Recent questions tagged gatein-2024 / GO Instrumentation

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41

GATE IN 2024 | Question: 31
In the figure shown, both the opamps $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are ideal, except that the opamp $\mathrm{A}_{1}$ has an offset voltage $\left(\mathrm{V}_{\text {os }}\right)$ of $1 \mathrm{mV}$. For $\mathrm{V}_{\text {in }}=0 \mathrm{~V}$, the values of the output voltages $V_{\text {out1 }}$ ... $-1 \mathrm{mV}$ $1 \mathrm{mV}$ and $0 \mathrm{mV}$ $1 \mathrm{mV}$ and $-1 \mathrm{mV}$ $2 \mathrm{mV}$ and $0 \mathrm{mV}$

In the figure shown, both the opamps $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are ideal, except that the opamp $\mathrm{A}_{1}$ has an offset voltage $\left(\mathrm{V}_{\tex...

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GATE IN 2024 | Question: 32
In the figure shown, the positive edge triggered $\mathrm{D}$ flip-flops are initially reset to $Q=0$. The logic gates and the multiplexers have no propagation delay. After reset, a train of clock pulses (CLK) are applied. The logic-states of the inputs DIN, $\mathrm{S}$ and the clock pulses are also shown in the figure. Assuming no timing violations, the ... clock to the $5^{\text {th }}$ clock, $\mathrm{Y}_{3} \mathrm{Y}_{4} \mathrm{Y}_{5}$ is $001$ $010$ $000$ $011$

In the figure shown, the positive edge triggered $\mathrm{D}$ flip-flops are initially reset to $Q=0$. The logic gates and the multiplexers have no propagation delay. Aft...

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43

GATE IN 2024 | Question: 33
In the figure shown, $R=1 \mathrm{k} \Omega$ and $C=0.1 \mu \mathrm{F}$. For a dc gain of -10 , the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal place) is Assume the opamp is ideal. $159.1 \mathrm{~Hz}$ $1591.5 \mathrm{~Hz}$ $1750.7 \mathrm{~Hz}$ $175.0 \mathrm{~Hz}$

In the figure shown, $R=1 \mathrm{k} \Omega$ and $C=0.1 \mu \mathrm{F}$. For a dc gain of -10 , the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal place) ...

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GATE IN 2024 | Question: 34
Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ is $\frac{K-1}{K}$ $\frac{1}{2}$ $0$ $\frac{1-K}{K}$

Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ is$\f...

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GATE IN 2024 | Question: 35
The transfer function of a system is \[ G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}} \] Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} / \mathrm{s}$ ) from the following options such that the poles lie on the shaded region of the $s$-plane as shown in the figure. $\xi \geq \frac{1}{2}$ ... $\omega_{n} \geq 2$ $\xi \geq \frac{1}{2}$ and $\omega_{n} \geq \sqrt{3}$ $\xi \geq \frac{1}{4}$ and $\omega_{n} \geq \sqrt{3}$

The transfer function of a system is\[G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}}\]Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} / ...

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GATE IN 2024 | Question: 36
Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1)$. The value of the line integral \[ \oint_{C}\left(-e^{y} d x+e^{x} d y\right) \] is $e^{2}+2 e-3$ $e^{2}-2 e-3$ $e^{2}+e-1$ $e^{2}+e+1$

Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1)$...

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GATE IN 2024 | Question: 37
In the figure shown, assume - $\alpha$ is the phase angle between the load current and the load voltage - $\quad \beta$ is the phase angle by which pressure coil current lags the pressure coil voltage of the wattmeter - $\quad \gamma$ ... $\alpha=\gamma \pm \delta \pm \theta+\beta$ $\alpha=\gamma \pm \delta \pm \theta-\beta$

In the figure shown, assume- $\alpha$ is the phase angle between the load current and the load voltage- $\quad \beta$ is the phase angle by which pressure coil current la...

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GATE IN 2024 | Question: 38
Consider an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ volts towards an object whose vibration is modeled as $m(t)=0.5 \sin \left(2 \pi f_{2} t\right)$ volts. Neglecting the phase shift due to any other effect, the received signal at ... 25 and $\pm 250 \mathrm{~Hz}$ 0.5 and $\pm 500 \mathrm{~Hz}$ 1 and $\pm 1000 \mathrm{~Hz}$ 0.75 and $\pm 1000 \mathrm{~Hz}$

Consider an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ volt...

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49

GATE IN 2024 | Question: 39
The complex functions $f(z)=u(x, y)+i v(x, y)$ and $\overline{f(z)}=u(x, y)-i v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the following. $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}=0$ $\frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x} \neq 0$ $\frac{d f(z)}{d z}=0$ $\frac{d f(z)}{d z} \neq 0$

The complex functions $f(z)=u(x, y)+i v(x, y)$ and $\overline{f(z)}=u(x, y)-i v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the followin...

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GATE IN 2024 | Question: 40
The readings recorded from a 20 -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04 x+10.32$. The regression coefficient of determination, $R^{2}=$ (rounded off to three decimal places). \begin{tabular}{|c|c|c|c|c|c|} \hline$x$ & 1 & 2 & 3 & 4 & 5 \\ \hline$y$ (psig) & 10.3 & 10.5 & 10.4 & 10.5 & 10.5 \\ \hline \end{tabular}

The readings recorded from a 20 -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04 x+10.32$. The regression coefficient of ...

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51

GATE IN 2024 | Question: 41
In the figure shown, $\mathrm{R}=4.5 \mathrm{k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is $\mathrm{k} \Omega$ (rounded off to nearest integer).

In the figure shown, $\mathrm{R}=4.5 \mathrm{k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance bet...

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52

GATE IN 2024 | Question: 42
Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal, the frequency of the output voltage $\mathrm{V}_{0}$ is $\mathrm{kHz}$ (rounded off to two decimal places).

Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal...

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53

GATE IN 2024 | Question: 43
The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular convolution of $x[n]$ and $y[n]$, the value of $z[0]$ is (rounded off to nearest integer). Note: The DFT of a $N$-point sequence $x[n]$ is defined as \[ X[k]=\sum_{n=0}^{N-1} x[n] e^{\frac{-j 2 \pi n k}{N}} \]

The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular con...

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54

GATE IN 2024 | Question: 44
Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\Omega$ (rounded off to nearest integer).

Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\Omega$ (rounded off to nearest integer).

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GATE IN 2024 | Question: 45
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value of $\alpha$ is (rounded off to nearest integer). Note: The poles are marked with $x$ in the figure.

Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value ...

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56

GATE IN 2024 | Question: 46
A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{pF}$ and $\mathrm{R}_{\text {wire }}=10 \Omega$ is used to connect the inductive sensors as shown in the figure. The RMS value of $V_{\text {out }}$ is $\mathrm{V}$ (rounded off to two decimal places). Note: Assume all components are ideal, and sensors are not magnetically coupled.

A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{pF}$ and $\mathrm{R}_{\text {wire }}=10 \Omega$ is used to connect the inductive sensors as shown in the fig...

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57

GATE IN 2024 | Question: 47
In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in Kelvin, $\alpha=1.16 \times 10^{4} \mathrm{~K} / \mathrm{V}$, and $I_{S}=10^{-15} \mathrm{~A}$ is the saturation ... independent. The change in the output voltage $\left(\mathrm{V}_{\text {out }}\right.$ ) per Kelvin change in temperature is $\mathrm{mV}$ (rounded off to one decimal place).

In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in ...

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58

GATE IN 2024 | Question: 48
An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 \mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $500 \mathrm{MHz}$, and it samples the data at the Nyquist rate. The parallel data output is converted to a serial bit stream using a parallel-to-serial converter. The data rate at the output of the parallel-to-serial converter is Gbps (rounded off to nearest integer).

An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 \mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $50...

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59

GATE IN 2024 | Question: 49
In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\mathrm{V}$ (rounded off to one decimal place).

In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\mathrm{V}$ (rounded of...

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60

GATE IN 2024 | Question: 50
In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the permanent magnet moving coil (PMMC) type voltmeter is $1 \mathrm{~Hz}$ ... $\mathrm{V}$ (rounded off to nearest integer). Note: Assume all components are ideal.

In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the p...

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61

GATE IN 2024 | Question: 51
A $50 \mathrm{kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer at $75 \%$ of the full load and 0.8 power factor is $\%$ (rounded off to one decimal place).

A $50 \mathrm{kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer...

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GATE IN 2024 | Question: 52
A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting the stator impedance, the slip at the maximum torque is $\%$ (rounded off to two decimal places).

A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting...

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GATE IN 2024 | Question: 53
Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{mH}$. When connected in series-opposing configuration, the coils have a total inductance of $300 \mathrm{mH}$. If the self-inductance of both the coils are equal, then the coupling coefficient is (rounded off to two decimal places).

Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{mH}$. When connected in series-opposing configurati...

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64

GATE IN 2024 | Question: 54
The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is \[ y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t^{3}\right) e^{-t} \] Given $y(0)=3, y^{\prime}(0)=-3$ and $y^{\prime \prime}(0)=-47$, the value of $\left(c_{0}+c_{1}+c_{2}+c_{3}\right)$ is (rounded off ... $c_{0}, c_{1}, c_{2}, c_{3}$ are constants.

The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is\[y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...

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GATE IN 2024 | Question: 55
A random variable $X$ has a probability density function \[ f_{X}(x)=\left\{\begin{array}{cc} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{array}\right. \] The probability of $X>2$ is (rounded off to three decimal places).

A random variable $X$ has a probability density function\[f_{X}(x)=\left\{\begin{array}{cc}e^{-x}, & x \geq 0 \\0, & \text { otherwise }\end{array}\right.\]The probabilit...

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