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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?

Solution:

From the given data, the following is formed

∴ The building "V‟ is in the middle

QUESTION: 2

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

Solution:

QUESTION: 3

Choose the option with words that are not synonyms.

Solution:

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

Solution:

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?

Solution:

x + y = 20 , x = MCQ

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

⇒ x = 15 , y = 5

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?

Solution:

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.

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?

Solution:

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.

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:

Solution:

QUESTION: 9

X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X^{3} will have

Solution:

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

Suppose ( 47)^{3} = 2 + 2 + 2 digits in (47)^{3}

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

QUESTION: 10

The number of roots of e^{x }+ 0.5x^{2} - 2 = 0 in the range [ -5, 5] is

Solution:

f ( x ) = e^{x} + 0.5x^{2} - 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].

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?

Solution:

QUESTION: 12

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

Solution:

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

Solution:

Here R is red ball, B is black ball

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

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

Solution:

QUESTION: 15

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

Solution:

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

QUESTION: 16

The figures show diagrammatic representations of vector fields respectively.

Which one of the following choices is true?

Solution:

*Answer can only contain numeric values

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 _________

Solution:

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.

Solution:

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

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

Solution:

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, Y_{bus} and Z_{bus} are bus admittance matrix and bus impedance matrix, respectively, each of size 2 x 2. Which one of the following statements is true?

Solution:

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

Solution:

*Answer can only contain numeric values

QUESTION: 22

Let x and y be integers satisfying the following equations

2x^{2 }+ y^{2} = 34

x + 2y = 11

The value of ( x +y ) is ________.

Solution:

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

∴ x + y = 7

*Answer can only contain numeric values

QUESTION: 23

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

f(x,y,z) = (x^{2} + y^{2} -2z^{2}) (x^{2} + y^{2} )

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

Solution:

*Answer can only contain numeric values

QUESTION: 24

For the given 2-port network, the value of transfer impedance Z_{21} in ohms is_______

Solution:

*Answer can only contain numeric values

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.)

Solution:

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

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 T_{1} and T_{2} are 90^{o} and 270^{o} , respectively.

The RMS value of the current through diode D_{3} in amperes is _____

Solution:

0A since D_{2} is OFF and it will not turn ON for R load.

*Answer can only contain numeric values

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 ________.

Solution:

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

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

Solution:

3 - Ø S.C.I.M

4 - P s = 0.02

400V Ø_{r} ⇒ N_{r}

flux speed is same as stator flux speed.

QUESTION: 29

Two resistors with nominal resistance values R_{1} and R_{2} have additive uncertainties

ΔR_{1 }and ΔR_{2} , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

Solution:

*Answer can only contain numeric values

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.)

Solution:

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?

Solution:

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

QUESTION: 32

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

Solution:

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

Solution:

*Answer can only contain numeric values

QUESTION: 34

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

Solution:

QUESTION: 35

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

Solution:

Higher than the terminal voltage.

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?

Solution:

*Answer can only contain numeric values

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 D_{ab} = D_{bc} = D_{ca} = 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 _______

Solution:

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

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.

Solution:

Assume No – load speed regulations are equal

From similar triangles method

Given that P_{1} + P_{2} = 600MW

150x = 600

x = 4

∴The load supplied by largest machine is P_{2} = 100 x 4 = 400MW

QUESTION: 39

For the network given in figure below, the Thevenin's voltage V_{ab} is

Solution:

The equivalent CKT is

Apply nodal

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

Solution:

Consider

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

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

Solution:

By solving above equation

We get E_{b1} = 219.39 and E_{b2} = 0.61

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

Solution:

QUESTION: 43

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

Solution:

*Answer can only contain numeric values

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.

Solution:

P_{a} = P_{m} - Pe

= 60 - 0 = 60mw

QUESTION: 45

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

Which one of the following is TRUE?

Solution:

QUESTION: 46

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

Solution:

C.E = s^{2} + 6ks + 2s + 5 = 0

*Answer can only contain numeric values

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

Solution:

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.

QUESTION: 48

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

Solution:

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

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.)

Solution:

Given is Buckboost converter

*Answer can only contain numeric values

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.)

Solution:

*Answer can only contain numeric values

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_________

Solution:

*Answer can only contain numeric values

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:R_{1} = 0.3Ω, R_{2} = 0.3Ω, X_{1} = 0.41Ω, X_{2} = 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 __________.

Solution:

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

*Answer can only contain numeric values

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 _________.

Solution:

Hint: Obtained regulation should be negative.

*Answer can only contain numeric values

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_____.

Solution:

25KVA, Y - D, 3.3kV - Δ

N : N = 5 :1

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

Solution:

*Answer can only contain numeric values

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 4πR^{2}a and that of the drop is 4/3πr^{3} .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.)

Solution:

Charge must be same

QUESTION: 57

The value of the contour integral in the complex-plane

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

Solution:

(Using Cauchy‟s Integral formula)

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:

Solution:

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

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 _______________.

Solution:

N ∝ E_{b}

*Answer can only contain numeric values

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 _______.

Solution:

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

Solution:

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 V_{DC} in volts is

Solution:

QUESTION: 63

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

Solution:

C.E = s^{3} + 3s^{2} + 2s + k = 0

If system to be stable

K > 0∩6 > K

0< K < 6

QUESTION: 64

The eigen values of the matrix given below are

Solution:

Characteristic equation is

⇒ -λ (4λ + λ^{2} + 3) = 0

⇒ λ(λ+1)(λ+3) = 0

⇒ λ = 0, -1, -3 are the eigen values

*Answer can only contain numeric values

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 ________.

Solution:

### GATE 2017 Solution, Set 1, Signal, Electrical Engineering, GATE

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