ANALYSIS OF GATE 2017* Electrical Engineering

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1 ANALYSS OF GATE 2017* Electrical Engineering Power Systems 10% General Aptitude 15% Engineering Mathematics 11% Network Theory 9% Signals & Systems 7% Electrical Machines 12% Control Systems 11% Power Electronics 7% Analog Circuits 6% Electromagnetic Theory 3% Measurement 4% Digital Circuits 5% : , info@thegateacademy.com Copyright reserved. Web: 1

2 EE ANALYSS-2017_11-Feb_Morning SUBJECT No. of Ques. Topics Asked in Paper(Memory Based) Engineering Mathematics Network Theory Signals & Systems Control Systems Analog Circuits Digital Circuits 1 Marks: 3 2 Marks: 4 1 Marks: 3 2 Marks: 3 1 Marks: 3 2 Marks: 2 1 Marks: 3 2 Marks: 4 1 Marks: 2 2 Marks: 2 1 Marks: 1 2 Marks: 2 Linear Algebra; Calculus; Complex ariables Differential Equations; Numerical Methods Network Solution Methodology; Two Port Networks; Transient/Steady State Analysis of LC Circuits to DC nput; Miscellaneous Fourier epresentation of Signals; Linear Time nvariant (LT) Systems;Z-Transform Stability & outh Hurwitz Criterion; Frequency esponse Analysis; State ariable Analysis; Time Domain Analysis; Basics of Control System; Time Domain Analysis Diode Circuits-Analysis and Application; Operational Amplifiers & ts Applications; AC & DC Biasing-BJT and FET; Miscellaneous Boolean Algebra and Karnaugh Maps Logic Gates Level of Ques. Total Marks Tough 11 Medium 9 Tough 7 Tough 11 Easy 6 Easy 5 Measurement 1 Marks: 2 2 Marks: 1 Measurements of Basic Electrical Quantities 1 Basic Electrical Quantities 2 Medium 4 Power Electronics 1 Marks: 3 2 Marks: 2 nverters; Basics of Power Semiconductor Devices; ectifiers; Choppers Tough 7 Electromagnetic Theory 1 Marks: 1 2 Marks: 1 Electromagnetic Field Medium 3 Electrical Machines Power Systems General Aptitude 1 Marks: 2 2 Marks: 5 1 Marks: 2 2 Marks: 4 1 Marks:5 2 Marks:5 Synchronous Machine; nduction Motor; DC Machines; Transformer Symmetrical Components and Faults Calculations; Transmission and Distribution; Power System Stability Easy 12 Tough 10 Medium 15 Total Faculty Feedback Majority of the question were concept based. Control, PS, Network EM, Maths weightage was comparatively high. GA was medium as compared to the last year. : , info@thegateacademy.com Copyright reserved. Web: 2

3 GATE 2017 Examination* Electrical Engineering Test Date: 11/02/2017 Test Time: 9:00 AM 12:00 PM Subject Name: Electrical Engineering Section: General Aptitude 1. Find the smallest number y such that y 162 is a perfect cube. (A) 24 (B) 27 (C) 32 (D) 36 [Ans. D] Factorization of 162 is y is a perfect cube y = Perfect cube For perfect cube s and s are two more required each i e y The smallest number of y 2. The probability that a k-digit number does NOT contain the digits 0, 5, or 9 is (A) (B) (C) (D) [Ans. C] K digits 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, 5, 6, 8. So required probability ( ) ( ) 3. After ajendra Chola returned from his voyage to ndonesia, he to visit the temple in Thanjavur. : , info@thegateacademy.com Copyright reserved. Web: 3

4 ahul rul. (A) was wishing (B) is wishing (C) wished (D) had wished [Ans. C] f the main clause is in the past the past tense, the subordinate clause also should be in the past tense. 4. ahul, Murali, Srinivas and Arul are seated around a square table. ahul 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? (A) ahul and Murali (B) Srinivas and Arul (C) Srinivas and Murali (D) Srinivas and ahul [Ans. C] From the given data, the following seated arrangement is possible around a square table. Srinivas ahul Murali rul Srinivas Murali Srinivas and Murali are opposite to each other 5. esearch in the workplace reveals that people work for many reasons. (A) money beside (B) beside money (C) money besides (D) besides money [Ans. D] Besides means in addition to. 6. 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 (A) 2 (B) 3 (C) 4 (D) Cannot be determined [Ans. A] The total Number of peoples are sitting around a circular table is 6, in which atleast 2 men, atleast 2 women and atleast three right handed persons are compulsory. From this data, the following circular form is possible. : , info@thegateacademy.com Copyright reserved. Web: 4

5 M() M() M() W(L) M(L) W(L) M = Male W = Women L = Left hand = ight hand The number of women on the table is 7. 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 dislike the colour white. Gulab and Neel like all the colours. n how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes? (A) 21 (B) 18 (C) 16 (D) 14 [Ans. D] Persons are Arun, Gulab, Neel and Shweta shirt colours are red, pink, blue and white run dislike red colour means he like remaining three other colours Shweta dislike white colour means he like remaining three other colours Gulab and Neel are likes all the four colours The total Number of ways to choose shifts 8. The expression ( ) is equal to (A) The maximum of x and y (B) The minimum of x and y (C) 1 (D) None of the above [Ans. B] (x y) x y x y (x y) if(x y) when x y if (x y) (y x)when y x (x y) (x y) x y x y Minimum of (x y) as (x y) (x y) (y x) x y y x y y : , info@thegateacademy.com Copyright reserved. Web: 5

6 as x y x x Minimum of (x y) 9. 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? (A) Nationalists are highly imaginative (B) History is viewed through the filter of nationalism (C) Our colonial past never happened (D) Nationalism has to be both adequately and properly imagined [Ans. B] To refer is to reach an opinion The right opinion of the author is History is viewed through the filter of nationalism so, option B is the right opinion of the author. The key words in the statement are history and nationalist imagination 10. 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 25 m intervals in this plot. f in a flood the water level rises to 525 m, which of the villages P, Q,, S, T get submerged? Q P S T (A) P, Q (B) P, Q, T (C), S, T (D) Q,, S [Ans. C] 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 525 m. So, the village of, S and T are under a contour of 500. Therefore these villages are submerged. : , info@thegateacademy.com Copyright reserved. Web: 6

7 Section: Technical 1. The equivalent resistance between the terminals and B is [Ans. *] ange: 2.9 to 3.1 ] 2. The matrix [ ] has three distinct eigen values and one of its eigen vectors is [ ] Which one of the following can be another eigen vector of A? ( ) [ ] (B) [ ] ( ) [ ] ( ) [ ] [Ans. C] Since eigen values are distinct and the matrix is symmetric then the corresponding eigen vectors are orthogonal Then X X By verification from options, Given X [ ] Let X [ ] X X : , info@thegateacademy.com Copyright reserved. Web: 7

8 3. A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are: Y j pu Y j pu and Y j pu. Bus Bus jq ~ jr Bus jp The per unit values of the line reactances p, q and r shown in the figure are (A) p q r (B) p q r (C) p q r (D) p q r [Ans. B] jr jq jq jp jp jr j j j r q q p p r ( ) p q r ( ) p q r ( ) ( ) p p ( ) ( ) r r pu ( ) ( ) q q pu 4. The following measurements are obtained on a single phase load: and W W. f the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is. (Give answer up to one decimal place.) [Ans. *] ange: 4 to 4 P Power factor cos n multiplication and division percentage values will be added up. : , info@thegateacademy.com Copyright reserved. Web: 8

9 5. 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, the particles are released but are constrained to move along the same straight line. Which of these will collide first? (A) The particles will never collide (B) All will collide together (C) Proton and neutron (D) Electron and neutron [Ans. D] r m r m e n P q coul coul B q coul t < 0: The particles are at rest. No ext. field is mentioned in the problem. So the only force is that acting on e & p. This has a magnitude force neglected). (attractive). No force on n. (Gravitational 6. n the converter circuit shown below, the switches are controlled such that the load voltage v (t) is a Hz square wave. s s s Load (t) s The MS value of the fundamental component of (t) in volts is [Ans. *] ange: 196 to 200 Given circuit is 1 phase full bridge voltage source inverter. t is mentioned that output voltage is a square wave and its amplitude will be 220 Therefore, MS value of fundamental component of output voltage 7. Let c xy dxdy, where is the region shown in the figure and c. The value of equals. (Give the answer up to two decimal places) : , info@thegateacademy.com Copyright reserved. Web: 9

10 y x [Ans. *] ange: 0.99 to 1.01 Let c XY dxdy y x Now, XY dxdy XY dxdy XY dxdy XY dxdy XY dxdy ( X ) Y dy ( X ) y dy ( ) y dy ( y ) y dy y dy ( y y ) dy ( y ) ( y y ) dy ( y y ) ( ) ( ) : , info@thegateacademy.com Copyright reserved. Web: 10

11 8. For a complex number z, z lim z z i(z ) is (A) i (B) i (C) i (D) 2i [Ans. D] z lim z z i(z ) ( form) Applying L Hospital rule lim z z i( z) (i) ( ) i( i) i i 9. 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 (A) bend closer to the cylinder axis (B) bend farther away from the axis (C) remain uniform as before (D) cease to exist inside the cylinder [Ans. A] ron is a ferrormagnetic material. n such a material, there will be magnetic dipoles associated with the spins of unpaired electrons, just like in a paramagnetic material. n the absence of any external magnetic field: n a paramagnetic material these dipoles are oriented in all possible directions, and so their dipole, moments are cancelled out, and the material as a whole is non-magnetic. n a ferromagnetic material, all the dipoles point in only one direction. (This can be explained using quantum mechanics). But in that case, every nail, every piece of iron, must be a powerful permanent magnet; why is it not so? The alignment occurs in small patches, called domains. Each domain has several billions of dipoles, all pointing in one direction; but in any small piece of iron, there are billions of such domains, dipoles of each domain oriented randomly in some direction. The net magnetization of all these dipoles is zero. When an external magnetic field B is applied, domains with the same direction as B grow, others shrink; the material is magnetized in the direction of B. : , info@thegateacademy.com Copyright reserved. Web: 11

12 So when a solid iron cylinder is placed in a uniform B with the axis of the cylinder along the direction of B, the field lines in the cylinder remain parallel and uniform as before, but their density increases. 10. The slope and level detector circuit in a CO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. n order to display correctly, a delay line of (A) 150 ns has to be inserted into the y-channel (B) 150 ns has to be inserted into the x-channel (C) 150 ns has to be inserted into both x and y channels (D) 100 ns has to be inserted into both x and y channels [Ans. A] n order to display correctly, a delay line of 150 ns has to be inserted in to the Y-channel between output of vertical amplifier and Y-input of CT 11. onsider g(t) { t t t t t otherwise } where t Here, t represent the largest integer less than or equal to t and t 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 [Ans. *] ange: 0 to 0 Given g(t) { t t t t t otherwise } f we plot the above signal, we get g(t) 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. 12. A 3-phase voltage source inverter is supplied from a 600 DC source as shown in the figure below. For a star connected resistive load of per phase, the load power for device conduction, in kw, is [Ans.*]ange: 8.5 to 9.5 MS value of phase voltage for conduction mode is : , info@thegateacademy.com Copyright reserved. Web: 12

13 (t) sin( t). Power delivered to load P ( ) kw 13. 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) (A) c x(ct) y(ct) (B) x(ct) y(ct) (C) c x(ct) y(ct) (D) c x(ct) y(t) [Ans. A] z(t) x(t) y(t) as per property of convolution x(ct) y(ct) c z(ct) z(ct) c x(ct) y(ct) Given c is a positive integer so z(ct) c x(ct) y(ct) 14. For the circuit shown in the figure below, assume that diodes, and are ideal. ~ The DC components of voltages v and v, respectively are (A) 0 and 1 (B) and (C) 1 and 0.5 (D) 1 and 1 [Ans. B] During ve cycle input: ON and OFF : , info@thegateacademy.com Copyright reserved. Web: 13

14 (t) sin( t) (t) sin( t). ~ ( ) During ve cycle input: OFF and ON ~ and (t) The voltage waveforms are shown in below figure. (t) t (t) (t) t t component of is component of is 15. For the power semiconductor devices GBT, MOSFET. Diode and Thyristor, which one of the following statements is TUE? (A) All the four are majority carrier devices (B) All the four are minority carrier devices : , info@thegateacademy.com Copyright reserved. Web: 14

15 (C) GBT and MOSFET are majority carrier devices, whereas Diode and Thyristor are minority carrier devices. (D) MOSFET is majority carrier device, whereas GBT, Diode, Thyristor are minority carrier devices. [Ans. D] Only MOSFET is majority carrier device. And remaining all other devices belongs to minority carrier devices 16. Consider the system with following input-output relation y n] ( ( ) )x n] Where, x[n] is the input and y[n] is the output. The system is (A) nvertible and time invariant (B) nvertible and time varying (C) Non-invertible and time invariant (D) Non-invertible and time varying [Ans. D] y(n) ( ) ]x(n) Y (n) ( ) ]x(n n ) y(n n ) ( ) ]x(n n ) y (n) y(n n so, time variant if x (n) u(n) y (n) ( n) ]u(n) ] x (n) ] y (n) ( ) ]x (n) ] Non-invertible, variant The system is time variant and non-invertible. 17. A three-phase, 50 Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 k grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is per phase. The load angle is. The power delivered to the motor in kw is (Give the answer up to one decimal place) [Ans. *] ange: 8.35 to 8.42 (Unity Pf) X By neglecting armature resistance the active power drawn by a synchronous motor is p sin X ( X ) Ph : , info@thegateacademy.com Copyright reserved. Web: 15

16 cos ph cos ( ) cos( ) P ( ) [ ] sin ( ) P= kw 18. 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 sin( t) and i sin( t) A respectively. Similarly for phase-b, the instantaneous voltage and current are v cos( t) and i cos( t), respectively. Source a i b i n a b n Load The total instantaneous power flowing from the source to the load is (A) 2200 W (B) sin ( t) W (C) 4400 W (D) sin( t) cos( t) W [Ans. A] Total instantaneous power: s [ ] [ ] [ W ] [ ] 19. A closed loop system has the characteristic equation given by s Ks (K )s. For this system to be stable, which one of the following conditions should be satisfied? (A) 0 < K < 0.5 (B) 0.5 < K < 1 (C) 0 < K < 1 (D) K > 1 [Ans. D] s K s K 3 K K s K s 3 For stability K and K K So, K K i e K 20. The transfer function of a system is given by : , info@thegateacademy.com Copyright reserved. Web: 16

17 (s) (s) s s Let the output of the system be v (t) sin( t ) for the input v (t) sin ( t). Then the minimum and maximum values of (in radians) are respectively ( ) and (B) and ( ) and ( ) and [Ans. D] ( j j ) ( tan tan ) t (Maximum) t (Minimum) 21. 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-aphson method in polar form is. [Ans. *] ange: 14 to 14 G Slack bus G having reactive power Q min Q Q max When it is operating at Q max means there is a reactive power divergent. Hence it is working as load bus. G 2 equations G 1 equation G 1 equation L 2 equations L 2 equations L 2 equations L 2 equations L 1 equation L 1 equation Total Number of equations are Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be is. (Give the answer up to two decimal places). : , info@thegateacademy.com Copyright reserved. Web: 17

18 U(s) Ke s Y(s) [Ans. *] ange: 1.01 to 1.06 PM Ke j And K PM K 23. 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 PM is (A) 1350 (B) 1650 (C) 1950 (D) 2250 [Ans. C] Supply frequency (f ) Hz Pole f N rpm P otor frequency (f ) = 5 Hz We know that f = sf (s)( ) But in induction generator, slip is a negative value N N rpm 24. The Boolean expression B B simplifies to (A) B (B) B B (C) B (D) B B [Ans. A] B B B( ) B B B B B ( ) (B ) : , info@thegateacademy.com Copyright reserved. Web: 18

19 B 25. The power supplied by the 25 source in the figure shown below is W. [Ans. *] ange: 248 to 252 From KCL, So, power supplied W 26. The figure below shows an uncontrolled diode bridge rectifier supplied from a 220, 50 Hz, 1-phase ac source. The load draws a constant. The conduction angle of the diode in degrees(rounded of to two decimal places) is L ~ mh Hz [Ans. *] ange: 220 to 230 When source inductance is not taken into account, each diode will conduct for 180 When source inductance is taken into account, each diode will conduct for ( ) Where is overlap angle and can be determined as follows: L cos cos Conduction angle for D1 is 27. The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: [ x (t) x (t) ] * [x (t) x (t) ] * u(t) y(t) ] [ x (t) x (t) ] (s ) ( ) (s s ) : , info@thegateacademy.com Copyright reserved. Web: 19

20 (s ) (B) (s s ) (s ) ( ) (s s ) (s ) ( ) (s s ) [Ans. D] TF S ] B S * s s TF TF s ] * s s (s )(s) s s * 28. A function f(x) is defined as f(x) e x { ln x ax bx x Where x Which one of the following statements is TUE? (A) f(x) is NOT differentiable at x = 1 for any values of a and b (B) f(x) is differentiable at x = 1 for the unique values of a and b (C) f(x) is differentiable at x = 1 for all values of a and b such that a b = e (D) f(x) is differentiable at x = 1 for all values of a and b [Ans. B] f(x) e x { log x ax bx x e x f (x) { x ax b x At x=1, L H e H a b Since f(x) is differentiable at x = 1, a b e a b e Since f(x) is continuous at x = 1, t x L H L e H L a b a b e Solving and a b e a and b have unique values. 29. The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be : , info@thegateacademy.com Copyright reserved. Web: 20

21 ( ) (B) ( ) ( ) [Ans. A] The given circuit is redrawn as When, Diode is ON, then replaced by SC When, Diode OFF, then replaced by OC : , info@thegateacademy.com Copyright reserved. Web: 21

22 The output characteristic is shown below. 30. n the circuit shown below, the maximum power transferred to the resistor is W. [Ans. *] ange: 3 to 3.1 To find By applying KL to the above loop ( ) = 2.1 To find Maximum power transferred is ( ) ( ) Maximum power transferred = : , info@thegateacademy.com Copyright reserved. Web: 22

23 31. A separately excited DC generator supplies 150 A to a 145 DC grid. The generator is running at 800 PM. The armature resistance of the generator is. f the speed of the generator is increased to 1000 PM, the current in amperes supplied by the generator to the DC grid is. [Ans. *] ange: 548 to 552 (Grid) N rpm N rpm (Grid)? r ( )( ) N [ K const] N ( ) ( ) 32. Consider a causal and stable LT system with rotational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, H( ). The poles of H(z) are p exp (j ) for k. The zeros of H(z) are all at z. Let g n] j h n]. The value of g[8] equals (Give the answer up to three decimal places). [Ans. *] ange: 0.06 to The magnitude of magnetic flux density (B) in micro Teslas ( T), at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current ( = 1A) and placed in vacuum as shown in the figure is. [Ans. *] ange: 0.65 to 0.75 : , info@thegateacademy.com Copyright reserved. Web: 23

24 H H H H H H H Since the figure is regular hexagon, the field magnitude is same and is in the same direction So H H tan d d H H d (sin sin ) d ( ) ( ) H H H B H B T 34. For a system having transfer function G(s) a unit step input is applied at time t = 0. The value of the response of the system at t = 1.5 sec (rounded off to three decimal places) is [Ans. *] ange: to s TF nput (unit step) s s Output (TF)(input) s ( s ) s Output L [ s s s ] e Output at(r ) e : , info@thegateacademy.com Copyright reserved. Web: 24

25 35. Consider the differential equation (t ) t y sin(t) with y( ). There exists a unique solution for this differential equation when t belongs to the interval (A) ( ) (B) ( ) (C) ( ) (D) ( ) [Ans. A] (t ) dy ty dt sint with y( ) dy dt t (t ) y sint (t ) The given differential equation has no solution when t. These values do not lie in the interval ( ) The solution of the given differential equation lies in the interval ( ) Option ( ) is correct 36. Consider the line integral (x iy ) dz, where z x iy. The line c is shown in the figure below. y i ( i) ( ) The value of is x ( ) i (B) i ( ) i ( ) i [Ans. B] Given is y x dy dx Then x varies from (x iy )dz to (x ix )(dx idx) : , info@thegateacademy.com Copyright reserved. Web: 25

26 ( i) x dx ( i i ) * x ( i ) ( ) i 37. The input voltage of the buck-boost converter shown below varies from 32 to 72. 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 steadystate output voltage remains constant at 48 is S L ( ) (B) ( ) ( ) [Ans. A] n Buck boost converter When When The range of will be or 38. The load shown in the figure is supplied by a 400 (line-to-line) 3-phase source (YB sequence). The load is balanced and inductive, drawing 3464 A. When the switch S is in position N, the three watt-meters W, W and W read W each. f the switch is moved to position Y, the readings of the watt-meters in watts will be: : , info@thegateacademy.com Copyright reserved. Web: 26

27 phase source LO. W Y W B W Y N (A) W and W W (B) W W and W (C) W W W (D) W W and W [Ans. D] S N P W W W Power factor cos lag When switch is in position N W W W W balanced load total power consumed by load is W W W W W W : , info@thegateacademy.com Copyright reserved. Web: 27

28 Given load is inductive And A draw from source = 3464 A W Power factor lag power factor angle ( lag) When switch is connected in Y position pressure coil of W is shorted So W diagrams for other two are as follows W cos( angle between and cos( ) W W cos( angle between and cos( ) W W1 = 0, W2 = 0, W3 = 1732 W and phasor 39. The circuit shown in the figure uses matched transistors with a thermal voltage m. The base currents of the transistors are negligible The value of the resistance in k that is required to provide bias current for the differential amplifier block shown is. Differential Amplifier m [Ans. *] ange: 170 to 174 : , info@thegateacademy.com Copyright reserved. Web: 28

29 Differential Amplifier m Q Q m As B&C shorted, Transistor behaves as diode. Then, e e e e e ( ) n ( nd ) n ( ) n ( ) n( ) k k 40. Two parallel connected, three-phase, 50 Hz, 11 k, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MA to a 11 k grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are and, respectively. Assuming the magnetic circuit to be linear, the : , info@thegateacademy.com Copyright reserved. Web: 29

30 ratio of excitation current of machine A to that of machine B is. (Give the answer up to two decimal places). [Ans. *] ange: 2.05 to 2.13 Synchronous ondencors urrent s supplied both the machines are same mps As the two motors, supplying reactive power only, the phasor diagram will be k i ~ ~ j X j X onsider magnitudes ( X ) ( X ) ( ) olts ( ) olts B X M 41. The output expression for the Karnaugh map shown below is CD AB (A) B B (B) B B (C) B B (D) B B : , info@thegateacademy.com Copyright reserved. Web: 30

31 [Ans. D] B F B B 42. The bus admittance matrix for a power system network is j j j [ j j j ] pu j j j There is a transmission line connected between buses 1 and 3, which is represented by the circuit shown in figure. eactance is pu Suceptance is pu Suceptance is pu f this transmission line is removed from service what is the modified bus admittance matrix? j j (A) [ j j j ] pu j j j j (B) [ j j j ] pu j j j j (C) [ j j j ] pu j j j j j (D) [ j j j ] pu j j j [Ans. C] When the line is removed from buses 1 and 3 z j y j y y y j Half line shunt susceptance Y mod Y old y Y mod Y old y y y j ( j ) j j j ( j ) j j : , info@thegateacademy.com Copyright reserved. Web: 31

32 43. A 375 W, 230, 50 Hz, capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Z ( j ) (main winding), Z ( j ) (auxiliary winding). Neglecting the magnetizing branch, the value of the capacitance (in F) to be added in series with the auxiliary winding to obtain maximum torque at staring is. [Ans. *] ange: 95 to 100 Given a single-phase capacitor start induction motor j j jx Fs To obtain maximum torque of starting, the main and auxiliary winding currents must have electrical tan ( X r ) tan ( X X r ) tan ( ) tan ( X ) X X fc F 44. Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1. ~ Two-port Network 1 Two-port Network 2 Port Port Port Given: B B, B,,,, B, and are the generalized circuit constants. f the Thevenin equivalent circuit at port 3 consists of a voltage source and an impedance Z, connected in series, then : , info@thegateacademy.com Copyright reserved. Web: 32

33 ( ) (B) ( ) ( ) [Ans. D] [ ] [ [ ] [ For Z Z B Z B B B B Z Z B B B B B B B B B ] [ ] [ ] B B B B Z ( ) ( B ) ( B B ) ( B B ) B B B Z B For and ( B ) B ] [ ] 45. Let the single x(t) ( ) (t ) be passed through an LT system with frequency response H( ), as given in the figure below. H( ) The Fourier series representation of the output is given as (A) cos( t) cos( t) (B) cos( t) cos( t) (C) cos( t) (D) cos( t) [Ans. C] : , info@thegateacademy.com Copyright reserved. Web: 33

34 X(t) t T x(t)e dt * x(t)e dt [ e ( ) ] [ e ( )( ) ] [ e ] ( ) ] X( ) ( n ) X( ) ( ( ) ) ( n ) X( ) ( ) ( ) ] X( ) ( ) ( ) ] X( ) cos( t) cos( t) ] H( ) The output of low part filter is y(t) cos( t) 46. 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). (Give the answer up to one decimal place) [Ans. *] ange: 0.1 to 0.1 X j X j X j X (zero fault reactance) : , info@thegateacademy.com Copyright reserved. Web: 34

35 X? L G Fault Z Z Z Z Z Z Z Z Z Z Z Z pu 47. The logical gate implemented using the circuit shown below where and are inputs (with 0 as digital 0 and 5 as digital 1) and is the output is k Q k k Q (A) NOT (B) NO (C) NAND (D) XO [Ans. B] 0 0 OFF OFF OFF ON ON 0FF ON ON 0 t is a NO gate 48. A 220 DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are and 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. (Give the answer up to two decimal places) [Ans. *] ange: 9.5 to 12 Given a DC series motor Before adding extra resistor : , info@thegateacademy.com Copyright reserved. Web: 35

36 ( ) ( )( ) After adding extra resistor speed reduced by 50% T N N N T ( N ) T N T ( ) T T T T Ka a a T a T ( ) T a a a a a (r r r ) ( r ) N N ( ) ( N ) N olts eplace in equation ( )( r ) r 49. Only one of the real roots of f(x) x x lies in the interval x and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is. [Ans. *] ange: 10 to 10 b a f(x) x x in ]we know that ln ln( ) n ln ln( ) n ln( ) ln : , info@thegateacademy.com Copyright reserved. Web: 36

37 n n 50. n the system whose signal flow graph is shown in the figure. U (s) and U (s) are inputs. The transfer function ( ) ( ) is U U L s k J s Y k k ( ) JLs Js k k k (B) JLs Js k k k U ( sl) ( ) JLs (J U L)s k k U k U (sl ) ( ) JLs (J U L)s k k U [Ans. A] Y(s) U (S) K *( ) ( ) (K ) ( ) ( ) ( K ) * K JLs JS K K 51. A three-phase, three winding Y (1.1 k/6.6 k/400 ) transformer is energized from AC mains at the 1.1 k side. t Supplies 900 ka load at 0.8 power factor lag from the 6.6 k winding and 300 ka load at 0.6 power factor lag from the 400 winding. The MS line current in ampere drawn by the 1.1 k winding from the mains is. [Ans. *] ange: 623 to 627 Given transformer is Y Wdg( ) Wdg( ) Wdg( ) Y k k By applying superposition theorem (a) Load on k ( ) side is k Pf lag (load) ph ph : , info@thegateacademy.com Copyright reserved. Web: 37

38 The current on k side will be (source) ( ) ph (b) Load on (Y) is k pf lag ph ph The current of source side ( k) will be (source) ] ph Total source phase current will be ph Pf lag ph The line current will be 52. A load is supplied by a 230, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that kw P kw and k k. A capacitor connected across the load for power factor correction generates 1 ka reactive power. The worst case power factor after power factor correction is (A) lag (B) lag (C) lag (D) 1 [Ans. B] Worst power factor corresponding to P and Q P kw Q K Q K P kw Q K Power Factor cos [tan ( Q )] lag P 53. Let a causal LT system be characterized by the following differential equation, with initial rest condition : , info@thegateacademy.com Copyright reserved. Web: 38

39 d y dt dy dt y(t) dx(t) x(t) dt 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) ( ) e u(t) e u(t) (B) e u(t) e u(t) ( ) e u(t) e u(t) ( ) e u(t) e u(t) [Ans. B] Taking the Laplace transform Y(s) s TF X(s) s s s (s )(s ) s s L TF] e u(t) e u(t) 54. The switch in the figure below was closed for a long time. t is opened at t = 0. The current in the inductor of 2 H for t, is H (A) e (B) e (C) e (D) e [Ans. A] This is source free, first order -L circuit i(t) e t i( ) L eq : , info@thegateacademy.com Copyright reserved. Web: 39

40 i(t) i(t) e e L 55. The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is sin where is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. f one of the transmission line circuits is removed, the maximum value of, as the rotor swings is radian. f the expression for electrical power with one transmission line circuit removed is P sin the value of P in pu is. [Ans. *] ange: 1.21 to 1.23 With two lines P P P sin sin ( P ) sin ( ) P m rad rad Pe a X X X b X (P P )d (P P )d : , info@thegateacademy.com Copyright reserved. Web: 40

41 [P P cos ] [P P cos ] P Ps P cos P cos P Ps P cos Pm cos P ( ) P (cos cos ) P P ( ) P (cos cos ) P ( ) : , info@thegateacademy.com Copyright reserved. Web: 41