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1121
GATE Electrical 2016 Set 1 | Question: 27
Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $\mid \alpha \mid < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.
Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $\mid \alpha \mid < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Signals and Systems
gate2016-ee-1
fourier-transform
sampling-theorem
z-transform
numerical-answers
+
–
0
votes
0
answers
1122
GATE Electrical 2016 Set 1 | Question: 28
Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, -2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}-3A+4I$ would, respectively, be $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1} - x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1} - x_{2}$
Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, -2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Linear Algebra
gate2016-ee-1
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
1123
GATE Electrical 2016 Set 1 | Question: 29
Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE? Rank of $A^{T} A$ is less than $2$. Rank of $A^{T} A$ is equal to $2$. Rank of $A^{T} A$ is greater than $2$. Rank of $A^{T} A$ can be any number between $1$ and $3$.
Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE?Rank of $A^{T} A$ is less than $2$.Rank of $A^{T} A$ is equal to $2$.Ran...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Linear Algebra
gate2016-ee-1
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
1124
GATE Electrical 2016 Set 1 | Question: 30
Consider the following asymptotic Bode magnitude plot ($\omega$ is in rad/s). Which one of the following transfer functions is best represented by the above Bode magnitude plot? $\dfrac{2s}{(1+0.5s)(1+0.25s)^{2}} \\$ $\dfrac{4(1+0.5s)}{s(1+0.25s)} \\$ $\dfrac{2s}{(1+2s)(1+4s)} \\$ $\dfrac{4s}{(1+2s)(1+4s)^{2}}$
Consider the following asymptotic Bode magnitude plot ($\omega$ is in rad/s).Which one of the following transfer functions is best represented by the above Bode magnitude...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Control Systems
gate2016-ee-1
logarithmic-plot
gain-k
integral-and-derivative-factor
+
–
0
votes
0
answers
1125
GATE Electrical 2016 Set 1 | Question: 31
Consider the following state-space representation of a linear time-invariant system. $x(t)=\begin{pmatrix} 1&0 \\ 0&2 \end{pmatrix} x(t), y(t)= c^{T} x(t), c =\begin{pmatrix} 1& \\ 1& \end{pmatrix} \text {and } x(0)= \begin{pmatrix} 1& \\ 1& \end{pmatrix}$ The value of $y(t)$ for $t =\log_{e} 2$ is __________.
Consider the following state-space representation of a linear time-invariant system.$x(t)=\begin{pmatrix}1&0 \\0&2\end{pmatrix}x(t), y(t)= c^{T} x(t), c =\begin{pmatrix}1...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Control Systems
gate2016-ee-1
transformation
state-space-equations
correlation
numerical-answers
+
–
0
votes
0
answers
1126
GATE Electrical 2016 Set 1 | Question: 32
Loop transfer function of a feedback system is $G(s)H(s)=\dfrac{s+3}{s^{2}(s-3)}$. Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of $G(s) H (s)$ encircles $-1 + j0$ Once in clockwise direction Twice in clockwise direction Once in anticlockwise direction Twice in anticlockwise direction
Loop transfer function of a feedback system is $G(s)H(s)=\dfrac{s+3}{s^{2}(s-3)}$. Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of $G(s) H ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Control Systems
gate2016-ee-1
closed-loop-system
nyquist-stability
mapping
+
–
0
votes
0
answers
1127
GATE Electrical 2016 Set 1 | Question: 33
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-1
calculus
degree-of-polynomial
numerical-answers
+
–
0
votes
0
answers
1128
GATE Electrical 2016 Set 1 | Question: 6
The transfer function of a system is $\dfrac{Y(s)}{R(s)}=\dfrac{s}{s+2}$. The steady state output $y(t)$ is $A \cos (2t + \phi)$ for the input $\cos (2t)$. The values of $A$ and $\phi$ respectively are $\dfrac{1}{\sqrt{2}}, -45^\circ$ $\dfrac{1}{\sqrt{2}}, +45^\circ$ $\sqrt{2}, -45^\circ$ $\sqrt{2}, +45^\circ$
The transfer function of a system is $\dfrac{Y(s)}{R(s)}=\dfrac{s}{s+2}$. The steady state output $y(t)$ is $A \cos (2t + \phi)$ for the input $\cos (2t)$. The values of ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Control Systems
gate2016-ee-1
laplace-transform
convolution-integral
feed-back-transfer-function
+
–
0
votes
0
answers
1129
GATE Electrical 2016 Set 1 | Question: 7
The phase cross-over frequency of the transfer function $G(s)=\dfrac{100}{(s+1)^{3}}$ in rad/s is $\sqrt{3} \\$ $\dfrac{1}{\sqrt{3}} \\$ $3 \\$ $3\sqrt{3}$
The phase cross-over frequency of the transfer function $G(s)=\dfrac{100}{(s+1)^{3}}$ in rad/s is$\sqrt{3} \\$$\dfrac{1}{\sqrt{3}} \\$$3 \\$$3\sqrt{3}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Control Systems
gate2016-ee-1
mathematical-representation
cross-over-frequency
180-phase-shift
bode-stability-criteria
+
–
0
votes
0
answers
1130
GATE Electrical 2016 Set 1 | Question: 8
Consider a continuous-time system with input $x(t)$ and output $y(t)$ given by $y(t)=x(t) \cos (t)$. This system is Linear and time-invariant Non-linear and time-invariant Linear and time-varying Non-linear and time-varying
Consider a continuous-time system with input $x(t)$ and output $y(t)$ given by $y(t)=x(t) \cos (t)$.This system isLinear and time-invariantNon-linear and time-invariantLi...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Signals and Systems
gate2016-ee-1
sampling-theorem
scaling-properties
causal-system
+
–
0
votes
0
answers
1131
GATE Electrical 2016 Set 1 | Question: 9
The value of $\int_{-\infty}^{+\infty} e^{-t} \delta (2t-2){d}t$, where $\delta (t)$ is the Dirac delta function, is $\dfrac{1}{2e} \\$ $\dfrac{2}{e} \\$ $\dfrac{1}{e^{2}} \\$ $\dfrac{1}{2e^{2}}$
The value of $\int_{-\infty}^{+\infty} e^{-t} \delta (2t-2){d}t$, where $\delta (t)$ is the Dirac delta function, is$\dfrac{1}{2e} \\$$\dfrac{2}{e} \\$$\dfrac{1}{e^{2}} \...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-1
calculus
definite-integral
+
–
0
votes
0
answers
1132
GATE Electrical 2016 Set 1 | Question: 10
A temperature in the range of $−40 ^\circ C$ to $55^\circ C$ is to be measured with a resolution of $0.1^\circ C$. The minimum number of $ADC$ bits required to get a matching dynamic range of the temperature sensor is $8$ $10$ $12$ $14$
A temperature in the range of $−40 ^\circ C$ to $55^\circ C$ is to be measured with a resolution of $0.1^\circ C$. The minimum number of $ADC$ bits required to get a ma...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
new
gate2016-ee-1
analog-to-digital-converter
sampling
micro-controller
+
–
2
votes
0
answers
1133
GATE Electrical 2016 Set 1 | Question: 11
Consider the following circuit which uses a $2$-to-$1$ multiplexer as shown in the figure below. The Boolean expression for output $F$ in terms of $A$ and $B$ is $A\oplus B$ $\overline{A+B}$ $A+B$ $\overline{A \oplus B}$
Consider the following circuit which uses a $2$-to-$1$ multiplexer as shown in the figure below. The Boolean expression for output $F$ in terms of $A$ and $B$ is$A\oplus ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Analog and Digital Electronics
gate2016-ee-1
analog-and-digital-electronics
combinational-circuits
multiplexer
+
–
0
votes
0
answers
1134
GATE Electrical 2016 Set 1 | Question: 12
A transistor circuit is given below. The Zener diode breakdown voltage is $5.3$ V as shown. Take base to emitter voltage drop to be $0.6$ V. The value of the current gain $\beta$ is _________.
A transistor circuit is given below. The Zener diode breakdown voltage is $5.3$ V as shown. Take base to emitter voltage drop to be $0.6$ V. The value of the current gain...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electric Circuits
gate2016-ee-1
semi-conductor-devices
reverse-saturation-mode
voltage-divider
numerical-answers
+
–
0
votes
0
answers
1135
GATE Electrical 2016 Set 1 | Question: 13
In cylindrical coordinate system, the potential produced by a uniform ring charge is given by $\phi = f(r, z)$ where $f$ is a continuous function of $r$ and $z$. Let $\overrightarrow{E}$ be the resulting electric field. Then the magnitude of $\nabla \times \overrightarrow{E}$ Increases with $r$ Is $0$. Is $3$. Decreases with $z$.
In cylindrical coordinate system, the potential produced by a uniform ring charge is given by $\phi = f(r, z)$ where $f$ is a continuous function of $r$ and $z$. Let $\ov...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electromagnetic Fields
gate2016-ee-1
electromagnetic-theory
magneto-motive-force
amperes-law
+
–
0
votes
0
answers
1136
GATE Electrical 2016 Set 1 | Question: 14
A soft-iron toroid is concentric with a long straight conductor carrying a direct current $I$. If the relative permeability $\mu_{r}$ of soft-iron is $100$, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is ________.
A soft-iron toroid is concentric with a long straight conductor carrying a direct current $I$. If the relative permeability $\mu_{r}$ of soft-iron is $100$, the ratio of ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electromagnetic Fields
gate2016-ee-1
current-carrying-conductor
electromagnetism
faradays-law
numerical-answers
+
–
0
votes
0
answers
1137
GATE Electrical 2016 Set 1 | Question: 15
$R_{A}$ and $R_{B}$ are the input resistances of circuits as shown below. The circuits extend infinitely in the direction shown. Which one of the following statements is TRUE? $R_{A}=R_{B}$ $R_{A}=R_{B}=0$ $R_{A}< R_{B}$ $R_{B}= R_{A} /(1+R_{A})$
$R_{A}$ and $R_{B}$ are the input resistances of circuits as shown below. The circuits extend infinitely in the direction shown. Which one of the following statements is ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electric Circuits
gate2016-ee-1
circuit-reduction
series-combination
parallel-combination
+
–
0
votes
0
answers
1138
GATE Electrical 2016 Set 1 | Question: 16
In a constant $V/f$ induction motor drive, the slip at the maximum torque Is directly proportional to the synchronous speed. Remains constant with respect to the synchronous speed. Has an inverse relation with the synchronous speed. Has no relation with the synchronous speed.
In a constant $V/f$ induction motor drive, the slip at the maximum torqueIs directly proportional to the synchronous speed.Remains constant with respect to the synchronou...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electrical Machines
gate2016-ee-1
slip-speed
synchronous-speed
+
–
0
votes
0
answers
1139
GATE Electrical 2016 Set 1 | Question: 17
In the portion of a circuit shown, if the heat generated in $5 \Omega$ resistance is $10$ calories per second, then heat generated by the $4 \Omega$ resistance, in calories per second, is ________.
In the portion of a circuit shown, if the heat generated in $5 \Omega$ resistance is $10$ calories per second, then heat generated by the $4 \Omega$ resistance, in calori...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electric Circuits
gate2016-ee-1
parallel-combination
series-combination
current-divider-circuit
numerical-answers
+
–
0
votes
0
answers
1140
GATE Electrical 2016 Set 1 | Question: 18
In the given circuit, the current supplied by the battery, in ampere, is ________.
In the given circuit, the current supplied by the battery, in ampere, is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Electric Circuits
gate2016-ee-1
voltage-divider
dependent-current-source
superposition
numerical-answers
+
–
0
votes
0
answers
1141
GATE Electrical 2016 Set 1 | Question: 19
In a $100$ bus power system, there are $10$ generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the $PV$ buses are converted to $PQ$ type. In this iteration, The ... decreases by two. The number of unknown voltage angles remains unchanged and the number of unknown voltage magnitudes decreases by two.
In a $100$ bus power system, there are $10$ generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the $PV$ buses are ...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Power Systems
gate2016-ee-1
power-system-operation
iterations
jacobi-matrix
+
–
0
votes
0
answers
1142
GATE Electrical 2016 Set 1 | Question: 1
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.
The maximum value attained by the function. $f(x) = x(x-1) (x-2)$ in the interval $[1, 2]$ is ___________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-1
calculus
maxima-minima
numerical-answers
+
–
0
votes
0
answers
1143
GATE Electrical 2016 Set 1 | Question: 2
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Linear Algebra
gate2016-ee-1
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
1144
GATE Electrical 2016 Set 1 | Question: 3
The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\dfrac{5}{s^{2}-4s+29} \\ $ $\dfrac{5}{s^{2}+5} \\ $ $\dfrac{s-2}{s^{2}-4s+29} \\$ $\dfrac{5}{s +5}$
The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\dfrac{5}{s^{2}-4s+29} \\ $$\dfrac{5}{s^{2}+5} \\ $$\dfrac{s-2}{s^{2}-4s+29} \\$$\dfrac{5}{s +5}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Signals and Systems
gate2016-ee-1
unit-step-function
fourier-transform
shifting-theorems
+
–
0
votes
0
answers
1145
GATE Electrical 2016 Set 1 | Question: 4
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation $\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is $5e^{-1}$ $5e^{-2}$ $7e^{-1}$ $7e^{-2}$
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation$\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is$5e^{-1}$$...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Differential Equations
gate2016-ee-1
differential-equations
+
–
0
votes
0
answers
1146
GATE Electrical 2016 Set 1 | Question: 5
The value of the integral $\oint _{c}\dfrac{2z+5}{\left ( z-\dfrac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$ over the contour $\mid z \mid=1$, taken in the anti-clockwise direction, would be $\dfrac{24 \pi i}{13} \\$ $\dfrac{48 \pi i}{13} \\$ $\dfrac{24}{13} \\$ $\dfrac{12}{13}$
The value of the integral$$\oint _{c}\dfrac{2z+5}{\left ( z-\dfrac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$$over the contour $\mid z \mid=1$, taken in the anti-cloc...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-1
calculus
definite-integral
+
–
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