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QUESTION: 1

Directions

Q. No. 1 – 5 Carry One Mark Each

Q. Research in the workplace reveals that people work for many reasons _______________ .

Solution:

Grammatically, besides is an adverb or a preposition, and beside a preposition. Beside means next to. As a preposition, besides means in addition to or apart from. As an adverb, besides means as well or furthermore.

Here, we use “besides” as a preposition meaning “in addition to”.

“besides money” is correct choice.

QUESTION: 2

The probability that a k-digit number does NOT contain the digits 0.5, or 9 is

Solution:

Each digit can be filled in 7 ways as 0, 5 and 9 is not allowed, so each of these places can be filled by 1, 2, 3, 4, 6, 7, 8.

So required probability is

QUESTION: 3

Find the smallest number y such that y x 162 is a perfect cube.

Solution:

Factorization of 162 is 2 x 3 x 3 x 3 x 3 x y= 162 is a perfect cube

y x 3 x 3 x 3 x 3 x 3 = Perfect cube

For perfect cube 2's & 3's are two more required each.

QUESTION: 4

After Rajendra Chola returned from his voyage to Indoneisa, he _______ to visit the temple in Thanjavur.

Solution:

QUESTION: 5

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

Solution:

Assume, they are looking to the center of circular table, then the possible arrangement is:

QUESTION: 6

Directions

Q. No. 6 – 10 Carry Two Marks Each

Q.

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

Solution:

Out of six people, 3 place definitely occupied by right handed people as atleast 2 women are there so these two will sit adjacently. Now as only one seat is left it will be occupied by a left handed man because on right side of this seat is sitting an right handed man.

Therefore, answer should be 2 women.

QUESTION: 7

The expression is equal to.

Solution:

QUESTION: 8

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m. Which of the villages P,Q,R,S,T get submerged?

Solution:

The given contour is a hill station, the peak point of this hill station is P, it is under a contour of 550. At floods, the water level is 525m. So the village of R, S and T are under a contour of 500. Therefore these villages are submerged.

QUESTION: 9

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white, Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

Solution:

As there are 4 people A,G,N,S and 4 colours so without any restriction total ways have to be 4 x 4= 16

Now, Arun → dislikes Red and

Shweta → dislies white

So, 16-2 = 14 ways

QUESTION: 10

“The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history.”

Which of the following statements best reflects the author‟s opinion?

Solution:

*Answer can only contain numeric values

QUESTION: 11

Directions

Q. No. 11 – 35 Carry One Mark Each

Q.

Consider g(t) =

Here, represents the largest integer less than or equal to t and denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

Solution:

If we plot the above signal, we get

Since this wave form contain hidden half wave symmetry, even harmonics does not exist.

Thus coefficient of second harmonic component of Fourier series will be zero.

QUESTION: 12

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are V_{an} =220sin (100πt ) V and

i_{a} = 10 sin(100πt)A, respectively. Similarly for phase-b the instantaneous voltage and current are V_{tm} = 220cos(100πt )V and i_{b} = 10 cos(100πt)A, respectively.

The total instantaneous power flowing form the source to the load is

Solution:

= 2200W

*Answer can only contain numeric values

QUESTION: 13

A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30Ω per phase. The load angle is 30^{o}. The power delivered to the motor in kW is _______

Solution:

P = 838.31 kW

QUESTION: 14

For a complex number z,

Solution:

QUESTION: 15

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?

Solution:

The Gravitational force of alteration between any two particles shown above is made much negligible when compared to coloumbic force of alteration between electron and proton.

Force of alteration

Due to this force, the electron as well as the proton will move towards each other, since

m_{o} << m_{p} , the speed and acceleration of the electron will be much greater than that of proton. This causes electron to collide with the neutron faster when compared to proton.

QUESTION: 16

Let z ( t ) = x ( t )* y ( t ) , where " * " denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).

Solution:

z ( t ) = x ( t ) * y ( t )

⇒ z(s) = x(s) . y(s)

Converting into Laplace transform and applying time sealing property.

z(ct) = c.x(ct) * y(ct)

QUESTION: 17

A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are Y11 = - j12pu, Y22 = - j15pu and Y33 = - j7pu The per unit values of the line reactances p, q and r shown in the figure are

Solution:

Y_{11} = y_{10} + y_{12} + y_{13} = - j12 =

-( jq^{1}+jr^{1} )

∴ q^{1} + r^{1} = +12

Y_{22}= j15 = y_{20} + y_{21} + y_{23} =

-(jq^{1 }+jp^{1} )

∴ p^{1} + q^{1} = +15

*Answer can only contain numeric values

QUESTION: 18

The equivalent resistance between the terminals A and B is ____ Ω.

Solution:

The Ckt will become

R_{AB } = 1 + 1.2 + 0.8 = 3Ω

QUESTION: 19

The Boolean expression simplifies to

Solution:

*Answer can only contain numeric values

QUESTION: 20

The following measurements are obtained on a single phase load:

If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ________.

Solution:

P = VIcosø

QUESTION: 21

The transfer function of a system is given by, Let the output of the system be

v_{o}( t ) = V_{m} sin( ωt + φ) for the input v_{i} (t) = V sin(ωt) . Then the minimum and maximum

values of φ (in radians) are respectively

Solution:

QUESTION: 22

The matrix has three distinct eigenvalues and one of its eigenvectors is Which one of the following can be another eigenvector of A?

Solution:

By the properties of Eigen values and Eigen vectors, another eigen vector of A is The eigen vectors corresponding to distinct eigen values of a real symmetric matrix are orthogonal i.e., pair wise dot product is zero.

QUESTION: 23

For the power semiconductor devices IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?

Solution:

MOSFET → Majority carrier device (NMOS, PMOS)

Diode→ both majority & minority carrier device

Transister → Npn, pnp

IGBT → input is MOSFET, Output is BJT

*Answer can only contain numeric values

QUESTION: 24

Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30^{o }is _______.

Solution:

PM = 180 + ∠G_{ω=ωgc}

QUESTION: 25

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

Solution:

Flux always chooses less reluctance path. So flux tried to flow inside the conductor and closer to the axis of the cylinder.

*Answer can only contain numeric values

QUESTION: 26

where R is the region shown in the figure and c = 6 x 10^{-4}. The value of I equals________.

Solution:

OR

QUESTION: 27

Consider the system with following input-output relation y[n] = (1 + ( -1)n ) x [ n ]where, x[n] is the input and y[n] is the output. The system is

Solution:

Given y [ n ] = (1 + ( -1)n ) x [ n ]

For time invariance

Since Since (1) is not equal to (2) system is time variant

For inverse system

For each unique x [n ] , there should be unique y [n ]

If x[n] = δ[n-1]

y[n] = [ 1 + (-1)^{n} ] δ[n-1]

⇒ y[1] = 0

if x[n] = 2δ[n-1]

y[n] = [ 1+(-1)^{n} ] 2δ (n-1)

y(1) = 0

For two different inputs we have same output. Thus one to one mapping is not possible. Hence the systems is non invertible

QUESTION: 28

The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of

Solution:

The delay line should be inverted in VDP (Y-channel) only.

*Answer can only contain numeric values

QUESTION: 29

A 3-phase voltage source inverter is supplied from a 600V DC source as shown in the figure below. For a star connected resistive load of 20Ω per phase, the load power for 120^{o} device conduction, in kW is __________.

Solution:

V_{dc} =600V

R_{L} = 20Ω / Ph 120^{o} mode

RMS value of phase voltage ( V_{p} ) = 0.4082V_{dc} =244.92V

QUESTION: 30

A closed loop system has the characteristic equation given by s^{3 }+ Ks^{2} + ( K + 2 )s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

Solution:

Given CE = s^{3} + ks^{2} + (k+ 2)s + 3 = 0

For stable

k(k+2) >3

k^{2} + 2k -3 >0

(k-1)(k+3) > 0

k > -1 ∩ k > -3

k >1

OR

by R-H criteria

QUESTION: 31

A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is

Solution:

Rotor speed should be greater than syn.speeed, to ge inductance generator mode.

QUESTION: 32

For the circuit shown in the figure below, assume that diodes D_{1}, D_{2} and D_{3} are ideal. The DC components of voltages v_{1} and v_{2}, respectively are

Solution:

*Answer can only contain numeric values

QUESTION: 33

A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______.

Solution:

Total no of buses=10

Given G_{1} = slack bus, G_{2}=generator/PQ bus

∴ G_{3}_{ }and G_{4 } are PV buses

PQ buses → L_{1},L_{2}, L_{5},L_{6} (4)

Voltage controlled PV buses → L_{3}, L_{4} (2)

Minimum no of nonlinear equations to be solved 2 x10-2-4=14

*Answer can only contain numeric values

QUESTION: 34

The power supplied by the 25 V source in the figure shown below is ________W.

Solution:

KCL

I + 0.4I = 1.4 I

⇒1.4I =14

⇒ I = 10A

The power supplied by 25 V = 25x 10= 250W

*Answer can only contain numeric values

QUESTION: 35

In the converter circuit shown below, the switches are controlled such that the load voltage v_{o}(t) is a 400 Hz square wave.

The RMS value of the fundamental component of v_{o}(t) in volts is _______.

Solution:

QUESTION: 36

Directions

Q. No. 36 – 65 Carry Two Marks Each

Q.

The output expression for the Karnaugh map shown below is

Solution:

*Answer can only contain numeric values

QUESTION: 37

A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4 Ω and 0.1 Ω respectively. The load torque varies as the square of the speed. The flux in the motor may be taken as being proportional to the armature current. To reduce the speed of the motor by 50% the resistance in ohms that should be added in series with the armature is _________.

Solution:

E_{b}_{1 }= 220 - 30(0.5) = 205 volts

E_{b2} = 220 - I_{a2} (0.5 + R_{x} )

Given T ∝ N^{2 } and Ø ∝ I_{R}

We know that, in series motor ⇒

QUESTION: 38

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is:

Solution:

QUESTION: 39

The load shown in the figure is supplied by a 400 V (line to line) 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three watt-meters W_{1}, W_{2} and W_{3} read 577.35 W each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

Solution:

If the switch is connected to Neutral, then each wattmeter will read 1 - Ø power.

QUESTION: 40

Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

Given V_{1 }= A_{1}V_{2} +B_{1}I_{2}

I_{1} = C_{1}V_{2}+ D_{1}I_{2}

V_{2} = A_{2}V_{3} +B_{2}I_{3}

I_{2} = C_{2}V_{3} + V_{2}I_{3}

A_{1} , B_{1} , C_{1} , D_{1} , A_{2} , B_{2} , C_{2} and D_{2} are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source V_{T} and impedance Z_{T} connected in series, then

Solution:

*Answer can only contain numeric values

QUESTION: 41

The circuit shown in the figure uses matched transistors with a thermal voltage V_{T} = 25mV.

The base currents of the transistors are negligible. The value of the resistance R in kΩ that is required to provide 1 μA bias current for the differential amplifier block shown is ______.

Solution:

*Answer can only contain numeric values

QUESTION: 42

The figure below shows an uncontrolled diode bridge rectifier supplied form a 220 V, 50 Hz 1-phase ac source. The load draws a constant current I_{o} = 14A. The conduction angle of the diode D_{1} in degrees is___________.

Solution:

Average reduction in output voltage due to Ls

QUESTION: 43

Consider the differential equation

There exists a unique solution for this differential equation when t belongs to the interval

Solution:

If t ≠ 9, 9 then the solution exists.

Options (b), (c), (d) contain either -9 or 9 or both. So answer is option A

QUESTION: 44

A separately excited DC generator supplies 150 A to a 145 V DC grid. The generator is running at 800 RPM. The armature resistance of the generator is 0.1 Ω . If the speed of the generator is increased to 1000 RPM, the current in amperes supplied by the generator to the DC grid is

Solution:

QUESTION: 45

In the circuit shown below, the maximum power transferred to the resistor R is _______ W.

Solution:

The maximum power transferred to

QUESTION: 46

Let a causal LTI system be characterized by the following differential equation, with initial rest condition

Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

Solution:

Given causal LTI system

QUESTION: 47

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

Solution:

QUESTION: 48

The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for t ≥ 0, is

Solution:

at t = 0^{-}

For t ≥ 0

QUESTION: 49

The bus admittance matrix for a power system network is There is a transmission line, connected between buses 1 and 3, which is represented by the circuit shown in figure.

If this transmission line is removed from service, What is the modified bus admittance matrix?

Solution:

When the line 1-3 is removed

z_{13} = 0.05 = z_{31 }

QUESTION: 50

In the system whose signal flow graph is shown in the figure, U_{1}(s) and U_{2} (s) are inputs. The

transfer function

Solution:

*Answer can only contain numeric values

QUESTION: 51

For a system having transfer function a unit step input is applied at time t=0.

The value of the response of the system at t=1.5 sec is __________.

Solution:

Apply Inverse L.T

y(t) = u(t) - 2e^{-t}u(t)

y(1.5) = 1 - 2e^{-1.5} = 1- 0.44626

y(1.5) = 0.5537

*Answer can only contain numeric values

QUESTION: 52

The magnitude of magnetic flux density (B) in micro Teslas ( μT ) at the center of a loop of wire wound as a regular hexagon of side length 1m carrying a current (I=1A), and placed in vacuum as shown in the figure is __________.

Solution:

For a finite length conductor B at a point P

QUESTION: 53

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sinδ , where δ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of δ as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is P_{max} Sinδ , the value of P_{max} , in pu is

Solution:

Using equal area criterion

A_{1} = A_{2}

*Answer can only contain numeric values

QUESTION: 54

A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Z_{m} = (12.50 + j15.75) Ω (main winding),

Z_{a} = (24.50 + j12.75) Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.

Solution:

QUESTION: 55

A function f(x) is defined Which one of the following statements is TRUE?

Solution:

does not exists, for any values of a and b

∴ f (x ) is not differentiable at x =1 , for any values of a and b.

*Answer can only contain numeric values

QUESTION: 56

Consider a causal and stable LTI system with rational transfer function H(z). Whose corresponding impulse response begins at n = 0. Furthermore, H(1) = 5/4. The poles of H(z) are for k = 1,2,3,4. The zeros of H(z) are all at z = 0. Let g[n] = j^{n}h[n]. The value of g[8] equals ----.

Solution:

*Answer can only contain numeric values

QUESTION: 57

Only one of the real roots of f ( x ) = x^{6} - x - 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is ________.

Solution:

*Answer can only contain numeric values

QUESTION: 58

Two parallel connected, three-phase, 50Hz, 11kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are 1Ω and 3Ω respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is ________.

Solution:

→ syn. Condencors

→ current‟s supplied both the machines are same

As the two motors, supplying reactive power only, the phasor diagaram will be

*Answer can only contain numeric values

QUESTION: 59

The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero).

Solution:

QUESTION: 60

Let the signal be passed through an LTI system with frequency

response H (ω) , as given in the figure below

The Fourier series representation of the output is given as

Solution:

Given x (t ) is a periodic signal for which Fourier transform x ( ω) is to be calculated

QUESTION: 61

The logical gate implemented using the circuit shown below where. V_{1} and V_{2} are inputs (with 0 V as digital 0 and 5 V as digital 1) and V_{out} is the output is

Solution:

So, this logic level o/p is showing the functionality of NOR-gate.

QUESTION: 62

A load is supplied by a 230 V, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that 1 kW ≤ P ≤ 2kW and 1 kVAR ≤ Q ≤ kVAR . A capacitor connected across the load for power factor correction generates 1 kVAR reactive power. The worst case power factor after power factor correction is

Solution:

Under worst case,

P_{max} = 2 kW

Q_{max} = 2 kVAR

cos 45 = 0.707lag

QUESTION: 63

The input voltage V_{DC} of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio D of the converter for which the magnitude of the steady state output voltage remains constant at 48 V is

Solution:

*Answer can only contain numeric values

QUESTION: 64

A three-phase, three winding Δ /Δ / Y (1.1kV/6.6kV/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV winding and 300 kVA load at 0.6 power factor lag from the 400 V winding. The RMS line current in ampere drawn by the 1.1 kV winding from the mains is _______.

Solution:

3 - Ø , 3 - winding T/F

Δ /Δ / Y

per phase representation

QUESTION: 65

Consider the line integral where z = x + iy. The line C is shown in the figure below.

Solution:

curve " C " is y = x ⇒ dy = dx

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

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

Video | 06:55 min

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