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GATE EE 2019 Set 1

All 65 solved GATE EE 2019 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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Difficulty mixEasy 27Medium 37Hard 1

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65 of 65 questions

Question typeDifficultyYour progress

Electrical Engineering

11
Q11MCQ1 markEasy
The inverse Laplace transform of $H(s) = \frac{s+3}{s^2+2s+1}$ for $t \geq 0$ is
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Question
$H(s) = \frac{s+3}{s^2+2s+1}$
Your answer
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A. $3te^{-t} + e^{-t}$ B. $3e^{-t}$ C. $2te^{-t} + e^{-t}$ D. $4te^{-t} + e^{-t}$
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$H(s) = \frac{s+3}{s^2+2s+1} = \frac{s+3}{(s+1)^2}$
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12
Q12MCQ1 markEasy
$M$ is a $2 \times 2$ matrix with eigenvalues 4 and 9. The eigenvalues of $M^2$ are
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Question
$M$
Your answer
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A. $4 and 9$ B. $2 and 3$ C. $-2 and -3$ D. $16 and 81$
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$\lambda$
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13
Q13MCQ1 markEasy
The partial differential equation $\frac{\partial^2 u}{\partial t^2} - c^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) = 0$ ; where…
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Question
$\frac{\partial^2 u}{\partial t^2} - c^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) = 0$
Your answer
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A. $heat equation$ B. $wave equation$ C. $Poisson's equation$ D. $Laplace equation$
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$\frac{\partial^2 u}{\partial t^2} = c^2 \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right)$
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14
Q14MCQ1 markEasy
Which one of the following functions is analytic in the region $|z| \leq 1$ ?
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Question
$|z| \leq 1$
Your answer
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A. $\frac{z^2-1}{z}$ B. $\frac{z^2-1}{z+2}$ C. $\frac{z^2-1}{z-0.5}$ D. $\frac{z^2-1}{z+j0.5}$
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$f(z)$
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15
Q15MCQ1 markEasy
The mean-square of a zero-mean random process is $\frac{kT}{C}$ , where $k$ is Boltzmann's constant, $T$ is the absolute temperature, and $C$ is a capacitance. The standard…
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Question
$\frac{kT}{C}$
Your answer
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A. $\frac{kT}{C}$ B. $\sqrt{\frac{kT}{C}}$ C. $\frac{C}{kT}$ D. $\frac{\sqrt{kT}}{C}$
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$X$
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16
Q16MCQ1 markEasy
A system transfer function is $H(s) = \frac{a_1 s^2 + b_1 s + c_1}{a_2 s^2 + b_2 s + c_2}$ . If $a_1 = b_1 = 0$ , and all other coefficients are positive, the transfer function…
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Question
$H(s) = \frac{a_1 s^2 + b_1 s + c_1}{a_2 s^2 + b_2 s + c_2}$
Your answer
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A. $low pass filter$ B. $high pass filter$ C. $band pass filter$ D. $notch filter$
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$H(s) = \frac{a_1 s^2 + b_1 s + c_1}{a_2 s^2 + b_2 s + c_2}$
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17
Q17MCQ1 markMedium
The symbols, $a$ and $T$ , represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal…
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Question
$a$
Your answer
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A. $e^{+at}u(t)$ B. $e^{-a(t+T)}u(t)$ C. $1 + e^{-at}u(t)$ D. $e^{-a(t-T)}u(t)$
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$h(t)$
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18
Q18MCQ1 markEasy
A $5\text{ kVA}$ , $50\text{ V}/100\text{ V}$ , single-phase transformer has a secondary terminal voltage of $95\text{ V}$ when loaded. The regulation of the transformer is
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Question
$5\text{ kVA}$
Your answer
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A. $4.5\%$ B. $9\%$ C. $5\%$ D. $1\%$
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$\text{Voltage Regulation} = \frac{V_{NL} - V_{FL}}{V_{NL}} \times 100$
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19
Q19MCQ1 markEasy
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, $50\text{ Hz}$ AC source. Assuming that the DC output current of the rectifier is constant, the…
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Question
$50\text{ Hz}$
Your answer
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A. $100\text{ Hz}$ B. $150\text{ Hz}$ C. $250\text{ Hz}$ D. $300\text{ Hz}$
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$n$
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20
Q20MCQ1 markMedium
The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is
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Question
$The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is$
Your answer
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A. $rotor resistance$ B. $rotor leakage reactance$ C. $magnetizing reactance$ D. $stator resistance$
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$X_m$
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21
Q21MCQ1 markMedium
A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of…
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Question
$A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of 0.5 leading is$
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A. $100 A$ B. $200 A$ C. $300 A$ D. $400 A$
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$P$
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22
Q22MCQ1 markMedium
In the circuit shown below, the switch is closed at $t = 0$ . The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of…
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Question
$t = 0$
Your answer
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A. $60$ B. $-45$ C. $90$ D. $-30$
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$RL$
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23
Q23MCQ1 markEasy
The output response of a system is denoted as $y(t)$ , and its Laplace transform is given by $Y(s) = \frac{10}{s(s^2+s+100\sqrt{2})}$ The steady state value of $y(t)$ is
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Question
$y(t)$
Your answer
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A. $\frac{1}{10\sqrt{2}}$ B. $10\sqrt{2}$ C. $\frac{1}{100\sqrt{2}}$ D. $100\sqrt{2}$
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$y(t)$
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24
Q24MCQ1 markMedium
The open loop transfer function of a unity feedback system is given by $G(s) = \frac{\pi e^{-0.25s}}{s}$ In $G(s)$ plane, the Nyquist plot of $G(s)$ passes through the negative…
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Question
$G(s) = \frac{\pi e^{-0.25s}}{s}$
Your answer
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A. $(-0.5, j0)$ B. $(-0.75, j0)$ C. $(-1.25, j0)$ D. $(-1.5, j0)$
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$G(j\omega) = \frac{\pi e^{-j0.25\omega}}{j\omega}$
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Q25MCQ1 markEasy

The characteristic equation of a linear time-invariant (LTI) system is given by

\Delta(s) = s^4 + 3s^3 + 3s^2 + s + k = 0.

The system is BIBO stable if

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Question

\Delta(s) = s^4 + 3s^3 + 3s^2 + s + k = 0.

s^4 + 3s^3 + 3s^2 + s + k = 0

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s^4 + 3s^3 + 3s^2 + s + k = 0

Row	$s^4$	$s^2$	$s^0$
$s^4$	1	3	$k$
$s^3$	3	1	0
$s^2$	$\frac{3(3) - 1(1)}{3} = \frac{8}{3}$	$k$	0
$s^1$	$\frac{\frac{8}{3}(1) - 3k}{\frac{8}{3}} = 1 - \frac{9k}{8}$	0	0
$s^0$	$k$

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26
Q26MCQ1 markEasy
Given, $V_{gs}$ is the gate-source voltage, $V_{ds}$ is the drain source voltage, and $V_{th}$ is the threshold voltage of an enhancement type NMOS transistor, the conditions for…
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Question
$V_{gs}$
Your answer
Choose one option, then check your answer.
A. $V_{gs} < V_{th} ; V_{ds} \geq V_{gs} - V_{th}$ B. $V_{gs} > V_{th} ; V_{ds} \geq V_{gs} - V_{th}$ C. $V_{gs} > V_{th} ; V_{ds} \leq V_{gs} - V_{th}$ D. $V_{gs} < V_{th} ; V_{ds} \leq V_{gs} - V_{th}$
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$V_{gs}$
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27
Q27MCQ1 markMedium
A current controlled current source (CCCS) has an input impedance of $10\ \Omega$ and output impedance of $100\ \text{k}\Omega$ . When this CCCS is used in a negative feedback…
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Question
$10\ \Omega$
Your answer
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A. $10\ \Omega$ B. $100\ \Omega$ C. $100\ \text{k}\Omega$ D. $1000\ \text{k}\Omega$
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$(1 + T)$
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28
Q28NAT1 markMedium
If $f = 2x^3 + 3y^2 + 4z$ , the value of line integral $\int_C \text{grad} f \cdot dr$ evaluated over contour $C$ formed by the segments…
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Question
$f = 2x^3 + 3y^2 + 4z$
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$\nabla f$
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29
Q29NAT1 markMedium
The current $I$ flowing in the circuit shown below in amperes (round off to one decimal place) is _______. [figure]
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$I$
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$2\ \Omega$
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30
Q30NAT1 markMedium
A co-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity $\epsilon_{r1} = 2$ . When one-fourth portion of the dielectric is replaced with…
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Question
$\epsilon_{r1} = 2$
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$C = \frac{2\pi \epsilon_0 \epsilon_r L}{\ln(R/r)}$
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31
Q31NAT1 markMedium
The $Y_{bus}$ matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as…
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$Y_{bus}$
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$Y_{bus}$
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32
Q32NAT1 markMedium
Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is ________.
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Question
$Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is________.$
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$S_{sc1} = \frac{S_{base}}{X_{pu}} = \frac{5 \text{ MVA}}{0.25} = 20 \text{ MVA}$
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33
Q33NAT1 markMedium
The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 $\Omega$ . If the fault current is 20 times the rated primary current of the CT, the VA output…
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$\Omega$
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$I_{s,rated} = 5$
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34
Q34NAT1 markEasy
The rank of the matrix, $M = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix}$ , is ________.
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Question
$M = \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix}$
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$3 \times 3$
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35
Q35NAT1 markMedium
The output voltage of a single-phase full bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms component of output…
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$75\%$
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$v_o(t)$
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36
Q36MCQ2 marksEasy
Consider a $2 \times 2$ matrix $M = [v_1 \quad v_2]$ , where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1} = \begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$ , where $u_1^T$ …
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Question
$2 \times 2$
Your answer
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A. $Statement 1 is true and statement 2 is false$ B. $Statement 2 is true and statement 1 is false$ C. $Both the statements are true$ D. $Both the statements are false$
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$M = [v_1 \quad v_2]$
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37
Q37MCQ2 marksMedium
The closed loop line integral $\oint_{|z|=5} \frac{z^3 + z^2 + 8}{z + 2} dz$ evaluated counter-clockwise, is
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Question
$\oint_{|z|=5} \frac{z^3 + z^2 + 8}{z + 2} dz$
Your answer
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A. $+8j\pi$ B. $-8j\pi$ C. $-4j\pi$ D. $+4j\pi$
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$\oint_{|z|=5} \frac{z^3 + z^2 + 8}{z + 2} dz$
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38
Q38MCQ2 marksMedium
A periodic function $f(t)$ , with a period of $2\pi$ , is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty} a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ If…
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Question
$f(t)$
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A. $a_1 = \frac{A}{\pi}; b_1 = 0$ B. $a_1 = \frac{A}{2}; b_1 = 0$ C. $a_1 = 0; b_1 = A/\pi$ D. $a_1 = 0; b_1 = \frac{A}{2}$
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$a_1$
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39
Q39MCQ2 marksMedium
The asymptotic Bode magnitude plot of a minimum phase transfer function $G(s)$ is shown below. [figure] Consider the following two statements. Statement I: Transfer function…
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Question
$G(s)$
Your answer
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A. $Statement I is true and statement II is false.$ B. $Statement I is false and statement II is true.$ C. $Both the statements are true.$ D. $Both the statements are false.$
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$-20$
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40
Q40MCQ2 marksEasy
The transfer function of a phase lead compensator is given by $D(s) = \frac{3(s + \frac{1}{3T})}{(s + \frac{1}{T})}$ The frequency (in rad/sec), at which $\angle D(j\omega)$ is…
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Question
$D(s) = \frac{3(s + \frac{1}{3T})}{(s + \frac{1}{T})}$
Your answer
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A. $\sqrt{\frac{3}{T^2}}$ B. $\sqrt{\frac{1}{3T^2}}$ C. $\sqrt{3T}$ D. $\sqrt{3T^2}$
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$D(s) = \frac{s+z}{s+p}$
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41
Q41MCQ2 marksEasy
Consider a state-variable model of a system…
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$\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -\alpha & -2\beta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ \alpha \end{bmatrix} r$
Your answer
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A. $\xi = \frac{\beta}{\sqrt{\alpha}}; \omega_n = \sqrt{\alpha}$ B. $\xi = \sqrt{\alpha}; \omega_n = \frac{\beta}{\sqrt{\alpha}}$ C. $\xi = \frac{\sqrt{\alpha}}{\beta}; \omega_n = \sqrt{\beta}$ D. $\xi = \sqrt{\beta}; \omega_n = \sqrt{\alpha}$
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$|sI - A| = 0$
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42
Q42MCQ2 marksEasy
A moving coil instrument having a resistance of $10\ \Omega$ , gives a full-scale deflection when the current is $10\ \text{mA}$ . What should be the value of the series resistance,…
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Question
$10\ \Omega$
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A. $9\ \Omega$ B. $99\ \Omega$ C. $990\ \Omega$ D. $9990\ \Omega$
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$R_m = 10\ \Omega$
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43
Q43MCQ2 marksMedium
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu_n C_{ox} = 100 \mu A/V^2$ , the threshold voltage ( $V_T$ ) is $500 mV$ . Ignore channel…
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Question
$\mu_n C_{ox} = 100 \mu A/V^2$
Your answer
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A. $100 mV$ B. $500 mV$ C. $600 mV$ D. $2 V$
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$V_{GS} = V_{DS}$
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44
Q44MCQ2 marksMedium
In the circuit below, the operational amplifier is ideal. If $V_1 = 10\text{ mV}$ and $V_2 = 50\text{ mV}$ , the output voltage ( $V_{\text{out}}$ ) is [figure]
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Question
$V_1 = 10\text{ mV}$
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A. $100\text{ mV}$ B. $400\text{ mV}$ C. $500\text{ mV}$ D. $600\text{ mV}$
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$V_{\text{out}}$
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45
Q45MCQ2 marksEasy
The output expression for the Karnaugh map shown below is [figure]
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$The output expression for the Karnaugh map shown below is$
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A. $Q\bar{R} + S$ B. $QR + \bar{S}$ C. $QR + S$ D. $Q\bar{R} + \bar{S}$
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$RS = 01$
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46
Q46MCQ2 marksEasy
In the circuit shown below, $X$ and $Y$ are digital inputs, and $Z$ is a digital output. The equivalent circuit is a [figure]
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$X$
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A. $NAND gate$ B. $NOR gate$ C. $XOR gate$ D. $XNOR gate$
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$\bar{X}$
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47
Q47MCQ2 marksMedium
A DC-DC buck converter operates in continuous conduction mode. It has 48 V input voltage, and it feeds a resistive load of $24\ \Omega$ . The switching frequency of the converter…
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Question
$24\ \Omega$
A. $6 W$
B. $12 W$
C. $24 W$
D. $48 W$
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$V_{in} = 48\text{ V}$
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48
Q48MCQ2 marksMedium
The line currents of a three-phase four wire system are square waves with amplitude of $100\text{ A}$ . These three currents are phase shifted by $120^\circ$ with respect to each…
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$100\text{ A}$
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A. $0\text{ A}$ B. $\frac{100}{\sqrt{3}}\text{ A}$ C. $100\text{ A}$ D. $300\text{ A}$
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$i_n(t)$
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49
Q49NAT2 marksMedium
If $\mathbf{A} = 2x\mathbf{i} + 3y\mathbf{j} + 4z\mathbf{k}$ and $u = x^2 + y^2 + z^2$ , then $\text{div}(u\mathbf{A})$ at $(1, 1, 1)$ is ______.
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$\mathbf{A} = 2x\mathbf{i} + 3y\mathbf{j} + 4z\mathbf{k}$
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$\text{div}(u\mathbf{A}) = \nabla \cdot (u\mathbf{A}) = u(\nabla \cdot \mathbf{A}) + \mathbf{A} \cdot (\nabla u)$
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50
Q50NAT2 marksMedium
A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded…
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Question
$A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a reactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is$
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$X_1$
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51
Q51NAT2 marksMedium
In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8 pu at 0.8 power factor lagging to the infinite bus. The power angle of the…
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Question
$In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8 pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is$
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$X_d = 0.25$
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52
Q52NAT2 marksMedium
In a 132 kV system, the series inductance up to the point of circuit breaker location is 50 mH. The shunt capacitance at the circuit breaker terminal is 0.05 $\mu$ F. The critical…
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Question
$\mu$
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$V = 132$
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53
Q53NAT2 marksMedium
The voltage across and the current through a load are expressed as follows $v(t) = -170 \sin \left( 377t - \frac{\pi}{6} \right) \text{ V}$ …
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$v(t) = -170 \sin \left( 377t - \frac{\pi}{6} \right) \text{ V}$
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$v(t) = -170 \sin \left( 377t - \frac{\pi}{6} \right) = 170 \sin \left( 377t - \frac{\pi}{6} + \pi \right) = 170 \sin \left( 377t + \frac{5\pi}{6} \right)$
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54
Q54NAT2 marksMedium
The magnetic circuit shown below has uniform cross-sectional area and air gap of $0.2 \text{ cm}$ . The mean path length of the core is $40 \text{ cm}$ . Assume that leakage and…
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Question
$0.2 \text{ cm}$
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$B$
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55
Q55NAT2 marksMedium
A single-phase transformer of rating $25 \text{ kVA}$ , supplies a $12 \text{ kW}$ load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off…
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$25 \text{ kVA}$
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$P_1 = 12 \text{ kW}$
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56
Q56NAT2 marksMedium
A 220 V DC shunt motor takes 3 A at no-load. It draws 25 A when running at full-load at 1500 rpm. The armature and shunt resistances are 0.5 $\Omega$ and 220 $\Omega$ ,…
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$\Omega$
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$V = 220 \text{ V}$
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57
Q57NAT2 marksHard
A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator:…
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$R_1 = 5.39 \text{ Ω}$
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$P_{rated} = 3.7 \text{ kW}$
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58
Q58NAT2 marksMedium
A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of $(0.25 + j2.5) \text{ Ω/phase}$ . The motor draws the rated current of 10 A at 0.8 pf…
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$(0.25 + j2.5) \text{ Ω/phase}$
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$V_L = 220 \text{ V}$
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59
Q59NAT2 marksMedium
A three-phase $50\text{ Hz}$ , $400\text{ kV}$ transmission line is $300\text{ km}$ long. The line inductance is $1\text{ mH/km}$ per phase, and the capacitance is…
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$50\text{ Hz}$
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$V_r$
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60
Q60NAT2 marksMedium
A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded…
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$A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a reactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is__________.$
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$I_{f3\phi} = \frac{E}{X_1} = \frac{1}{0.25} = 4$
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61
Q61NAT2 marksMedium
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8\text{ pu}$ at $0.8$ power factor lagging to the infinite bus. The power…
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$0.8\text{ pu}$
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$P = 0.8\text{ pu}$
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62
Q62NAT2 marksMedium
In a 132 kV system, the series inductance up to the point of circuit breaker location is 50 mH. The shunt capacitance at the circuit breaker terminal is $0.05\ \mu\text{F}$ . The…
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$0.05\ \mu\text{F}$
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$R$
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63
Q63NAT2 marksMedium
In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at 48 V. The input DC voltage is 24 V. The output power is 120 W. The switching frequency…
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$\mu\text{H}$
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$D$
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64
Q64NAT2 marksMedium
A fully-controlled three-phase bridge converter is working from a $415\text{ V}$ , $50\text{ Hz}$ AC supply. It is supplying constant current of $100\text{ A}$ at $400\text{ V}$ to…
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$415\text{ V}$
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$I_d$
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65
Q65NAT2 marksMedium
A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC…
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$A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC supply of 230 V, 50 Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is________.$
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$V_o = 180$
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