Recent questions tagged gateece-2024 / GO Electronics

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41

GATE ECE 2024 | Question: 24
A source transmits symbols from an alphabet of size $16$. The value of maximum achievable entropy (in bits) is $\_\_\_\_\_\_$.

A source transmits symbols from an alphabet of size $16$. The value of maximum achievable entropy (in bits) is $\_\_\_\_\_\_$.

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42

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 $\_\_\_\_\_\_$.

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 di...

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43

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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44

GATE ECE 2024 | Question: 34
Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is $\_\_\_\_\_\_$. $-4 X(4 f) e^{-j \pi f}$ $-4 X(4 f) e^{-j 4 \pi f}$ $-\frac{1}{4} X(f / 4) e^{-j \pi f}$ $-\frac{1}{4} X(f / 4) e^{-j 4 \pi f}$

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is $\_\_\_\_...

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45

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: 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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47

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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48

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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49

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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50

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 oscillatio...

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51

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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52

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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53

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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54

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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55

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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56

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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57

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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58

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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59

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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60

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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61

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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62

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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63

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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64

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: 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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