaussian random vari...
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685 views
GATE ECE 2025 | Question: 30
The $Z$-parameter matrix of a two port network relates the port voltages and port currents as follows:$$ \left[\begin{array}{l} V_{1} \\ V_{2} \end{array}\right]=Z\left[\...
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GATE ECE 2025 | Question: 29
In the circuit below, $M_{1}$ is an ideal AC voltmeter and $M_{2}$ is an ideal AC ammeter. The source voltage (in Volts) is $v_{s}(t)=100 \cos (200 t)$.What should be the...
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GATE ECE 2025 | Question: 28
Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $\left[-\omega_{c}, \omega_{c}\right]$, where $\ome...
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GATE ECE 2025 | Question: 27
Consider the polynomial $p(s)=s^{5}+7 s^{4}+3 s^{3}-33 s^{2}+2 s-40$. Let $(L, I, R)$ be defined as follows.$L$ is the number of roots of $p(s)$ with negative real parts....
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GATE ECE 2025 | Question: 26
Let $G(s)=\frac{1}{10 s^{2}}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below.Co...
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747 views
GATE ECE 2025 | Question: 25
A $4$-bit weighted-resistor DAC with inputs $b_{3}, b_{2}, b_{1}$, and $b_{0}$ (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when...
1 1 answer
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GATE ECE 2025 | Question: 24
All the components in the bandpass filter given below are ideal. The lower $-3$ dB frequency of the filter is $1$ MHz.The upper $-3$ dB frequency (in MHz , rounded off to...