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561
GATE Electrical 2017 Set 1 | Question: 28
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below.The value of $I$ is$\frac{1}{2}i \\ $$\frac{2}{3}i \\ ...
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562
GATE Electrical 2017 Set 1 | Question: 29
The passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port $1$. Given $V_{1}=A_{1}V_{2}+B_{1}I_{2}$ $I_{1}=C_{1}V_{2}+D_{1}I_{2}$ $V_{2}=A_{2}V_{3}+B_{2}I_{3}$ $I_{2}=C_{2}V_{3}+D_{2}I_{3}$ ...
The passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port $1$.Given$V_{1}=A_{1}V_{2}+B_{1}I_{2}$$I_{1}=C_{1}V_{2}+D...
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564
GATE Electrical 2017 Set 1 | Question: 11
A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be satisfied? $0 < K < 0.5$ $0.5 < K < 1$ $0 < K < 1$ $K > 1$
A closed loop system has the characteristic equation given by $s^{3}+Ks^{2}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be sat...
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566
GATE Electrical 2017 Set 1 | Question: 13
The Boolean expression $AB+A\bar{C}+BC$ simplifies to $BC + A\bar{C}$ $AB + A\bar{C} + B$ $AB + A\bar{C}$ $AB + BC$
The Boolean expression $AB+A\bar{C}+BC$ simplifies to$BC + A\bar{C}$$AB + A\bar{C} + B$$AB + A\bar{C}$$AB + BC$
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567
GATE Electrical 2017 Set 1 | Question: 14
For the circuit shown in the figure below, assume that diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal. The $DC$ components of voltages $v_{1}$ and $v_{2}$, respectively are $0$V and $1$V $-0.5$V and $0.5$V $1$V and $0.5$V $1$V and $1$V
For the circuit shown in the figure below, assume that diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal. The $DC$ components of voltages $v_{1}$ and $v_{2}$, respectively are$...
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570
GATE Electrical 2017 Set 1 | Question: 17
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two decimal places.)
Let $I= c\int \int _{R} xy^{2} dxdy$, where $R$ is the region shown in the figure and $c= 6 \times 10^{-4}$. The value of $I$ equals _________. (Give the answer up to two...
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571
GATE Electrical 2017 Set 1 | Question: 18
The power supplied by the $25$V source in the figure shown below is __________ $W$.
The power supplied by the $25$V source in the figure shown below is __________ $W$.
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572
GATE Electrical 2017 Set 1 | Question: 19
The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.
The equivalent resistance between the terminals $A$ and $B$ is __________ $\Omega$.
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574
GATE Electrical 2017 Set 1 | Question: 2
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is $-2i$ $-i$ $i$ $2i$
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is$-2i$$-i$$i$$2i$
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575
GATE Electrical 2017 Set 1 | Question: 3
Let $z(t) = x(t) *y(t)$, where "*" denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct)$. $c . x(ct) * y (ct)$ $x (ct) * y (ct)$ $c . x (t) * y(ct)$ $c . x (ct) * y(t)$
Let $z(t) = x(t) *y(t)$, where "*" denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct)$.$c . x(ct) * y (ct)$$x (ct) ...
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579
GATE Electrical 2017 Set 1 | Question: 7
Consider the system with following input-output relation $y[n]=(1+(-1)^{n}x[n]$ where, $x[n]$ is the input and $y[n]$ is the output. The system is Invertible and time invariant Invertible and time varying Non-invertible and time invariant Non-invertible and time varying
Consider the system with following input-output relation$y[n]=(1+(-1)^{n}x[n]$where, $x[n]$ is the input and $y[n]$ is the output. The system isInvertible and time invari...
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580
GATE Electrical 2017 Set 1 | Question: 8
A $4$ pole induction machine is working as an induction generator. The generator supply frequency is $60$Hz. The rotor current frequency is $5$Hz. The mechanical speed of the rotor in $RPM$ is $1350$ $1650$ $1950$ $2250$
A $4$ pole induction machine is working as an induction generator. The generator supply frequency is $60$Hz. The rotor current frequency is $5$Hz. The mechanical speed of...
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583
GATE Electrical 2013 | Question: 56
They were requested not to $\textbf{quarrel}$ with others. Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$? make out call out dig out fall out
They were requested not to $\textbf{quarrel}$ with others.Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$?make outcall outdig ...
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585
GATE Electrical 2013 | Question: 61
What is the chance that a leap year, selected at random, will contain $53$ Saturdays? $2/7$ $3/7$ $1/7$ $5/7$
What is the chance that a leap year, selected at random, will contain $53$ Saturdays?$2/7$$3/7$$1/7$$5/7$
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587
GATE Electrical 2013 | Question: 63
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is $(-\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is$(-\infty ,0)$$(0,1)$$(1,\infty )$$(0,\infty )$
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588
GATE Electrical 2013 | Question: 64
A car travels $8$ km in the first quarter of an hour, $6$ km in the second quarter and $16$ km in the third quarter. The average speed of the car in km per hour over the entire journey is $30$ $36$ $40$ $24$
A car travels $8$ km in the first quarter of an hour, $6$ km in the second quarter and $16$ km in the third quarter. The average speed of the car in km per hour over the...
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589
GATE Electrical 2013 | Question: 65
Find the sum to $n$ terms of the series $10+84+ 734 +\dots $ $\dfrac{9(9^n+1)}{10}+1 \\$ $\dfrac{9(9^n-1)}{8}+1 \\$ $\dfrac{9(9^n-1)}{8}+n \\$ $\dfrac{9(9^n-1)}{8}+n^2$
Find the sum to $n$ terms of the series $10+84+ 734 +\dots $$\dfrac{9(9^n+1)}{10}+1 \\$$\dfrac{9(9^n-1)}{8}+1 \\$$\dfrac{9(9^n-1)}{8}+n \\$$\dfrac{9(9^n-1)}{8}+n^2$
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590
GATE Electrical 2013 | Question: 46
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly$20$$25$$...
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591
GATE Electrical 2013 | Question: 47
When the $\text{Newton-Raphson}$ method is applied to solve the equation $f(x)=x^3+2x-1=0$ ,the solution at the end of the first iteration with the initial guess value as $x_0$ =$1.2$ is $-0.82$ $0.49$ $0.705$ $1.69$
When the $\text{Newton-Raphson}$ method is applied to solve the equation $f(x)=x^3+2x-1=0$ ,the solution at the end of the first iteration with the initial guess value a...
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594
GATE Electrical 2013 | Question: 50
The state variable formulation of a system is given as ... The system is controllable but not observable not controllable but observable both controllable and observable both not controllable and not observable
The state variable formulation of a system is given as$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x...
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