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Practice Test: Gate Electrical Engineering GATE 2017 Paper


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65 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Practice Test: Gate Electrical Engineering GATE 2017 Paper

Practice Test: Gate Electrical Engineering GATE 2017 Paper for GATE 2022 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Practice Test: Gate Electrical Engineering GATE 2017 Paper questions and answers have been prepared according to the GATE exam syllabus.The Practice Test: Gate Electrical Engineering GATE 2017 Paper MCQs are made for GATE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Practice Test: Gate Electrical Engineering GATE 2017 Paper below.
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Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 1

Directions

Q. No. 1 – 5 Carry One Mark Each

Q.

There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W, Z is to the East of X and the West of V, W is to the West of Y. Which is the building in the middle?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 1

From the given data, the following is formed

∴ The building "V‟ is in the middle

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 2

Saturn is _________ to be seen on a clear night with the naked eye.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 3

Choose the option with words that are not synonyms.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 4

There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 4

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 5

A test has twenty questions worth 100 marks in total.  There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

 

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 5

x + y = 20 , x = MCQ

3x + 11y = 100 , y = esaay type

⇒ x = 15 , y = 5

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 6

Directions:

Q. No. 6 – 10 Carry Two Marks Each

Q.

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot

.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 6

In general thunder storms are occurred in a region where suddenly air pressure changes (i.e.,) should rise (or) sudden fall of air pressure. From the given contour map in "R‟ region only more changes in air pressure. So, the possibility of a thunder storms in this region.
So option (C) is correct.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 7

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 7

The person who is opening the boxes, he knew that all 3 are marked wrong.
Suppose if 3 boxes are labelled as below.

If he inspected from Box(1), picked one fruit, found orange, then he don't know whether box contains oranges (or) both apples and oranges.
Similarly, if he picked one fruit from box(2), found apple then he don't know whether box contain apples (or) both apples and oranges.
But if he picked one fruit from box(3), i.e., labelled is “apples and oranges‟, if he found apple then he can decide compulsorily that box(3) contains apples and as he knew all boxes are labelled as incorrect, he can tell box(2) contains both apples and oranges, box(1) contain remaining oranges. So, he should open box labelled "Apples and Oranges‟ to determine contents of all the three boxes.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 8

“We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”The author‟s belief that ideology is not as important as literature is revealed by the word:

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 9

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 9

X = ( 47...........) 30 digits

Suppose ( 47)3 = 2 + 2 + 2 digits in (47)3

Similarly ( 47 )3 = contains 30 + 30 + 30 digits = 90 digits.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 10

The number of roots of e+ 0.5x2 - 2 = 0 in the range [ -5, 5] is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 10

f ( x ) = ex + 0.5x2 - 2

f (-5) = 10.50; f ( -4) = 6.01, f ( -2 ) = 0.135; f ( -1) = -1.13;

f(0) = -1, f (1) = 1.21, f ( 2 ) = 7.38, f(3) , f (4) , f (5) also + ve.

∴  As there are 2 sign changes from +ve to –ve and –ve to +ve, two roots will be there in the range [-5, 5].

 

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 11

Directions:

Q. No. 11 – 35 Carry One Mark Each

Q.

In the circuit shown, the diodes are ideal, the inductance is small, and Io ≠ 0. Which one of the following statements is true?

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 12

For a 3-input logic circuit shown below, the output Z can be expressed as

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 12

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 13

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 13

Here R is red ball, B is black ball

∴ The probability to get a red ball in the second draw is 

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 14

When a unit ramp input is applied to the unity feedback system having closed loop transfer 
function  the steady state error will be

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 14

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 15

A three-phase voltage source inverter with ideal devices operating in 180o conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is Vdc. The peak of the fundamental component of the phase voltage is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 15

Fourier series expansion of line to neutral voltage Vao is given by

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 16

The figures show diagrammatic representations of vector fields  respectively. 
Which one of the following choices is true?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 16

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 17

Assume that in a traffic junction, the cycle of traffic signal lights is 2 minutes of green(vehicle does not stop) and 3 minutes of red (vehicle stops). Consider the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time in minutes for the vehicle at the junction is _________


Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 18

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 18

For a perfect conductor the charge is present only on the surface.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 19

The transfer function C (s ) of a compensator is given below.

The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 20

The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts.

For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 x 2. Which one of the following statements is true?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 20

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 21

A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 21

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 22

Let x and y be integers satisfying the following equations 

2x+ y2 = 34

x + 2y = 11

The value of ( x +y ) is ________.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 22

Clearly x = 3 and y = 4 satisfies the given two equation

∴ x + y = 7

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 23

Consider a function f ( x, y, z ) given by

f(x,y,z) = (x2 + y2 -2z2) (x2 + y2 )

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 23

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 24

For the given 2-port network, the value of transfer impedance Z21 in ohms is_______


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 24

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 25

The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 25

Before initial charge on the capacitor = 0 ⇒ Vc ( 0 ) = 0V

Final voltage  V (α) = 10V
To find time constant τ

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 26

The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T1 and T2 are 90o and 270o , respectively.

The RMS value of the current through diode D3 in amperes is _____


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 26

0A since D2 is OFF and it will not turn ON for R load.

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 27

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 x 100. If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 27

Given the size of bus is 100*100.

so [J]= 100

we have formula for [J] = [2n-m-2] 100= [2n-20-2]

total no.of buses ,n = 61

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 28

A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 28

3 - Ø     S.C.I.M
4 - P      s = 0.02

400V      Ør ⇒ Nr
flux speed is same as stator flux speed.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 29

Two resistors with nominal resistance values R1 and R2 have additive uncertainties
ΔRand ΔR2 , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 29

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 30

The nominal- π circuit of a transmission line is shown in the figure.

Impedance  and reactance X = 3300Ω . The magnitude of the characteristic impedance of the transmission line, in Ω , is _______________. (Give the answer up to one decimal place.)


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 30

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 31

The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Which one of the following is TRUE about the frequency selectivity of these systems?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 31

Ω = 0 rad / samples reprsent low frequencies

Ω = π rad / samples reprsent high frequencies Since zeros are located at Ω = 0 rad / samples and Ω = πrad / samples they cannot be high pass and low pass filters. Thus they all represent band pass filters.

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 32

The mean square value of the given periodic waveform f (t ) is_________


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 32

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 33

A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHZ. The frequency of the vertical input is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 33

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 34

Let y2 - 2y + 1 = x and  . The value of   equals _________. (Give the answer up to three decimal places)


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 34

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 35

If a synchronous motor is running at a leading power factor, its excitation  induced voltage ( Ef ) is 

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 35

Higher than the terminal voltage.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 36

Directions:

Q. No. 36 – 65 Carry Two Marks Each

Q.

Which of the following systems has maximum peak overshoot due to a unit step input?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 36

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 37

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab = Dbc = Dca = 1m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω / km (rounded off to three decimal places) is _______


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 37

Inductance/phase/km = 9.21 x 10-4 H

Reactance = ωL = 2π x 50 x 9.21 x 10-4 =  0.2892 Ω/km

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 38

Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the  load shared by the larger  unit is _______ MW.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 38

Assume No – load speed regulations are equal 

From similar triangles method

Given that P1 + P2 = 600MW

150x = 600

x = 4

∴The load supplied by largest machine is P2 = 100 x 4 = 400MW

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 39

For the network given in figure below, the Thevenin's voltage Vab is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 39

The equivalent CKT is

Apply nodal

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 40

The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 40

Consider  

If the input signal is defined as w(t) then its Fourier transform can be drawn as follows:

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 41

A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance Ra= 0.02Ω.When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 41

By solving above equation

We get Eb1 = 219.39 and Eb2 = 0.61

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 42

A cascade system having the impulse responses  is shown in the 
figure below, where symbol ↑ denotes the time origin.

The input sequence x (n ) for which the cascade system produces an output sequence 

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 42

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 43

For the circuit shown in the figure below, it is given that  The transistor has β = 29 and VBE = 0.7V when the B-E junction is forward biased

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 43

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 44

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ________ electrical degrees.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 44

Pa = Pm - Pe

   = 60 - 0 = 60mw

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 45

For the circuit shown below, assume that the OPAMP is ideal.

Which one of the following is TRUE?

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 45

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 46

The root locus of the feedback control system having the characteristic equation s2 + 6Ks + 2s + 5 = 0 where K > 0, enters into the real axis at

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 46

C.E = s2 + 6ks + 2s + 5 = 0

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 47

For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions 

The minimum number of clock cycles after which the output Z would again become zero is 


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 47

Upper part of the circuit is ring counter and lower part of the circuit is Johnson counter as per the connection established. Outputs of the Ring counter and Johnson counter is given to Ex-OR. Gates, whose output is given to the three inputs OR-gate.
Ring counter output

So, output Z will become again 1 after 6 clock pulses.

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 48

In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 48

To get the maximum power the load Ckt must be at resonance i.e. imaginary part of load impedance is zero.

From options C = 10mF will satisfy the about equation

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 49

In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is ________. (Give the answer up to one decimal place.)


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 49

Given is Buckboost converter

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 50

In the circuit shown in the figure, the diode used is ideal. The input power factor is _______. (Give the answer up to two decimal places.)


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 50

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 51

Consider the system described by the following state space representation

If u (t ) is a unit step input and  the value of output y (t ) at t = 1 sec (rounded 
off to three decimal places) is_________

 


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 51

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 52

A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator:R1 = 0.3Ω, R2 = 0.3Ω, X1 = 0.41Ω, X2 = 0.41Ω. Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3-phase AC source is __________.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 52

Reactance offered by stator and Rotor will be changes, because of change in frequency.

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 53

A 25 kVA, 400 V, D - connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 53

Hint: Obtained regulation should be negative.

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 54

If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA. Y -Δ  transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is_____.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 54

25KVA, Y - D, 3.3kV - Δ

N : N = 5 :1

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 55

For the balanced Y-Y connected 3-Phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

 

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 55

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 56

A thin soap bubble of radius R = 1 cm, and thickness a = 3.3mm ( a << R ) , is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is 4πR2a and that of the drop is 4/3πr3 .The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.)


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 56

Charge must be same 

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 57

The value of the contour integral in the complex-plane

Along the contour |Z| = 3, taken counter-clockwise is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 57

(Using Cauchy‟s Integral formula)

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 58

Consider the composition of f and g, i.e., ( f o g ) ( x ) = f (g ( x )). The number of discontinuities in ( f o g ) ( x ) present in the interval ( -∝ ,0 ) is:

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 58

Alternative Method:

f ( x ) = 1 - x for x ≤ 0 and g ( x ) = - x for x < 0

∴ Both f(x) and g(x) are continuous when x < 0

⇒ (fog) (x) is also continuous for x< 0

(Since the composite function of two continuous functions is continuous)

∴ The number of discontinuities in the interval ( -∝ ,0 ) i.e., x < 0 is '0'

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 59

A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω , and the shunt field resistance is 240Ω . The no load speed, in rpm, is _______________.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 59

N ∝ Eb

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 60

A 10 ½ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.


Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 61

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y} , where var {.} denotes the variance, equals

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 62

he figure below shows a half-bridge voltage source inverter supplying an RL-load with 
R = 40Ω and L = (0.3/π)H. The desired fundamental frequency of the load voltage is 50 Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. M = 0.6. At 50 Hz, the RL-load draws an active power of 1.44 kW. The value of DC source voltage VDC in volts is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 62

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 63

The range of K for which all the roots of the equation s3 + 3s2 + 2s + K = 0 are in the left half of the complex s-plane is

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 63

C.E = s3 + 3s2 + 2s + k = 0

If system to be stable

K > 0∩6 > K

0< K < 6

Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 64

The eigen values of the matrix given below are

Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 64

Characteristic equation is 

⇒ -λ (4λ + λ2 + 3) = 0

⇒ λ(λ+1)(λ+3) = 0

⇒ λ = 0, -1, -3 are the eigen values

*Answer can only contain numeric values
Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 65

A 3-phase 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25Ω and 3.925Ω respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.


Detailed Solution for Practice Test: Gate Electrical Engineering GATE 2017 Paper - Question 65

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