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GATE EE 2018 Set 1

All 65 solved GATE EE 2018 Set 1 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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100

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MCQ · NAT

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Difficulty mixEasy 17Medium 43Hard 5

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65 of 65 questions

Question typeDifficultyYour progress

General Aptitude (GA)

1
Q1MCQ1 markEasy
“Since you have gone off the ______, the _______ sand is likely to damage the car.” The words that best fill the blanks in the above sentence are
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Question
$“Since you have gone off the______, the_______ sand is likely to damage the car.” The words that best fill the blanks in the above sentence are$
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A. $course, coarse$ B. $course, course$ C. $coarse, course$ D. $coarse, coarse$
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$Correct answer (A) course, coarse Step-by-step solution The first blank refers to a path or route, which is 'course'. The second blank refers to rough or large-grained sand, which is 'coarse'. Therefore, the correct pair is 'course, coarse'. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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2
Q2MCQ1 markEasy
“A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas.” The word that best fills the…
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Question
$“A common misconception among writers is that sentence structure mirrors thought; the more_________the structure, the more complicated the ideas.” The word that best fills the blank in the above sentence is$
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A. $detailed$ B. $simple$ C. $clear$ D. $convoluted$
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$Correct answer (D) convoluted Step-by-step solution The sentence suggests a parallel between the complexity of the structure and the complexity of the ideas. 'Convoluted' means extremely complex and difficult to follow, which fits the context of 'more complicated ideas'. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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3
Q3MCQ1 markEasy
The three roots of the equation $f(x) = 0$ are $x = \{-2, 0, 3\}$ . What are the three values of $x$ for which $f(x - 3) = 0$ ?
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Question
$f(x) = 0$
Your answer
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A. $-5, -3, 0$ B. $-2, 0, 3$ C. $0, 6, 8$ D. $1, 3, 6$
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$f(x) = 0$
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4
Q4MCQ1 markMedium
For what values of k given below is $\frac{(k+2)^2}{k-3}$ an integer?
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Question
$\frac{(k+2)^2}{k-3}$
Your answer
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A. $4, 8, 18$ B. $4, 10, 16$ C. $4, 8, 28$ D. $8, 26, 28$
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$E = \frac{(k+2)^2}{k-3}$
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5
Q5MCQ1 markEasy
Functions $F(a, b)$ and $G(a, b)$ are defined as follows: $F(a, b) = (a - b)^2$ and $G(a, b) = |a - b|$ , where $|x|$ represents the absolute value of $x$ . What would be the value…
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Question
$F(a, b)$
Your answer
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A. $2$ B. $4$ C. $6$ D. $36$
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$F(a, b) = (a - b)^2$
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6
Q6MCQ2 marksMedium
An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How…
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Question
$An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?$
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A. $6,760$ B. $13,520$ C. $40,560$ D. $1,05,456$
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$10 \times 26 \times 26 = 6,760$
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7
Q7MCQ2 marksEasy
In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?
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Question
$In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ . How will DHLP be written in that code?$
Your answer
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A. $RSTN$ B. $TLPH$ C. $HLPT$ D. $XSVR$
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$A \xrightarrow{+4} E$
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8
Q8MCQ2 marksMedium
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the…
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Question
$A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?$
A. $0$
B. $\frac{325}{864}$
C. $\frac{525}{864}$
D. $\frac{5}{12}$
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$B$
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9
Q9MCQ2 marksMedium
A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles…
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Question
$A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design? Blue Black Red Yellow 40% 25% 20% 15%$
Your answer
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A. $35.75$ B. $40.25$ C. $43.75$ D. $46.25$
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$1 + 25\% \text{ of } 1 = 1.25$
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10
Q10MCQ2 marksMedium
P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available. (i) The boat held two…
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Question
$P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available. (i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips. (ii) P is unable to row when someone else is in the boat. (iii) Q is unable to row with anyone else except R. (iv) Each person rowed for at least one trip. (v) Only one person can row during a trip. Who rowed twice?$
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A. $P$ B. $Q$ C. $R$ D. $S$
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$4 + 1 = 5$
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Blue	Black	Red	Yellow
40%	25%	20%	15%

ELECTRICAL ENGINEERING

11
Q11MCQ1 markEasy
A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage…
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Question
$A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is$
Your answer
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A. $4.8$ B. $6.8$ C. $8.8$ D. $10.8$
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$Z_{pu} = 5\% = 0.05$
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12
Q12MCQ1 markEasy
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is
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Question
$In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is$
Your answer
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A. $0$ B. $45$ C. $60$ D. $90$
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$T_{rel} = \frac{3}{\omega_s} \frac{V^2}{2} \left( \frac{1}{X_q} - \frac{1}{X_d} \right) \sin(2\delta)$
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13
Q13MCQ1 markMedium
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is…
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Question
$A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?$
Your answer
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A. $v_o \geq 0$ B. $v_o < 0$ C. $v_o \geq 0$ D. $v_o < 0$
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$v_o$
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14
Q14MCQ1 markMedium
Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when…
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Question
$Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are)$
Your answer
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A. $Triac only$ B. $Triac and MOSFET$ C. $Triac and GTO$ D. $Thyristor and Triac$
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$I$
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15
Q15MCQ1 markEasy
Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other…
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Question
$Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is$
Your answer
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A. $0.532$ B. $0.632$ C. $0.707$ D. $0.866$
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$W_1 = V_L I_L \cos(30^\circ - \phi)$
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16
Q16MCQ1 markMedium
Consider a lossy transmission line with $V_1$ and $V_2$ as the sending and receiving end voltages, respectively. $Z$ and $X$ are the series impedance and reactance of the line,…
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Question
$V_1$
Your answer
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A. $|\frac{V_1 V_2}{X}|$ B. $|\frac{V_1 V_2}{X}|$ C. $|\frac{V_1 V_2}{X}|$ D. $|\frac{V_1 V_2}{Z}|$
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$R=0$
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17
Q17MCQ1 markEasy
The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is
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Question
$The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is$
Your answer
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A. $11$ B. $12$ C. $13$ D. $14$
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$L$
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18
Q18MCQ1 markHard
In the figure, the voltages are $v_1(t) = 100\cos(\omega t)$ , $v_2(t) = 100\cos(\omega t + \pi/18)$ and $v_3(t) = 100\cos(\omega t + \pi/36)$ . The circuit is in sinusoidal steady…
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Question
$v_1(t) = 100\cos(\omega t)$
Your answer
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A. $P_1 = P_2 = P_3 = 0$ B. $P_1 < 0, P_2 > 0, P_3 > 0$ C. $P_1 < 0, P_2 > 0, P_3 < 0$ D. $P_1 > 0, P_2 < 0, P_3 > 0$
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$V_i$
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Q19MCQ1 markEasy

Match the transfer functions of the second-order systems with the nature of the systems given below. | Transfer functions | Nature of system | | :--- | :--- | | P:…

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Question

\frac{15}{s^2 + 5s + 15}

Transfer functions	Nature of system
P: $\frac{15}{s^2 + 5s + 15}$	I: Overdamped
Q: $\frac{25}{s^2 + 10s + 25}$	II: Critically damped
R: $\frac{35}{s^2 + 18s + 35}$	III: Underdamped

s^2 + 2\zeta\omega_n s + \omega_n^2 = 0

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s^2 + 2\zeta\omega_n s + \omega_n^2 = 0

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20
Q20MCQ1 markMedium
A positive charge of $1$ nC is placed at $(0, 0, 0.2)$ where all dimensions are in metres. Consider the $x - y$ plane to be a conducting ground plane. Take…
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Question
$1$
Your answer
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A. $899.18 V/m$ B. $-899.18$ C. $999.09 V/m$ D. $-999.09$
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$z = 0$
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21
Q21MCQ1 markEasy
Let $f$ be a real-valued function of a real variable defined as $f(x) = x^2$ for $x \geq 0$ , and $f(x) = -x^2$ for $x < 0$ . Which one of the following statements is true?
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Question
$f$
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A. $f(x)$ B. $f(x)$ C. $f(x)$ D. $f(x)$
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$f(x) = \begin{cases} x^2, & x \geq 0 \\ -x^2, & x < 0 \end{cases}$
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22
Q22MCQ1 markEasy
The value of the directional derivative of the function $\Phi(x, y, z) = xy^2 + yz^2 + zx^2$ at the point (2, -1, 1) in the direction of the vector…
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Question
$\Phi(x, y, z) = xy^2 + yz^2 + zx^2$
Your answer
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A. $1$ B. $0.95$ C. $0.93$ D. $0.9$
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$\Phi(x, y, z)$
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23
Q23MCQ1 markMedium
The value of the integral $\oint_C \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle C of radius 1 with center at the point z = -2 is
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Question
$\oint_C \frac{z+1}{z^2-4} dz$
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A. $\frac{\pi i}{2}$ B. $2\pi i$ C. $-\frac{\pi i}{2}$ D. $-2\pi i$
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$I = \oint_C \frac{z+1}{z^2-4} dz$
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24
Q24MCQ1 markEasy
In the logic circuit shown in the figure, Y is given by [figure]
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Question
$In the logic circuit shown in the figure, Y is given by$
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A. $Y = ABCD$ B. $Y = (A + B)(C + D)$ C. $Y = {A} + {B} + {C} + {D}$ D. $Y = {AB} + {CD}$
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$O_1$
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25
Q25MCQ1 markMedium
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{in}}{i_{in}}$ is given by [figure]
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Question
$\frac{v_{in}}{i_{in}}$
Your answer
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A. $Z \frac{R_1}{R_2}$ B. $-Z \frac{R_2}{R_1}$ C. $Z$ D. $-Z \frac{R_1}{R_1+R_2}$
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$V_+ = V_- = v_{in}$
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26
Q26MCQ1 markEasy
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is
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Question
$x(t)$
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A. $k x(t)$ B. $k e^{j\omega t} x(t)$ C. $x(t) e^{j\omega t}$ D. $k H(\omega)$
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$x(t)$
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27
Q27NAT1 markEasy
Consider a non-singular $2 \times 2$ square matrix A. If $trace(\mathbf{A}) = 4$ and $trace(\mathbf{A}^2) = 5$ , the determinant of the matrix A is _________(up to 1…
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$2 \times 2$
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$\lambda_1$
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28
Q28NAT1 markMedium
Let $f$ be a real-valued function of a real variable defined as $f(x) = x - [x]$ , where $[x]$ denotes the largest integer less than or equal to $x$ . The value of…
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$f$
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$f(x) = x - [x]$
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29
Q29NAT1 markMedium
In the two-port network shown, the $h_{11}$ parameter $\left( \text{where, } h_{11} = \frac{V_1}{I_1}, \text{ when } V_2 = 0 \right)$ in ohms is _____________ (up to 2 decimal…
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$h_{11}$
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$h_{11}$
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30
Q30NAT1 markMedium
The series impedance matrix of a short three-phase transmission line in phase coordinates is…
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Question
$Z_{abc} = \begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$
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$Z_s$
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31
Q31NAT1 markMedium
The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are $j0.1$ pu, $j0.05$ pu and $j0.01$ pu respectively on the…
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$j0.1$
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$I_b$
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32
Q32NAT1 markMedium
A $1000 \times 1000$ bus admittance matrix for an electric power system has $8000$ non-zero elements. The minimum number of branches (transmission lines and transformers) in this…
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Question
$1000 \times 1000$
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$Y_{bus}$
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33
Q33NAT1 markMedium
The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If $I_0 = 20$ A, the rms value of fundamental component of the…
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$I_0 = 20$
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$I_0$
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34
Q34NAT1 markMedium
A separately excited dc motor has an armature resistance $R_a = 0.05\text{ }\Omega$ . The field excitation is kept constant. At an armature voltage of $100\text{ V}$ , the motor…
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Question
$R_a = 0.05\text{ }\Omega$
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$T = K\phi I_a$
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35
Q35NAT1 markEasy
Consider a unity feedback system with forward transfer function given by $G(s) = \frac{1}{(s+1)(s+2)}$ The steady-state error in the output of the system for a unit-step input…
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Question
$G(s) = \frac{1}{(s+1)(s+2)}$
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$H(s) = 1$
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36
Q36MCQ2 marksMedium
A transformer with toroidal core of permeability $\mu$ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius $r \ll R$ , and…
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Question
$\mu$
Your answer
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A. $\frac{\mu V r^2 N_P^2 \omega}{I}$ B. $\frac{\mu I r^2 N_P N_S \omega}{V}$ C. $\frac{\mu V r^2 N_P^2 \omega}{2I}$ D. $\frac{\mu I r^2 N_P^2 \omega}{2V}$
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$l = 2\pi R$
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37
Q37MCQ2 marksMedium
A 0-1 Ampere moving iron ammeter has an internal resistance of $50\text{ m}\Omega$ and inductance of $0.1\text{ mH}$ . A shunt coil is connected to extend its range to 0-10 Ampere…
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Question
$50\text{ m}\Omega$
Your answer
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A. $2, 5.55$ B. $2, 1$ C. $2.18, 0.55$ D. $11.1, 2$
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$R_m = 50\text{ m}\Omega$
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38
Q38MCQ2 marksMedium
The positive, negative and zero sequence impedances of a three phase generator are $Z_1, Z_2$ and $Z_0$ respectively. For a line-to-line fault with fault impedance $Z_f$ , the…
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Question
$Z_1, Z_2$
Your answer
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A. $Z_f = \frac{(Z_1+Z_2)(1-k)}{k}$ B. $Z_f = \frac{(Z_1+Z_2)(1+k)}{k}$ C. $Z_f = \frac{(Z_1+Z_2)k}{1-k}$ D. $Z_f = \frac{(Z_1+Z_2)k}{1+k}$
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$Z_f$
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39
Q39MCQ2 marksMedium
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator…
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Question
$G_1$
Your answer
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A. $5.00, 12.68, 2.68$ B. $6.34, 10.00, 1.34$ C. $6.34, 11.34, 2.68$ D. $5.00, 11.34, 1.34$
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$P_1 = P_{G1} - P_{L1} = 20 - 15 = 5$
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40
Q40MCQ2 marksMedium
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, $P = 1.4 \sin \delta + 0.15 \sin 2\delta$ , where $\delta$ …
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Question
$P = 1.4 \sin \delta + 0.15 \sin 2\delta$
Your answer
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A. $15^\circ$ B. $28.48^\circ$ C. $28.74^\circ$ D. $31.20^\circ$
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$P(\delta) = 1.4 \sin \delta + 0.15 \sin 2\delta$
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41
Q41MCQ2 marksMedium
A DC voltage source is connected to a series L-C circuit by turning on the switch S at time $t = 0$ as shown in the figure. Assume $i(0) = 0, v(0) = 0$ . Which one of the following…
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Question
$t = 0$
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A.B.C.D.
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$V_s = 5V$
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42
Q42MCQ2 marksMedium
The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is [figure]
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Question
$Z_{eq}$
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A. $j12 \Omega$ B. $-j12 \Omega$ C. $j13 \Omega$ D. $13 \Omega$
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$Z_{eq}$
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43
Q43MCQ2 marksMedium
Consider a system governed by the following equations $\frac{dx_1(t)}{dt} = x_2(t) - x_1(t)$ $\frac{dx_2(t)}{dt} = x_1(t) - x_2(t)$ The initial conditions are such that…
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Question
$\frac{dx_1(t)}{dt} = x_2(t) - x_1(t)$
Your answer
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A. $x_{1f} < x_{2f} < \infty$ B. $x_{2f} < x_{1f} < \infty$ C. $x_{1f} = x_{2f} < \infty$ D. $x_{1f} = x_{2f} = \infty$
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$\frac{d}{dt}(x_1 + x_2) = (x_2 - x_1) + (x_1 - x_2) = 0$
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44
Q44MCQ2 marksMedium
The number of roots of the polynomial, $s^7 + s^6 + 7s^5 + 14s^4 + 31s^3 + 73s^2 + 25s + 200$ , in the open left half of the complex plane is
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Question
$s^7 + s^6 + 7s^5 + 14s^4 + 31s^3 + 73s^2 + 25s + 200$
Your answer
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A. $3$ B. $4$ C. $5$ D. $6$
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$P(s) = s^7 + s^6 + 7s^5 + 14s^4 + 31s^3 + 73s^2 + 25s + 200$
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45
Q45MCQ2 marksMedium
If $C$ is a circle $|z| = 4$ and $f(z) = \frac{z^2}{(z^2-3z+2)^2}$ , then $\oint_C f(z) dz$ is
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Question
$C$
Your answer
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A. $1$ B. $0$ C. $-1$ D. $-2$
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$f(z) = \frac{z^2}{(z^2-3z+2)^2} = \frac{z^2}{((z-1)(z-2))^2} = \frac{z^2}{(z-1)^2(z-2)^2}$
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46
Q46MCQ2 marksHard
Which one of the following statements is true about the digital circuit shown in the figure [figure]
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Question
$Which one of the following statements is true about the digital circuit shown in the figure$
Your answer
Choose one option, then check your answer.
A. $It can be used for dividing the input frequency by 3.$ B. $It can be used for dividing the input frequency by 5.$ C. $It can be used for dividing the input frequency by 7.$ D. $It cannot be reliably used as a frequency divider due to disjoint internal cycles.$
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$Q_2, Q_1, Q_0$
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47
Q47MCQ2 marksEasy
Digital input signals $A, B, C$ with $A$ as the MSB and $C$ as the LSB are used to realize the Boolean function $F = m_0 + m_2 + m_3 + m_5 + m_7$ , where $m_i$ denotes the $i^{th}$ …
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Question
$A, B, C$
Your answer
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A. $\bar{A}\bar{C} + \bar{B}C + AC$ B. $\bar{A} + C$ C. $\bar{C} + A$ D. $\bar{A}C + BC + A\bar{C}$
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$F(A, B, C) = \sum m(0, 2, 3, 5, 7) + d(1)$
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48
Q48MCQ2 marksMedium
Consider the two continuous-time signals defined below:…
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Question
$x_1(t) = \begin{cases} |t|, & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases}, \quad x_2(t) = \begin{cases} 1 - |t|, & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases}$
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A. $x_1[n]$ B. $x_2[n]$ C. $x_1[n]$ D. $x_1[n]$
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$t = nT = 0.25n$
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49
Q49MCQ2 marksMedium
The signal energy of the continuous-time signal $x(t) = [(t-1)u(t-1)] - [(t-2)u(t-2)] - [(t-3)u(t-3)] + [(t-4)u(t-4)]$ is
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Question
$x(t) = [(t-1)u(t-1)] - [(t-2)u(t-2)] - [(t-3)u(t-3)] + [(t-4)u(t-4)]$
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A. $11/3$ B. $7/3$ C. $1/3$ D. $5/3$
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$x(t)$
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50
Q50NAT2 marksMedium
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10 + j\omega)^2}, -\infty < \omega < \infty$ where $j = \sqrt{-1}$ and $\omega$ …
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Question
$x(t)$
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Numerical answer
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$X(\omega) = \frac{1}{(10 + j\omega)^2}$
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51
Q51NAT2 marksMedium
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain $\beta = 100$ . The base-emitter voltage drop is a constant, $V_{BE} = 0.7 V$ . The…
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Question
$\beta = 100$
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$R_{Th}$
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52
Q52NAT2 marksMedium
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2 + y^2 = 9$ . The value of the integral…
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$C$
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$M = y^2 + 2yx$
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53
Q53NAT2 marksMedium
Let $f(x) = 3x^3 - 7x^2 + 5x + 6$ . The maximum value of $f(x)$ over the interval $[0, 2]$ is _______ (up to 1 decimal place).
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Question
$f(x) = 3x^3 - 7x^2 + 5x + 6$
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Numerical answer
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$f(x) = 3x^3 - 7x^2 + 5x + 6$
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54
Q54NAT2 marksMedium
Let A = $\begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^{3}-A^{2}-4A+5I$ , where I is the $3 \times 3$ identity matrix. The determinant…
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Question
$\begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$
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Numerical answer
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$|\mathbf{A} - \lambda \mathbf{I}| = 0$
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55
Q55NAT2 marksMedium
The capacitance of an air-filled parallel-plate capacitor is $60$ pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the…
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Question
$60$
Your answer
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$C_0 = \frac{\epsilon_0 A}{d} = 60$
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56
Q56NAT2 marksMedium
The unit step response y(t) of a unity feedback system with open loop transfer function $G(s)H(s) = \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of K is ______ (up to…
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Question
$G(s)H(s) = \frac{K}{(s+1)^2(s+2)}$
Your answer
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Numerical answer
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$G(s) = \frac{K}{(s+1)^2(s+2)}$
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57
Q57NAT2 marksMedium
A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{an} = 100 \angle 0^\circ$ V, $V_{bn} = 100 \angle -120^\circ$ V and…
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Question
$V_{an} = 100 \angle 0^\circ$
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Numerical answer
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$I_a + I_b + I_c = 0$
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58
Q58NAT2 marksMedium
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: $v(t) = 5 – 10 \cos(\omega t + 60^\circ) V$ …
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Question
$v(t) = 5 – 10 \cos(\omega t + 60^\circ) V$
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Numerical answer
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$P_{avg}$
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59
Q59NAT2 marksMedium
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given…
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Question
$V_o = \frac{V_m}{2\pi} (3 + \cos \alpha)$
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$V_m = 80\pi$
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60
Q60NAT2 marksHard
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value.…
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Question
$\Omega$
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Numerical answer
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$V_{in} = 100$
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61
Q61NAT2 marksMedium
A 3-phase 900 kVA, 3 kV / $\sqrt{3}$ kV ( $\Delta$ /Y), 50 Hz transformer has primary (high voltage side) resistance per phase of 0.3 $\Omega$ and secondary (low voltage side)…
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Question
$\sqrt{3}$
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Numerical answer
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$S = 900$
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62
Q62NAT2 marksMedium
A 200 V DC series motor, when operating from rated voltage while driving a certain load, draws 10 A current and runs at 1000 r.p.m. The total series resistance is 1 $\Omega$ . The…
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Question
$\Omega$
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$V = 200\text{ V}$
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63
Q63NAT2 marksHard
A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value…
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Question
$A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value of the inductor, L is 5 mH and the ideal switch, S is operated with a switching frequency of 5 kHz with a duty ratio of 0.4. Once the circuit has attained steady state and assuming the diode D to be ideal, the power transferred from B1 to B2 (in Watt) is___________(up to 2 decimal places).$
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$V_{in} = 50\text{ V}$
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64
Q64NAT2 marksHard
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are $R_1 = R_2' = X_{l1} = X_{l2}' = 12\text{ }\Omega$ ,…
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Question
$R_1 = R_2' = X_{l1} = X_{l2}' = 12\text{ }\Omega$
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Numerical answer
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$s \approx 0$
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65
Q65NAT2 marksMedium
The voltage $v(t)$ across the terminals $a$ and $b$ as shown in the figure, is a sinusoidal voltage having a frequency $\omega = 100$ radian/s. When the inductor current $i(t)$ is…
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Question
$v(t)$
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$Z$
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Row	$s^7$	$s^5$	$s^3$	$s^1$
$s^7$	1	7	31	25
$s^6$	1	14	73	200
$s^5$	-7	-42	-175	0
$s^4$	8	48	200	0

Row	Col 1	Col 2
$s^3$	4	12
$s^2$	24	200
$s^1$	-21.33	0
$s^0$	200	0

$A$ \ $BC$	00	01	11	10
0	1 ( $m_0$ )	X ( $m_1$ )	1 ( $m_3$ )	1 ( $m_2$ )
1	0 ( $m_4$ )	1 ( $m_5$ )	1 ( $m_7$ )	0 ( $m_6$ )

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