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1001

GATE Electrical 2015 Set 1 | Question: 39
The op-amp shown in the figure has a finite gain $A = 1000$ and an infinite input resistance. A step-voltage $V_{i} = 1 \: mV$ is applied at the input at time $t = 0$ as shown. Assuming that the operational amplifier is not saturated, the time constant (in millisecond) of the output voltage $V_{o}$ is $1001$ $101$ $11$ $1$

The op-amp shown in the figure has a finite gain $A = 1000$ and an infinite input resistance. A step-voltage $V_{i} = 1 \: mV$ is applied at the input at time $t = 0$ as ...

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1002

GATE Electrical 2015 Set 1 | Question: 41
Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below: ... $200 \: MW$ is _______.

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are give...

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1003

GATE Electrical 2015 Set 1 | Question: 33
The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of $50 \: \text{ Hz}$. It uses unipolar pulse width modulation with switching frequency of $50$ kHz and modulation index of $0.7$. ... the amplitude of the fundamental component in the output voltage $V_{\text{o}}$ (in Volt) under steady-state is ________.

The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of $50 \: \text{ Hz}$. It uses unipolar pulse width modulation with s...

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1004

GATE Electrical 2015 Set 1 | Question: 36
A parallel plate capacitor is partially filled with glass of dielectric constant $4.0$ as shown below. The dielectric strengths of air and glass are $30$ kV/cm and $300$ kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______.

A parallel plate capacitor is partially filled with glass of dielectric constant $4.0$ as shown below. The dielectric strengths of air and glass are $30$ kV/cm and $300$ ...

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1005

GATE Electrical 2015 Set 1 | Question: 37
The figure shows a digital circuit constructed using negative edge triggered $J-K$ flip flops. Assume a starting state of $Q_{2}Q_{1}Q_{0}=000$. This state $Q_{2}Q_{1}Q_{0}=000$ will repeat after _______ number of cycles of the clock $CLK$.

The figure shows a digital circuit constructed using negative edge triggered $J-K$ flip flops. Assume a starting state of $Q_{2}Q_{1}Q_{0}=000$. This state $Q_{2}Q_{1}Q_{...

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1006

GATE Electrical 2015 Set 1 | Question: 20
An inductor is connected in parallel with a capacitor as shown in the figure. As the frequency of current $i$ is increased, the impedance $(Z)$ of the network varies as

An inductor is connected in parallel with a capacitor as shown in the figure.As the frequency of current $i$ is increased, the impedance $(Z)$ of the network varies as

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1007

GATE Electrical 2015 Set 1 | Question: 21
A separately excited $DC$ generator has an armature resistance of $0.1 \Omega$ and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is $200 V$. When this generator is operated at half the rated speed, with ... capacitor is connected will the voltage across it reach $25 V$? $62.25$ $69.3$ $73.25$ $77.3$

A separately excited $DC$ generator has an armature resistance of $0.1 \Omega$ and negligible armature inductance. At rated field current and rated rotor speed, its open-...

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1008

GATE Electrical 2015 Set 1 | Question: 27
A solution of the ordinary differential equation $\dfrac{d^{2}y}{dt^{2}}+5\dfrac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\dfrac{1-3e}{e^{3}}$. The value of $\dfrac{dy}{dt}(0)$ is _______.

A solution of the ordinary differential equation $\dfrac{d^{2}y}{dt^{2}}+5\dfrac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= -\dfrac{1-3e}{e^{3}}$. The value of $\df...

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1009

GATE Electrical 2015 Set 1 | Question: 30
An unbalanced $DC$ Wheatstone bridge is shown in the figure. At what value of $P$ will the magnitude of $V_{0}$ be maximum? $\sqrt{(1+x)}$ $(1+x)$ $1/\sqrt{(1+x)}$ $\sqrt{(1-x)}$

An unbalanced $DC$ Wheatstone bridge is shown in the figure. At what value of $P$ will the magnitude of $V_{0}$ be maximum?$\sqrt{(1+x)}$$(1+x)$$1/\sqrt{(1+x)}$$\sqrt{(1-...

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1010

GATE Electrical 2015 Set 1 | Question: 19
For the given circuit, the Thevenin equivalent is to be determined. The Thevenin voltage, $V_{Th}$ (in Volt), seen from terminal $AB$ is __________.

For the given circuit, the Thevenin equivalent is to be determined. The Thevenin voltage, $V_{Th}$ (in Volt), seen from terminal $AB$ is __________.

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1011

GATE Electrical 2015 Set 1 | Question: 24
A Bode magnitude plot for the transfer function $G(s)$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant? $\dfrac{1000(s+10)}{s+1000} \\$ $\dfrac{10(s+10)}{s(s+1000)} \\$ $\dfrac{s+1000}{10s(s+10)} \\$ $\dfrac{s+1000}{10(s+10)}$

A Bode magnitude plot for the transfer function $G(s)$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?$\dfrac{1...

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1012

GATE Electrical 2015 Set 1 | Question: 22
The self inductance of the primary winding of a single phase, $50$ Hz, transformer is $800$ mH, and that of the secondary winding is $600$ mH. The mutual inductance between these two windings is $480$ mH. The secondary winding of this transformer is ... . In this condition, what is the effective inductance (in mH) seen by the source? $416$ $440$ $200$ $920$

The self inductance of the primary winding of a single phase, $50$ Hz, transformer is $800$ mH, and that of the secondary winding is $600$ mH. The mutual inductance betwe...

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1013

GATE Electrical 2015 Set 1 | Question: 28
The signum function is given by $sgn(x)= \begin{cases} \dfrac{x}{ \mid x \mid }; x \neq 0& \\ 0;x=0& \end{cases}$ The Fourier series expansion of $sgn (\cos (t) )$ has Only sine terms with all harmonics. Only cosine terms with all harmonics. Only sine terms with even numbered harmonics. Only cosine terms with odd numbered harmonics.

The signum function is given by $sgn(x)= \begin{cases} \dfrac{x}{ \mid x \mid }; x \neq 0& \\ 0;x=0& \end{cases}$ The Fourier series expansion of $sgn (\cos (t) )$ hasO...

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1014

GATE Electrical 2015 Set 1 | Question: 25
For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function $\dfrac{Y(s)}{X_{2}(s)}\bigg \vert _{X_{1}(s)=0}$ ? $\dfrac{G_{1}}{1+G_{2}(1+G_{1})} \\$ $\dfrac{G_{2}}{1+G_{1}(1+G_{2})} \\$ $\dfrac{G_{1}}{1+G_{1}G_{2}} \\$ $\dfrac{G_{2}}{1+G_{1}G_{2}}$

For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function $\dfrac{Y(s)}{X_{2}(s)}\bigg \vert _{X_{1}(s)=0}$ ...

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1015

GATE Electrical 2015 Set 1 | Question: 26
The maximum value of "a" such that the matrix $\begin{pmatrix} -3&0&-2 \\ 1&-1&0 \\ 0&a&-2 \end{pmatrix}$ has three linearly independent real eigenvectors is $\dfrac{2}{3\sqrt{3}} \\$ $\dfrac{1}{3\sqrt{3}} \\$ $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$ $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$

The maximum value of "a" such that the matrix $\begin{pmatrix} -3&0&-2 \\ 1&-1&0 \\ 0&a&-2 \end{pmatrix}$ has three linearly independent real eigenvectors is$\dfrac{2}{...

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1016

GATE Electrical 2015 Set 1 | Question: 29
Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is $5/11$ $1/2$ $7/13$ $6/11$

Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $...

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1017

GATE Electrical 2015 Set 1 | Question: 23
The primary mmf is least affected by the secondary terminal conditions in a Power transformer. Potential transformer. Current transformer. Distribution transformer.

The primary mmf is least affected by the secondary terminal conditions in aPower transformer.Potential transformer.Current transformer.Distribution transformer.

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1018

GATE Electrical 2015 Set 1 | Question: 12
A steady current $I$ is flowing in the $-x$ direction through each of two infinitely long wires at $y = \pm \dfrac{L}{2}$ as shown in the figure. The permeability of the medium is $\mu_{0}$. The $\overrightarrow{B}$-field at $(0,L,0)$ ... $+\dfrac{4\mu _{0}I}{3\Pi L} \hat{Z} \\$ $0 \\$ $-\dfrac{3\mu _{0}I}{4\Pi L} \hat{Z}$

A steady current $I$ is flowing in the $-x$ direction through each of two infinitely long wires at $y = \pm \dfrac{L}{2}$ as shown in the figure. The permeability of the ...

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1019

GATE Electrical 2015 Set 1 | Question: 18
The voltages developed across the $3 \Omega$ and $2 \Omega$ resistors shown in the figure are $6 V$ and $2 V$ respectively, with the polarity as marked. What is the power (in Watt) delivered by the $5 V$ voltage source? $5$ $7$ $10$ $14$

The voltages developed across the $3 \Omega$ and $2 \Omega$ resistors shown in the figure are $6 V$ and $2 V$ respectively, with the polarity as marked. What is the power...

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1020

GATE Electrical 2015 Set 1 | Question: 15
In the $4 \times 1$ multiplexer, the output $F$ is given by $F = A \oplus B$. Find the required input $'I_{3}, I_{2}, I_{1}, I_{0}'$. $1010$ $0110$ $1000$ $1110$

In the $4 \times 1$ multiplexer, the output $F$ is given by $F = A \oplus B$. Find the required input $'I_{3}, I_{2}, I_{1}, I_{0}'$.$1010$$0110$$1000$$1110$

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1021

GATE Electrical 2015 Set 1 | Question: 10
The impulse response $g(t)$ of a system, $G$, is as shown in Figure $(a)$. What is the maximum value attained by the impulse response of two cascaded blocks of $G$ as shown in Figure $(b)$? $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{4}{5} \\$ $1$

The impulse response $g(t)$ of a system, $G$, is as shown in Figure $(a)$. What is the maximum value attained by the impulse response of two cascaded blocks of $G$ as sho...

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1022

GATE Electrical 2015 Set 1 | Question: 16
Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of $750$ MW from System $1$ to System $2$ ... $V_{1} = −500 \text{ kV} , V_{2} = −485 \text{ kV} $ and $I = −1.5 \text{ kA}$

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of $750$ MW from System $1$ to System $2$, the voltage...

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1023

GATE Electrical 2015 Set 1 | Question: 13
Consider the circuit shown in the figure. In this circuit $R=1 k\Omega$, and $C=1 \mu F$. The input voltage is sinusoidal with a frequency of $50$ Hz, represented as a phasor with magnitude $V_{i}$ and phase angle $0$ radian as shown in the figure. The output ... to the phase angle of the input voltage? $0 \\$ $\pi \\$ $\dfrac{\pi}{2} \\$ $-\dfrac{\pi}{2}$

Consider the circuit shown in the figure. In this circuit $R=1 k\Omega$, and $C=1 \mu F$. The input voltage is sinusoidal with a frequency of $50$ Hz, represented as a ph...

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1024

GATE Electrical 2015 Set 1 | Question: 14
In the given circuit, the silicon transistor has $\beta = 75$ and a collector voltage $V_{C} = 9V$. Then the ratio of $R_{B}$ and $R_{C}$ is _________.

In the given circuit, the silicon transistor has $\beta = 75$ and a collector voltage $V_{C} = 9V$. Then the ratio of $R_{B}$ and $R_{C}$ is _________.

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1025

GATE Electrical 2015 Set 1 | Question: 7
Of the four characteristics given below, which are the major requirements for an instrumentation amplifier? P. High common mode rejection ratio Q. High input impedance R. High linearity S. High output impedance P, Q and R only P and R only P, Q and S only Q, R and S only

Of the four characteristics given below, which are the major requirements for an instrumentation amplifier?P. High common mode rejection ratioQ. High input impedanceR. Hi...

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1026

GATE Electrical 2015 Set 1 | Question: 8
In the following chopper, the duty ratio of switch $S$ is $0.4$. If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the charging current (in Ampere) of the $5 V$ battery, under steady-state, is _______.

In the following chopper, the duty ratio of switch $S$ is $0.4$. If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple fre...

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1027

GATE Electrical 2015 Set 1 | Question: 17
Base load power plants are P: wind farms. Q: run-of-river plants. R: nuclear power plants. S: diesel power plants. P, Q and S only P, R and S only P, Q and R only Q and R only

Base load power plants areP: wind farms.Q: run-of-river plants.R: nuclear power plants.S: diesel power plants.P, Q and S onlyP, R and S onlyP, Q and R onlyQ and R only

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1028

GATE Electrical 2015 Set 1 | Question: 9
A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{2T}Hz$ then in steady state, the output $y$ will lag $u$ (in degree) by __________ .

A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{...

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1029

GATE Electrical 2015 Set 1 | Question: 11
Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is $0.4\Omega$, and its inductance is negligible. The ... radian/second. The power absorbed (in Watt) by the loop from the magnetic field is _________.

Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The res...

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1030

GATE Electrical 2015 Set 1 | Question: 5
When the Wheatstone bridge shown in the figure is used to find the value of resistor $R_{X}$, the galvanometer $G$ indicates zero current when $R_{1}=50\Omega, R_{2}=65\Omega$ and $R_{3}=100\Omega$. If $R_{3}$ is known with $ \pm 5 \%$ tolerance on its nominal ... $R_{X}$ in Ohms? $[123.50, 136.50]$ $[125.89, 134.12]$ $[117.00, 143.00]$ $[120.25, 139.75]$

When the Wheatstone bridge shown in the figure is used to find the value of resistor $R_{X}$, the galvanometer $G$ indicates zero current when $R_{1}=50\Omega, R_{2}=65\O...

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1031

GATE Electrical 2015 Set 1 | Question: 2
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$

If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE?$f(a) . f(b)=0$$f(a) . f(b) < 0$$f(a) . ...

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1032

GATE Electrical 2015 Set 1 | Question: 3
If the sum of the diagonal elements of a $2 \times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is ________

If the sum of the diagonal elements of a $2 \times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is ________

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1033

GATE Electrical 2015 Set 1 | Question: 6
A $(0-50 A)$ moving coil ammeter has a voltage drop of $0.1 V$ across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to $(0 – 500 A)$ is _______.

A $(0-50 A)$ moving coil ammeter has a voltage drop of $0.1 V$ across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to exten...

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1034

GATE Electrical 2015 Set 1 | Question: 1
A random variable $X$ has probability density function $f(x)$ as given below: $ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$ If the expected value $E[x] = 2/3$, then $Pr[x < 0.5]$ is __________.

A random variable $X$ has probability density function $f(x)$ as given below:$ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$If...

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1035

GATE Electrical 2015 Set 1 | Question: 4
Consider a function $\overrightarrow{f}=\dfrac{1}{r^{2}} \hat{r}$ where $r$ is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The divergence of this function over a sphere of radius $R$, which includes the origin, is $0$ $2 \pi$ $4 \pi$ $R \pi$

Consider a function $\overrightarrow{f}=\dfrac{1}{r^{2}} \hat{r}$ where $r$ is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The ...

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1036

GATE Electrical 2015 Set 1 | GA Question: 3
Which one of the following combinations is incorrect? Acquiescence - Submission Wheedle - Roundabout Flippancy - Lightness Profligate - Extravagant

Which one of the following combinations is incorrect?Acquiescence - SubmissionWheedle - RoundaboutFlippancy - LightnessProfligate - Extravagant

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1037

GATE Electrical 2015 Set 1 | GA Question: 5
Given set $A=\left\{ 2, 3, 4, 5\right\}$ and set $B=\left\{ 11, 12, 13, 14, 15\right\}$, two numbers are randomly selected, one from each set. What is the probability that the sum of two numbers equal $16$? $0.20$ $0.25$ $0.30$ $0.33$

Given set $A=\left\{ 2, 3, 4, 5\right\}$ and set $B=\left\{ 11, 12, 13, 14, 15\right\}$, two numbers are randomly selected, one from each set. What is the probability tha...

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1038

GATE Electrical 2015 Set 1 | GA Question: 10
The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking. ... the average of the marks obtained by the class in the examination? $2.290$ $2.970$ $6.795$ $8.795$

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each quest...

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1039

GATE Electrical 2015 Set 1 | GA Question: 4
Based on the given statements, select the most appropriate option to solve the given question. If two floors in certain building are $9$ feet apart, how many steps are there in a set of stairs that extends from the first ... statement together are sufficient, but neither statement alone is sufficient. Statement $I$ and $II$ together are not sufficient.

Based on the given statements, select the most appropriate option to solve the given question.If two floors in certain building are $9$ feet apart, how many steps are the...

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1040

GATE Electrical 2015 Set 1 | GA Question: 2
Which of the following options is the closest in meaning to the sentence below? She enjoyed herself immensely at the party. She had a terrible time at the party. She had a horrible time at the party. She had a terrific time at the party. She had a terrifying time at the party.

Which of the following options is the closest in meaning to the sentence below?She enjoyed herself immensely at the party.She had a terrible time at the party.She had a h...

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