Recent questions tagged gateece-2022 / GO Electronics

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41

GATE ECE 2022 | Question: 31
For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________. $15 \; \text{V}$ $27 \; \text{V}$ $13 \; \text{V}$ $14 \; \text{V}$

For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________.$15 \...

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42

GATE ECE 2022 | Question: 32
A circuit with an ideal $\text{OPAMP}$ is shown. The Bode plot for the magnitude $\text{(in dB)}$ of the gain transfer function $(A_{V} (j \omega) = V_{\text{out}} (j \omega) / V_{\text{in}} (j \omega))$ of the circuuit is also provided (here, $\omega$ is the angular frequency ... $R = 3 \; \text{k} \Omega, C = 2 \; \mu \text{F}$

A circuit with an ideal $\text{OPAMP}$ is shown. The Bode plot for the magnitude $\text{(in dB)}$ of the gain transfer function $(A_{V} (j \omega) = V_{\text{out}} (j \om...

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43

GATE ECE 2022 | Question: 33
For the circuit shown, the clock frequency is $f_{0}$ and the duty cycle is $25 \%.$ For the signal at the $\text{Q}$ output of the Flip-Flop, _______________. frequency is $f_{0}/4$ and duty cycle is $50 \%$ frequency is $f_{0}/4$ and duty cycle is $25 \%$ frequency is $f_{0}/2$ and duty cycle is $50 \%$ frequency is $f_{0}$ and duty cycle is $25 \%$

For the circuit shown, the clock frequency is $f_{0}$ and the duty cycle is $25 \%.$ For the signal at the $\text{Q}$ output of the Flip-Flop, _______________.frequency i...

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44

GATE ECE 2022 | Question: 34
Consider an even polynomial $p(s)$ given by $p(s) = s^{4} + 5s^{2} + 4 + K,$ where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all its roots on the imaginary axis is _____________. $ – 4 \leq K \leq \frac{9}{4}$ $ – 3 \leq K \leq \frac{9}{2}$ $ – 6 \leq K \leq \frac{5}{4}$ $ – 5 \leq K \leq 0$

Consider an even polynomial $p(s)$ given by$$p(s) = s^{4} + 5s^{2} + 4 + K,$$where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all it...

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45

GATE ECE 2022 | Question: 35
Consider the following series: $ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$ For which of the following combinations of $c, d$ values does this series converge? $ c= 1, d = – 1$ $ c= 2, d = 1$ $ c= 0.5, d = – 10$ $ c= 1, d = – 2$

Consider the following series:$$ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$$For which of the following combinations of $c, d$ values does this series converge?$ c= 1, d = �...

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46

GATE ECE 2022 | Question: 36
The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure. Based on the given information, which of the four systems is/are definitely $\text{NOT LTI}$ (linear and time-invariant)? $S_{1}$ $S_{2}$ $S_{3}$ $S_{4}$

The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure.Based on th...

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47

GATE ECE 2022 | Question: 37
Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices. Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium. Collector region is generally more heavily doped than Base region in a $\text{BJT}.$ ... under steady state condition. Mobility of electrons always increases with temperature in Silicon beyond $300 \; \text{K}.$

Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices.Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.Collector r...

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48

GATE ECE 2022 | Question: 38
A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the probability of transition from state $A$ to $B$). For this state diagram, select the statement(s) which is/are ... $p_{1} + p_{4} + p_{7} = 1$ $p_{2} + p_{5} + p_{7} = 1$

A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the...

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49

GATE ECE 2022 | Question: 39
Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation. The Boolean inputs $'0'$ and $'1'$ are also ... $\text{OR}$ logic cannot be implemented $\text{NOR}$ logic can be implemented $\text{AND}$ logic cannot be implemented

Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation...

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50

GATE ECE 2022 | Question: 40
Two linear time-invariant systems with transfer functions $G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$ have unit step responses $y_{1}(t)$ and $y_{2}(t),$ respectively. Which of the following ... and $y_{2}(t)$ have the same damped frequency of oscillation. $y_{1}(t)$ and $y_{2}(t)$ have the same $2\%$ settling time.

Two linear time-invariant systems with transfer functions$$G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$$have unit step resp...

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51

GATE ECE 2022 | Question: 41
Consider an $\text{FM}$ broadcast that employs the pre-emphasis filter with frequency response $H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}},$ where $\omega_{0} = 10^{4} \; \text{rad/sec}.$ For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate ... $R = 1 \; k \Omega, C = 2 \; \mu F$ $R = 2 \; k \Omega, C = 0.5 \; \mu F$

Consider an $\text{FM}$ broadcast that employs the pre-emphasis filter with frequency response$$H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}},$$where $\omega_{0} = 10^...

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52

GATE ECE 2022 | Question: 42
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light in air to be $3 \times 10^{8} \; \text{m/s}.$ The frequency/frequencies of $\text{TM}$ waves which can ... $8 \times 10^{14} \; \text{Hz}$ $1 \times 10^{13} \; \text{Hz}$

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light...

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53

GATE ECE 2022 | Question: 43
The value of the integral $ \iint_{D} 3(x^{2} + y^{2})dxdy,$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).

The value of the integral$$ \iint_{D} 3(x^{2} + y^{2})dxdy,$$where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest in...

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54

GATE ECE 2022 | Question: 44
A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance $R$ is connected across Port $2.$ As $R$ is varied, the measured voltage ... by the load shown in $\text{Fig.(c)},$ the current $I_{2}$ is ___________ $\text{mA}$ (rounded off to one decimal place).

A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance...

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55

GATE ECE 2022 | Question: 45
For a vector $\overline{x} = \left[ x [0], x[1], \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\overline{x}) = \left[ X [0], X[1], \dots, X[7] \right],$ ... $\overline{y} = DFT (DFT(\overline{x})),$ then the value of $y[0]$ is _____________ (rounded off to one decimal place).

For a vector $\overline{x} = \left[ x [0], x , \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\ov...

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56

GATE ECE 2022 | Question: 46
A $p-$type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at $x = \pm 2l_{n},$ where $l_{n} = 10 ^{-4} \; \text{cm}$ is the diffusion length of ... photo-generated electrons at $x = + 2l_{n}$ is ______________ $\text{mA/cm}^{2}$ (rounded off to two decimal places).

A $p-$type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at $x = \...

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57

GATE ECE 2022 | Question: 47
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{out}}}{\partial V_{\text{in}}}$ is ____________ (rounded off to two decimal places).

A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{ou...

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58

GATE ECE 2022 | Question: 48
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).

Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).

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59

GATE ECE 2022 | Question: 49
Consider the circuit shown with an ideal long channel $n \text{MOSFET}$ (enhancement-mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with $V_{GG}$ and $V_{DD}$ such that it acts as a linear amplifier ... $\dfrac{v_{A}}{v_{B}}$ is _____________ (rounded off to one decimal place).

Consider the circuit shown with an ideal long channel $n \text{MOSFET}$ (enhancement-mode, substrate is connected to the source). The transistor is appropriately biased i...

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60

GATE ECE 2022 | Question: 50
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and $d(t),$ ... $e (\infty),$ due to a unit step disturbance $d(t),$ is __________ (rounded off to two decimal places).

The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and...

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61

GATE ECE 2022 | Question: 51
The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked. The parameter $\alpha$ lies in the interval $[0.25, 1].$ The value of $\alpha$ for which the capacity of this channel is maximized, is ___________ (rounded off to two decimal places).

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as mark...

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62

GATE ECE 2022 | Question: 52
Consider communication over a memoryless binary symmetric channel using a $(7, 4)$ Hamming code. Each transmitted bit is received correctly with probability $(1 - \in),$ and flipped with probability $\in.$ For each codeword transmission, the ... the probability that a transmitted codeword is decoded correctly is ___________(rounded off to two decimal places).

Consider communication over a memoryless binary symmetric channel using a $(7, 4)$ Hamming code. Each transmitted bit is received correctly with probability $(1 – \in),...

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63

GATE ECE 2022 | Question: 53
Consider a channel over which either symbol $x_{A}$ or symbol $x_{B}$ is transmitted. Let the output of the channel $Y$ be the input to a maximum likelihood $\text{(ML)}$ detector at the receiver. The conditional probability density ... the standard unit step function. The probability of symbol error for this system is _____________ (rounded off to two decimal places).

Consider a channel over which either symbol $x_{A}$ or symbol $x_{B}$ is transmitted. Let the output of the channel $Y$ be the input to a maximum likelihood $\text{(ML)}$...

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64

GATE ECE 2022 | Question: 54
Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, $f(x),$ as shown in the figure. Consider a $1$ bit quantizer that maps positive samples to value $\alpha$ and others to ... error, then $(\alpha^{\ast} - \beta^{\ast}) = $____________ (rounded off to two decimal places).

Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, $f(x),$ as shown in the fi...

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GATE ECE 2022 | Question: 55
In an electrostatic field, the electric displacement density vector, $\overrightarrow{D},$ is given by $\overrightarrow{D} (x, y, z) = (x^{3} \overrightarrow{i} + y^{3} \overrightarrow{j} + xy^{2} \overrightarrow{k}) \; \text{C/m}^{2},$ where ... $R$ is _____________ $\text{C}$ (rounded off to two decimal places).

In an electrostatic field, the electric displacement density vector, $\overrightarrow{D},$ is given by$$\overrightarrow{D} (x, y, z) = (x^{3} \overrightarrow{i} + y^{3} \...

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