1487180513EE_2017-_Session_2_(Kreatryx_Solutions) (1)
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GATE 2017 EE - Session 2
Kreatryx GATE 2017 EE – Session 2 Answer Key and Solutions
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GATE 2017 EE - Session 2
01. In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 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 _________ . 01. Ans: 61 Solution: Size of Jacobian = 2 × PQ buses + PV buses 100 = 2 × PQ + 20 PQ = 40 Total no. of buses = PQ + PV + Slack bus= 40 + 20 + 1 = 61 bus 02. For a 3-input logic circuit shown below, the output Z can be expressed as
(a) Q R (c) Q R
(b) PQ R (d) P Q R
02. Ans: (c) X PQ (P Q)
Y QR (Q R) Z XYQ (P Q) (Q R) Q
Z (PQ PR RQ)Q PRQ RQ RQ(P 1) RQ Q R
03. Let y 2 2y 1 x and
x y 5 . The value of x y equals _________. (Give the answer
up to three decimal places) 03. Ans: 5.732 x y 5
x 5 y ………….(i)
Since, y2 – 2y + 1 = x y2 – 2y + 1 = (5 – y)2 y2 2y 1 25 y 2 10y 8y = 24 y=3 © Kreatryx. All Rights Reserved.
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From eq. (i) x 53 x=4
Hence, x y 4 3 5.732 04. The mean square value of the given periodic waveform f(t) is ______
04. Ans: 6 The period of given waveform is 4 sec Rams value of the periodic wave form f(t) 1
frms
1 T f 2 t dt T T
2
frms
2.7 3.7 1 0.7 2 1 2 42 dt ( 2)2 dt 02 dt 16 1 4 2 6 4 0.7 2.7 4 0.3
1
Hence, mean square value =
6
2
1
6
05. 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 (a) 1500 (b) 1470 (c) 157 (d) 154 05. Ans: (c) 120 120 50 f 1500 rpm P 4 This speed is in terms of mechanical angle. 2 Speed in mechanical rad/sec = 1500 50 mech rad/sec 60 Since, both stator & rotor flux rotate at synchronous speed with respect to stator. Hence, speed sensed by stationery observer = 50 rad/ sec
Synchronous speed =
Speed 50 157 rad/ sec © Kreatryx. All Rights Reserved.
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06. Consider a function f(x,y,z) given by f(x, y,z) (x2 y 2 2z2 ) (y 2 z2 ) . The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is ____________ . 06. Ans: 40 f(x, y, z) (x2 y2 2 z2 ) (y2 z2 ) x2 y 2 y 4 2y 2 z2 x2z2 y 2 z2 2z 4 f 2xy 2 2xz 2 x at point (2, 1, 3) f 2 2 12 2 2 32 40 x
07. The pole-zero plots of three discrete-times 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? (a) All three are high-pass filters. (b) All three are band-pass filters. (c) All three are low-pass filters. (d) P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter. 07. Ans: (b) The transfer function of three filters shown are z2 1 1 P: H(z) 1 2 2 z z j j2 H(e ) (1 e ) e j (e j e j ) 2 je j sin
This is amplitude response of band pass filter z2 1 Q: H(z) 2 z 0.25 In frequency domain © Kreatryx. All Rights Reserved.
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e j2 1 e j2 0.25 This function again will have zero crossing at 0 & and hence acts as Band pass H(e j )
filter. z2 1 z2 1 In frequency domain e j2 1 H(e j ) j2 e 1 This function has zero crossing at 0 & . So, this also acts as Band pass filter.
R: H(z)
08. The nominal- circuit of a transmission line is shown in the figure.
Impedance Z 10080 and reactance X 3300 . The magnitude of the characteristic impedance of the transmission line, in , is ______________ . (Give the answer up to one decimal place) 08. Ans: 406.2 In nominal pi-model
Hence, reactance X represents admittance
Y 2
Y 1 2 X 2 Y X Characteristic Impedance,
Zc
Z Z ZX 100800 3300900 406.20185 Y 2/X 2 2
ZC 406.2
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09. 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 (a) 1.5 kHz (b) 2 kHz (c) 3 kHz (d) 4.5 kHz 09. Ans: (d) fy no. of horizontal tangencies 3 fx no. of vertical tangencies 2 fy 3
3 4.5 kHz 2
10. The figures show diagrammatic representations of vector fields X, Y, and Z . Respectively. Which one of the following choices is true?
(a) .X 0, Y 0, Z 0
(b) .X 0, Y 0, Z 0
(c) .X 0, Y 0, Z 0
(d) .X 0, Y 0, Z 0
10. Ans: (c) The vector field X diverges from a point Hence .X 0 The other two vector field are rotating or curling Hence Y 0 and Z 0 11. In the circuit shown, the diodes are ideal, the inductance is small, and I0 0 . Which one of the following statements is true?
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(a) D1 conducts for greater than 180° and D2 conducts for greater than 180°. (b) D2 conducts for more than 180° and D1 conducts for 180°. (c) D1 conducts for 180° and D2 conducts for 180°. (d) D1 conducts for more than 180° and D2 conducts for 180°. 11. Ans: (a) The inductance given in the problem is source inductance due to which there is overlap between the two diodes. Hence, each diode conducts for (180 ) where is overlap angle. 12. 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 90° and 270°, respectively.
The RMS value of the current though diode D3 in amperes is ___________ 12. Ans: 0 Since the load is purely resistance, the conduction does not go beyond 180°. Hence, the freewheeling diode does not come into conduction. So, rms current through D3 is 0. 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 color. The probability to get a red ball in the second draw is 1 4 (a) (b) 2 9 5 6 (c) (d) 9 9 13. Ans: (a) There can be two possibilities Case-1: First ball drawn is red 4 P(second red) 9 © Kreatryx. All Rights Reserved.
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Case-2: First ball drawn is black 5 P(second red) 9 5 1 10 2 4 1 5 1 1 Hence, P(second red) 9 2 9 2 2
The P(first = red) or P(first = black) =
14. Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that 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 __________. 14. Ans: 0.9 let time of arrival be a random variable X
Uniform distribution is shown above Assuming waiting time to be g(x), a function of arrival time. If 0 x 2, g(x) 0 (green light) (red light)
2 x 5, g(x) 5 x
The second case says that vehicle will wait till next green light occurs. Average waiting time 5 5 2 1 1 E g(x) g(x) fx (x) dx 0 dx (5 x) dx 5 5 0 0 2 5
1 1 x2 1 1 21 9 E g(x) 5x 5(5 2) (52 22 ) 15 0.9 5 2 2 5 2 2 10 5
15. The figure shows the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where is a complex number with non-zero real and imaginary parts.
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For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 × 2. Which one of the following statements is true? (a) Both Ybus and Zbus are symmetric (b) Ybus is symmetric and Zbus is unsymmetric (c) Ybus is unsymmetric and Zbus is symmetric (d) Both Ybus and Zbus are unsymmetric 15. Ans: (d)
For the above network V E1 2 I1 I2 By KVL V1 E1 I1 Z
V2 ( Z) I2
In matrix form, V1 1/ Z V2 I2 I1 0 Since A D , the system is asymmetric and hence YBus and ZBus will also be asymmetric. 16. 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).
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16. Ans: 100 The given circuit can be redrawn as.
The network of resistors is a balanced bridge, so the network is reduced to
Reg (10 || 10) 5
Current in RC circuit will be = RC 5
V t/ e R
10 t/5 e 2e t/5 5 Power supplied by source = Vi 20et/5 i(t)
energy delivered 20e t/5dt 20 5 e t/5 100 J 0
0
17. Two resistors with nominal resistance values R1 and R2 have additive uncertainties R1 and R2 , respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is 2
2
2
R R R1 R 2 (a) R1 R 2 2
2
R R R1 R 2 (b) R 2 R1
2
2
R R (c) R 2 R1 R1 R 2
2
R R (d) R1 R 2 R1 R 2
17. Ans: (a) When two resistances are connected in parallel equivalent resistance, R
R1 R 2 R1 R 2
R = f(R1, R2) Standard deviation in R 1
2 R 2 2 R 2 2 R R1 R 2 R 2 R1
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18. The transfer function C(s) of a compensator is given below. s s 1 1 0.1 100 C(s) 1 s 1 10s The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is (a) 0.1 1 (b) 1 10 (c) 10 100
(d) 100
18. Ans: (a) The pole zero plot for the compensator is,
This is pole zero plot of lead lag compensator and hence produces phase lead for 0.1 1 and phase lag for 10 100 19. Let x and y be integers satisfying the following equations 2x2 y 2 34
x 2y 11 The value of (x + y) is ________ . 19. Ans: 7 2x2 + y2 = 34 and x + 2y = 11 Substitute x = 11 – 2y in first equation 2(11 2y)2 y 2 34
2(121 4 y2 44y) y 2 34 9y2 – 88y + 208 = 0 y = 4 and 5.77 since x and y are integers y=4 x = 11 – 2 × 4 = 3 Hence x + y = 7 20. For the given 2-port network, the value of transfer impedance z21 in ohms is _________
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20. Ans: 3 By star delta transformation
2 4 1 242 22 R2 0.5 242 2 4 R3 1 2 42 This network is now converted to a standard T-network 13 3 4 3 Z 0.5 3 3 3.5 3 Hence, Z21 3 R1
21. If a synchronous motor is running at a leading power factor, its excitation induced voltage (Ef) is (a) Equal to terminal voltage Vt (b) Higher than the terminal voltage Vt (c) Less than terminal voltage Vt (d) Dependent upon supply voltage Vt 21. Ans: (b) Synchronous motor operates at leading pf in case of over-excitation. Hence, excitation is more than terminal voltage. 22. A three-phase voltage source inverter with ideal devices operating in 180° 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 (a) (c)
Vdc
(b)
3Vdc
(d)
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22. Ans: (b) The waveform for phase voltage of three phase inverter in 180° conduction mode is
RMS value of phase voltage =
2 V 3 dc
RMS value of fundamental = DF × RMS phase voltage = Peak value of fundamental.
2
3 2 2 Vdc V 3 dc
2 2 Vdc Vdc
23. 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 (a) Uniformly over the entire volume of the sphere (b) Uniformly over the outer surface of the sphere (c) Concentrated around the center of the sphere (d) Along a straight line passing through the center of the sphere 23. Ans: (b) In case of perfect conductor, no charge can be inside the surface of conductor & hence charge will be uniformly distributed over the surface of sphere. 24. 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 (a) 25 (b) 50 (c) 100 (d) 300 24. Ans: (c) In single phase full bridge rectifier, the output voltage is as shown below,
Hence, fo = 2fs Ripple frequency at output = 2 × 50 = 100 Hz © Kreatryx. All Rights Reserved.
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25. When a unit ramp input is applied to the unity feedback system having closed loop transfer function
C(s) Ks b 2 , a 0, b 0, K 0 , the steady rate error will be R(s) s as b
a b aK (d) b
(a) 0 (c)
(b)
aK b
25. Ans: (d) The transfer function is, Ks b G(s) 2 s as b Ks b 1 C(s) R(s) G(s) 2 2 s as b s
1 R(s) 2 s
Ks b 1 2 s as b 2 1 s a K s E(s) 2 s s2 as b Steady state error, e() lim sE(s) error R(s) C(s)
1 s2
s0
e() lim s0
s s (a K)s a K b s2 s2 as b 2
26. 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 (a) 0 K 6 (b) 0 K 16 (c) 6 K 36 (d) 6 K 16 26. Ans: (a) Equation: s3 + 3s2 + 2s + K = 0 Forming Routh Array 1 2 s3 2 3 K s 1 6 k s 3 K s0 For all roots in left half plane, all coefficients in first column must be positive K 0 and 6 K 0, K 6 Hence, range 0 < K < 6
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27. 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 (a) 33 53.1
(b) 60 53.1
(c) 60 53.1
(d) 180 53.1
27. Ans: (c) For a star connected load
P 3 VL IL cos 432 3 208 IL 0.6
IL 1.9985 A Assuming voltage as reference Van
208 3
0 V
Ia 1.9985 53.13 A Z
Van 60 53.13 Ia
28. A star-connected, 12.5kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R1 0.3 , R2 0.3 , X1 0.41 , X2 0.41 . 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 ___________. 28. Ans: 70.0533 For star connected motor, Vph Ist (R1 R2 )2 (X1 X2 )2 At 20 Hz frequency, the reactance changes Xf © Kreatryx. All Rights Reserved.
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f 20 x x x f 60 3 0.41 x1 x2 3 80
x
Ist
3 0.82 0.62 3
2
70.0533 A
29. 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
(a) 1000 samples/s (c) 2000 samples/s
(b) 1500 samples/s (d) 3000 samples/s
29. Ans: (b) The spectrum of signal after multiplication with cos (1000 t) is ,
After passing through LPF,
Maximum frequency, m 1500 By Nyquist criteria, s 2m 3000 rad/ sec fs
3000 1500 Hz 2
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x,
30. Let g(x)
x 1,
x 1
1 x, x 0 and f(x) 2 . x 1 x , x0
Consider the composition of f and g. i.e., f g x f g x . The number of discontinuities in
f g x
present in the interval ,0 is:
(a) 0 (c) 2
(b) 1 (d) 4
30. Ans: (a) x, x 1 g(x) x 1, x 1
1 g(x), g(x) 0 fog(x) 2 g(x) 0 g(x) , Since g(x) 0, 0 x 1 1 ( x), fog(x) 2 g(x) ,
( x) , fog(x) 1 x, (x 1)2 , 2
0 x 1 x 0 , 1 x
x 0 0 x 1 1x
Hence, there are a total of 2 discontinuities at x = 0 and at x = 1 but not in ( , 0) 31. 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. 31. Ans: 400 Assuming both machine have equal no-load frequency ‘f’. fFL1 f(1 0.06) 0.94 f
fFL2 f(1 0.04) 0.96 f The load shared by machine 1
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f f P1 300 f 0.94f The load shared by machine 2 f f P2 400 f 0.96f
Total load P1 + P2 = 600
300 (f f ) 400 (f f ) 600 0.06 f 0.04 f 50 (f f) 100 (f f ) 6f 144 f 150 Load shared by larger machine i.e. machine 2 144 f f 150 6 16 P2 400 400 400 MW 0.04 f 150 0.04 0.04 144f 150 f ; f
32. The figure below shows a half-bridge voltage source inverter supplying an RL-load with 0.3 R 40 and L 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
(a) 300 2 (c) 500 2
(b) 500 (d) 1000 2
32. Ans: (c) The peak value of fundamental voltage Vpf 0.6 Vdc 0.3 30 Z R jX 40 j30 50 36.86
At 50 Hz, X 2f L 100
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Since, active power drawn = 1.44 kW Irms2 R 1440 1440 36 40 6A
Irms2
Irms
Vrms Irms Z 50 6 300 V peak value 300 2 0.6 Vdc Vdc
300 2 500 2 V 0.6
33. 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 (a) s = –1 (b) s 5 (c) s = –5 (d) s 5 33. Ans: (b) The characteristic equation can be reframed as s2 6Ks 2s 5 0 (s2 2s 5) 6Ks 0 6Ks 0 s 2s 5 So, it can be considered as unity feedback system with 6Ks and poles = 1 2j G(s) 2 s 2s 5 The intersection with real axis is break away point (s2 2s 5) K 6s 2 dk 2s 2 6s 6(s 2s 5) 0 2 ds 6s 1
2
6s2 30 0
s 5
The root locus looks like as shown,
Hence, valid intersection with real axis is at s 5 © Kreatryx. All Rights Reserved.
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34. A cascade system having the impulse responses h1 (n) 1, 1 and h2 (n) 1,1 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
y (n) 1,2,1, 1, 2, 1 is
(c) x(n) 11,1,1,1
(d) x(n) 1,2,2,1
(a) x(n) 1,2,1,1
(b) x(n) 1,1,2,2
34. Ans: (d)
1 z
H1 (z) 1. z 1. z 1 1 z 1 H2 (z) 1. z 1. z 1
1
H(z) H1 (z) H2 (z) (1 z 1 ) (1 z 1 ) (1 z 2 )
Y(z) 1. z 2. z 1 1.z 2 1z 3 2z 4 1z 5 Y(z) (1 z 3 ) 2 z 1 (1 z 3 ) z 2 (1 z 3 ) Y(z) (1 z 3 ) (1 2z 1 z 2 )
Y(z) (1 z 1 ) (1 z 2 z 1 ) (1 z 1 )2 X(z)
Y(z) (1 z 1 ) (1 z 1 )2 (1 z 1 z 2 ) H(z) (1 z 1 )(1 z 1 )
X(z) (1 z 1 ) (1 z 1 z 2 ) 1 2z 1 2z 2 z 3
x[n] 1, 2, 2, 1 35. Which of the following systems has maximum peak overshoot due to a unit step input? 100 s 10s 100 100 (c) 2 s 5s 100
(a)
100 s 15s 100 100 (d) 2 s 20s 100
(b)
2
2
35. Ans: (c) For maximum peak overshoot, 1 For all 4 options, n 10 rad/ sec 10 0.5 2 10 15 For (b), 0.75 2 10 For (a),
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5 0.25 2 10 20 For (d), 1 2 10 Lowest value of gives highest overshoot. For (c),
Hence, (c) will have maximum peak overshoot. 36. In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is
(a) 1 nF
(b) 1 F
(c) 1 mF
(d) 10 mF
36. Ans: (d) For maximum power transfer ZL = Zs* Since Zs 0.5
ZL 0.5 for maximum power transfer j R c ZL jL j R c
[ 100 rad/ sec]
j 1 100c ZL j100 0.005 j 1 100c j j 1 100 c ZL j0.5 1 100 c 1 2 10000 c
For ZL to be purely real 1 0.5 0 1 100 c 1 10000 c2 © Kreatryx. All Rights Reserved.
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5000 c2 – 100c + 0.5 = 0 1 C F 10 mF 100 37. A 25 kVA, 400 V, –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 ___________. 37. Ans: –14.55 Open circuit voltage = 360 V 360 In pu, Voc 0.9 pu 400 Short circuit current = 1 pu V Synchronous reactance = oc 0.9 pu Isc Since, machine delivers rated load at 0.8 pf lead at rated voltage Ia 1 pu Vt 1pu
Ef 1 136.86 ( j0.9)
Ef 1 0.9 126.86 0.85457.42 pu Voltage regulation =
0.854 1 100 % 14.55% 1
38. 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)
38. Ans: 0.71 The circuit is a half wave rectifier whose output voltage is shown below.
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1
Vo(rms)
1 2 (Vm sin t)2 d( t) 2 o 1
1 1 cos 2 t 2 Vm Vo(rms) Vm d( t) 2 2 2 o 2 I R Po Input power factor = o(rms) Vs(rms) Is(rms) Vs(rms) Is(rms)
Is(rms) = Io(rms) Vm 1 IPF 2 0.707 0.71 Vm Vs(rms) 2 2 39. For the network given in figure below, the Thevenin’s voltage Vab is Vo(rms)
(a) – 1.5 V (c) 0.5 V
(b) – 0.5 V (d) 1.5 V
39. Ans: (a) Apply Source Transformation,
Apply KVL in first loop 30 10(I1 I2 ) 15I1 0
30 25I1 10 I2
(i)
Apply KVL in second loop 16 20 Iz 10 I1 (ii) Solving (i) and (ii) I1 = 1.9A, I2 = 1.75A Current in10 resistor I1 I2 0.15A
Vth (I1 I2 )10 1.5V Vab (I1 I2 )10 1.5V
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40. In the circuit shown all elements are ideal and the switch S is operated at 10kHz 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).
40. Ans: 40 The given circuit is buck-boost converter D 0.6 Vo Vs 50 75V 1 D 1 0.6 Since Vo is given to be –75V, the converter operates in continuous conduction mode. V 75 Io o 15 A R 5 I 15 Average Inductor Current, IL o 37.5 A 1 D 0.4 Peak to peak ripple I L L Vs 50 D Ts ( IL ) 50 1 0.6 4 10 50 0.6 104 IL 5A 0.6 103 I IL(max) Is(max) IL L 37.5 2.5 40 A 2
L
41. 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 and the shunt field resistance is 240 . The no load speed, in rpm, is ___________. 41. Ans. 1241.82 Shunt field current =
Vt
Rf
120 0.5A 240
Ia(nL) 2 0.5 1.5A Ia(FL) 7 0.5 6.5A
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Induced emf, E(NL) 120 1.5 0.8 118.8 V E(FL) 120 6.5 0.8 114.8 V
E N
Since, IF constant , const & E N
ENL NNL EFL NFL NNL
118.8 1200 1241.8118rpm 114.8
42. For the circuit shown below, assume that the OPAMP is ideal
(a) O s
(b) O 1.5 s
(c) O 2.5 s
(d) O 5 s
42. Ans. (c) The given circuit can be redrawn as,
Apply Delta-Star Transformation
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By voltage division, voltage at non-inverting terminal V 2R V Vs s 2R 2R 2 The resistance at inverting terminal does not play any role 4R R f Vs V0 V 1 1 3 R R1 2 3 5 V0 Vs 2.5 Vs 2 43. A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature Ra 0.02 . 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 (a) 34.2 A (b) 30 A (c) 22 A (d) 4.84 A 43. Ans: (b) In separately excited machine cons tant
T Ia or T km Ia 70 k m Ia or Ia
70 km
Similarly E km km 900 By KVL E V Ia R a Km (30) 220
----(i) 2 km (30) 60
70 0.02 km
2 km (30) 220km 1.4 2 km (30) 220km 1.4 0
km 2.3278 Ia
70 30.07 A km
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GATE 2017 EE - Session 2
44. The eigenvalues of the matrix given below are 0 1 0 0 0 1 0 3 4
(a) (0, –1, –3) (c) (0, 2, 3)
(b) (0, –2, –3) (d) (0, 1, 3)
44. Ans: (a) 0 1 0 A 0 0 1 0 3 4 1 0 I A 0 1 0 3 4
I A 4 3 0
2 4 3 0
1 3 0
0, 1, 3
45. The value of the contour integral in the complex-plane
z3 2z 3 dz . Along the contour z2
z 3 , taken counter-clockwise is
(a) 18i (c) 14i
(b) 0 (d) 48i
45. Ans: (c) f z dz 2i Residue z3 2z 3 z2 The function f(z) has a simple pole at z=2 Res(z 2) lim(z 2) f(z) f(z)
z 2
z 2z 3 dz 2i 7 14i z 2 3
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46. For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions QAQBQC Q'A Q'B Q'C 100
The minimum number of clock cycles after which the output Z would again become zero is ___________. 46. Ans: 6 The output will be 0 if all inputs are zero and this happens if QA QB QC QA 'QB 'QC ' On careful observation, QA QB QC is a ring counter and QA 'QB 'QC ' is a Johnson counters so whenever their states are same the output is zero CLK 0 1
QA 1 0
QB 0 1
QC 0 0
2 3
0 1
0 0
1 0
4 5
0 0
1 0
0 1
6
1
0
0
Q A ' QB ' Q C ' 1
0
0
1
1
0
1
1
1
0 0
1 0
1 1
0
0
0
1
0
0
Hence, after 6 cycles output is zero. 47. Consider the system described by the following state space representation x1 (t) 0 1 x2 (t) 0 2
x1 (t) 0 x1 (t) u(t) and y(t) 1 0 x2 (t) 1 x2 (t) x (0) 0 If u(t) is a unit step input and 1 , the value of output y(t) at t = 1 sec (rounded off x2 (0) 1
to three decimal places ) is ___________ . © Kreatryx. All Rights Reserved.
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GATE 2017 EE - Session 2
47. Ans: 1.2838 0 1 The matrix A 0 2 s
sI A 0
sI A
1
1 s 2
s 2 1 1 s s s 2 0
State transition matrix (t) L1 sI A
1 (t) 0
1 1 e2t 2 e2t
1
1 L1 s 0
1 1 1 2 s s 2 1 s2
u(t)
1 Free response (t) x(0) 0
1 1 e2t 2 e2t
1 1 0
0
s 2 1 0 1 1 1 1 1 1 L 2 Forced response L1 sI A B u(s) L1 s s s 2 1 s 0 s s s 2 1 1 1 2 1 1 t 1 e2t 4s 2s 4 s 2 4 2 4 L1 ut 1 1 1 1 2t e 2s 2 s 2 2 2 1 1 3 1 1 2t 1 2t t e 1 4 2 t 4 e 4 Response x(t) ut 4 2 ut 0 1 1 1 1 e2t e2t 2 2 2 2 3 1 1 2t t e 3 t 1 4 y(t) Cx(t) 1 0 4 2 u t e2t u t 1 1 e2t 4 2 4 2 2 3 1 1 y(t 1) e2 1.2838 4 2 4
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GATE 2017 EE - Session 2
48. A 10 1/2 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 ___________ . 48. Ans: 1 For a gating time of 1 sec, reading obtained 1 1 Reading 8 108 TCLK 10 In period mode of operation, 108 reading corresponds to
T 108 10 109 1sec
f
1 1hz T
49. 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 7 8 7 (c) 64
49 64 105 (d) 64
(a)
(b)
Ans.49. [c] The experiment stops at 3 tosses or if person gets a head So the possible outcomes & their probabilities are Outcome H TH TTH TTT
1 1 1 1 2 4 8 8 So, there can be 0 or 1 heads 1 1 1 1 7 E(Head) no. of head P 1 1 1 0 2 4 8 8 8 2 1 1 1 1 7 E(Head2 ) no. of head P 12 12 12 02 2 4 8 8 8 Pr obability
Var (Head) E (Head)2 E(Head)
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7 49 7 8 64 64
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50 For the circuit shown in the figure below, it is given that VCE 29 and VBE 0.7 V when the B-E junction is forward biased.
For this circuit, the value of (a) 43 (c) 121
RB R
VCC 2
. The transistor has
is (b) 92 (d) 129
50. Ans: (d) By KVL VCE VCC IE 4R R 10 5R IE
5 10 5R IE 5 5R IE IE R 1 ………………………(i) Applying KVL through base emitter junction 10 4R IE RB IB VBE R IE 0
10 5R IE RB
IE 0.7 0 1
R 9.3 5R B IE …….(ii) 30 Divide (ii) by (i) R 5R B 30 9.3 R R 5 B 9.3 30R RB 4.3 30R RB 30 4.3 129 R
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51. 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 resistances of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01 m. Neglecting the effect of ground, the magnitude of positive sequence reactance in / km (rounded off to three decimal places ) is ___________
51. Ans: 0.28935 1
1
Mutual GMD Dab Dbc Dca 3 1 1 1 3 1m D 1 Lph 0 ln m 0.2 ln 0.2ln100 0.92103 mH / km 2 Ds 0.01 Reac tance Lph 2 50 0.92103 0.28935 / km
52. A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 m (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 4R2a and that of the drop is
4 3 r . The 3
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.)
52. Ans: 317.82 The potential of spherical soap bubble Q V 4 0 R
Q 40 R V © Kreatryx. All Rights Reserved.
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Potential of drop R Q V V 40r r Since volume remains same 4 R 2a
r 3R a 2
V V
4 3 r 3
1 3
R
3R a 2
1 3
1
102
3 10
4
3.3 10
1 6 3
10.03 V
53. If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA, Y transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is ___________ . 53. Ans: 37.878 Line to Line voltage ratio of Y transformer Vsec Ns 1 Vpri 3N 5 3 p
KVA rating remains same on both sides of transformer s 25 125 IL 37.878 A 3.3 3.3 3 VL 3 5 3 54. 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. 54. Ans: 12.7 By swing equation H d2 Pm Pe 180f dt2 Initially, Pm Pe 60MW Pm Pe
60 pu 250
Kinetic energy = GH = 1000 MJ © Kreatryx. All Rights Reserved.
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GATE 2017 EE - Session 2
H
1000 4MJ / MUA 250
If load is suddenly removed, Pe 0 4 d2 60 180 f dt2 250 d2 60 180 50 540 elect deg/ sec2 2 250 4 dt 1 By equation of motion 0 t2 2 5 t 5cycles 0.1sec 50 1 10 540 0.01 12.7 elect deg 2
Acceleration
55. 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 0.25 and 3.925 respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ___________ . 55. Ans: 0.8084 Impedance, Z 3.9329 86.355
Vs VR V2 cos ( ) R cos Z z 17.32 17.87 (17.32)2 3 cos (86.355 ) cos 86.355 3.9329 3.9329 17.32 17.87 7.8491 cos (86.355 ) 3.9329 86.355 84.2758 2.079 17.87 17.32 2.079 0 3 3 Ia 0.12369 36.056 3.9329 86.355
3
pf cos 36.056 0.8084 lag
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GATE 2017 EE - Session 2
General Aptitude 01. Choose the option with words that are not synonyms. (a) aversion, dislike (b) luminous, radiant (c) plunder, loot (d) yielding, resistant 01. Ans: (d) Yielding: giving way under pressure Resistant: Offering resistance 02. Saturn is ___________ to be seen on a clear night with the naked eye. (a) enough bright (b) bright enough (c) as enough bright (d) bright as enough 02. Ans: (b) Saturn is bright enough to be seen on a clean might with the naked eye. 03. 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? (a) V (b) W (c) X (d) Y 03. Ans: (a) Based on data given, the arrangement is x z v w y Hence, V is in middle 04. There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same color is (a) 1/5 (b) 7/30 (c) 1/4 (d) 4/15 04. Ans: (d) Total socks = 10 P(same color) = P(same color)
3
C2 4 C2 3 C2 10
C2
3 6 3 12 45 45
4 15
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05. 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? (a) 12 (b) 15 (c) 18 (d) 19 05. Ans: (b) Let x question are MCQ Y questions are essay type Since, there are 20 questions in total -(i) x y 20 Since, total marks = 100 3x 11y 100 -(ii) From (i) & (ii) y 5
x 15
So, there are 15 MCQ 06. 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? (a) The box labelled ‘Apples’ (b) The box labelled ‘Apples and Oranges’ (c) 18 (d) 19 06. Ans: (b) We will open box labeled apple and oranges & we draw one fruit If it is apple, then it cannot be box containing apples & oranges as it must be incorrectly labeled. So, it must contain apples. Same case will happen if drawn fruit is orange Then, we are left with two boxes & two labels & we know label is incorrect on box so we can place correct label. 07. X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have (a) 90 digits (b) 91 digits (c) 92 digits (d) 93 digits 07. Ans: (a) We can assume the number to be 47 1028 The number x3 473 1084 103823 1084 Hence x3 has 90 digits © Kreatryx. All Rights Reserved.
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08. “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: (a) ‘culture’ (b) ‘seemingly’ (c) ‘urgent’ (d) ‘political’ 08. Ans: (b) The author says it seemed that ideology is more important than literature so he believes otherwise. 09. The number of roots of ex 0.5x2 2 0 in the range [–5, 5] is (a) 0 (b) 1 (c) 2 (d) 3 09. Ans: (c) 0.5 x2 2 ex
Hence, there are 2 intersection so 2 roots 10 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.
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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? (a) P (b) Q (c) R (d) S 10. Ans: (c) The region most likely to have a thunderstorm must have contour lines closer to each other. This ensures that pressure drops very rapidly. . Hence, region R is most likely to have thunderstorm.
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