GATE Solved Question Papers for Electrical Engineering [EE] by AglaSem.Com

SOLVED PAPERS

GATE ELECTRICAL ENGINEERING (EE)

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CONTENTS • • • • • •

Introduction Question Paper Pattern Design of Questions Marking Scheme Syllabus Previous Year Solved Papers o Solved Question Paper 2014 (Set – 1) o Answer Key 2014 (Set – 1) o Solved Question Paper 2014 (Set – 2) o Answer Key 2014 (Set – 2) o Solved Question Paper 2014 (Set – 3) o Answer Key 2014 (Set – 3) o Solved Question Paper 2013 o Answer Key 2013 o Solved Question Paper 2012 o Answer Key 2012

Introduction The Graduate Aptitude Test in Engineering (GATE) is the all India level examination conducted by the Indian Institute of Science and seven Indian Institutes of Technology (IITs). A crucial part of GATE preparation is to solve and practice using previous year GATE papers. Solving previous year GATE papers help the candidate in understanding the exam pattern, knowing the level of difficulty of questions, and analyzing preparation. While attempting to solve any previous year GATE paper, it is advisable that it is done in a simulated test environment. This means, that the candidate sets a timer to countdown to test time, makes sure there is no other distraction, and then sits down to take the test as if he / she is in the exam hall. After attempting the paper, check how many questions you could get right in the first attempt. Analyse the strong and weak areas of preparation, and accordingly devise a study schedule or revision pattern. After going through those areas where in the first attempt could not do well, try the next paper. Almost all of the engineering colleges in India take admission in M.Tech courses on the basis of GATE scores. Apart from that, PSUs also recruit students directly on this basis. To score high in this elite examination is tough, but quite achievable.

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Question Paper Pattern In all the papers, there will be a total of 65 questions carrying 100 marks, out of which 10 questions carrying a total of 15 marks are in General Aptitude (GA). In the papers bearing the codes AE, AG, BT, CE, CH, CS, EC, EE, IN, ME, MN, MT, PI, TF and XE, the Engineering Mathematics will carry around 13% of the total marks, the General Aptitude section will carry 15% of the total marks and the remaining percentage of the total marks is devoted to the subject of the paper. In the papers bearing the codes AR, CY, EY, GG, MA, PH and XL, the General Aptitude section will carry 15% of the total marks and the remaining 85% of the total marks is devoted to the subject of the paper. GATE would contain questions of two different types in various papers: (i) Multiple Choice Questions (MCQ) carrying 1 or 2 marks each in all papers and sections. These questions are objective in nature, and each will have a choice of four answers, out of which the candidate has to mark the correct answer(s). (ii) Numerical Answer Questions of 1 or 2 marks each in all papers and sections. For these questions the answer is a real number, to be entered by the candidate using the virtual keypad. No choices will be shown for this type of questions.

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Design of Questions The questions in a paper may be designed to test the following abilities: (i) Recall: These are based on facts, principles, formulae or laws of the discipline of the paper. The candidate is expected to be able to obtain the answer either from his/her memory of the subject or at most from a one-line computation. (ii) Comprehension: These questions will test the candidate's understanding of the basics of his/her field, by requiring him/her to draw simple conclusions from fundamental ideas. (iii) Application: In these questions, the candidate is expected to apply his/her knowledge either through computation or by logical reasoning. (iv) Analysis and Synthesis: In these questions, the candidate is presented with data, diagrams, images etc. that require analysis before a question can be answered. A Synthesis question might require the candidate to compare two or more pieces of information. Questions in this category could, for example, involve candidates in recognising unstated assumptions, or separating useful information from irrelevant information.

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Marking Scheme For 1-mark multiple-choice questions, 1/3 marks will be deducted for a wrong answer. Likewise, for2-marks multiple-choice questions, 2/3 marks will be deducted for a wrong answer. There is no negative marking for numerical answer type questions. General Aptitude (GA) Questions In all papers, GA questions carry a total of 15 marks. The GA section includes 5 questions carrying 1 mark each (sub-total 5 marks) and 5 questions carrying 2 marks each (sub-total 10 marks). Question Papers other than GG, XE and XL These papers would contain 25 questions carrying 1 mark each (sub-total 25 marks) and 30 questions carrying 2 marks each (sub-total 60 marks). The question paper will consist of questions of multiple choice and numerical answer type. For numerical answer questions, choices will not be given. Candidates have to enter the answer (which will be a real number, signed or unsigned, e.g. 25.06, -25.06, 25, -25 etc.) using a virtual keypad. An appropriate range will be considered while evaluating the numerical answer type questions so that the candidate is not penalized due to the usual round-off errors. GG (Geology and Geophysics) Paper Apart from the General Aptitude (GA) section, the GG question paper consists of two parts: Part A and Part B. Part A is common for all candidates. Part B contains two sections: Section 1 (Geology) and Section 2 (Geo-physics). Candidates will have to attempt questions in Part A and either Section 1 or Section 2 in Part B. Part A consists of 25 multiple-choice questions carrying 1-mark each (sub-total 25 marks and some of these may be numerical answer type questions). Each section in Part B (Section 1 and Section 2) consists of 30 multiple choice questions carrying 2 marks each (sub-total 60 marks and some of these may be numerical answer type questions). XE Paper (Engineering Sciences)


In XE paper, Engineering Mathematics section (Section A) is compulsory. This section contains 11 questions carrying a total of 15 marks: 7 questions carrying 1 mark each (subtotal 7 marks), and 4 questions carrying 2 marks each (sub-total 8 marks). Some questions may be of numerical answer type questions. Each of the other sections of the XE paper (Sections B through G) contains 22 questions carrying a total of 35 marks: 9 questions carrying 1 mark each (sub-total 9 marks) and 13 questions carrying 2 marks each (sub-total 26 marks). Some questions may be of numerical answer type. XL Paper (Life Sciences) In XL paper, Chemistry section (Section H) is compulsory. This section contains 15 questions carrying a total of 25 marks: 5 questions carrying 1 mark each (sub-total 5 marks) and 10 questions carrying 2-marks each (sub-total 20 marks). Some questions may be of numerical answer type. Each of the other sections of the XL paper (Sections I through M) contains 20 questions carrying a total of 30 marks: 10 questions carrying 1 mark each (sub-total 10 marks) and 10 questions carrying 2 marks each (sub-total 20 marks). Some questions may be of numerical answer type. Note on Negative Marking for Wrong Answers For a wrong answer chosen for the multiple choice questions, there would be negative marking. For1-mark multiple choice questions, 1/3 mark will be deducted for a wrong answer. Likewise, for 2-mark multiple choice questions, 2/3 mark will be deducted for a wrong answer. However, there is no negative marking for a wrong answer in numerical answer type questions.


Syllabus for General Aptitude (GA) Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction. Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.

Syllabus for Electrical Engineering (EE) ENGINEERING MATHEMATICS Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors. Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method. Complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals. Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson,Normal and Binomial distribution, Correlation and regression analysis. Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations. Transform Theory: Fourier transform,Laplace transform, Z-transform.

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ELECTRICAL ENGINEERING Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere’s and Biot-Savart’s laws; inductance; dielectrics; capacitance. Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms. Electrical Machines: Single phase transformer – equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers – connections, parallel operation; auto-transformer; energy conversion principles; DC machines – types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors – principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines – performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors. Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of over-current, differential and distance protection; solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transmission and FACTS concepts. Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state space model; state transition matrix, controllability and observability.


Electrical and Electronic Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; instrument transformers; digital voltmeters and multimeters; phase, time and frequency measurement; Q-meters; oscilloscopes; potentiometric recorders; error analysis. Analog and Digital Electronics: Characteristics of diodes, BJT, FET; amplifiers – biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers – characteristics and applications; simple active filters; VCOs and timers; combinational and sequential logic circuits; multiplexer; Schmitt trigger; multi-vibrators; sample and hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing. Power Electronics and Drives: Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs – static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters – fully controlled and half controlled; principles of choppers and inverters; basis concepts of adjustable speed dc and ac drives.


GATE Previous Year Solved Papers Electrical Engineering - EE

2012 - 14

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SET - 1

GATE 2014 Solved Paper Duration: 180 minutes

EE: Electrical Engineering

Maximum Marks: 100

Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of⅓ marks for a 1-mark question and ⅔ marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: “I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition”.

______________________________________________________________ GATE Previous Year Solved Papers by

GATE 2014

SET-1

General Aptitude - GA

Q. 1 – Q. 5 carry one mark each. Q.1

Which of the following options is the closest in meaning to the phrase underlined in the sentence below? It is fascinating to see life forms cope with varied environmental conditions. (A) adopt to

Q.2

(B) adapt to

(C) adept in

(D) accept with

Choose the most appropriate word from the options given below to complete the following sentence. He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________. (A) superb

Q.3

(B) medium

(C) mediocre

(D) exhilarating

In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement? (A) He wants all the money (C) He will assume final responsibility

(B) He will return the money (D) He will resist all enquiries

Q.4

If (� + 1/�)2 = 98, compute (� 2 + 1/� 2 ).

Q.5

The roots of �� 2 + �� + � = 0 are real and positive. a, b and c are real. Then �� 2 + �|�| + � = 0 has

(A) no roots (C) 3 real roots

(B) 2 real roots (D) 4 real roots

Q. 6 – Q. 10 carry two marks each.

Q.6

The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. What can be inferred from this passage? (A) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala (B) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low-lying (C) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala (D) Higher summer temperatures result in higher rainfall near the Palghat Gap area

GATE Previous Year Solved Papers by

GATE 2014 Q.7

SET-1


Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely? (A) Strategies are now available for eliminating psychiatric illnesses (B) Certain psychiatric illnesses have a genetic basis (C) All human diseases can be traced back to genes and how they are expressed (D) In the future, genetics will become the only relevant field for identifying psychiatric illnesses

Q.8

Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________.

Q.9

In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?

Own vehicle

Car Scooter Both

Do not own vehicle Q.10

Men 40 30 60

Women 34 20 46

20

50

When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________

END OF THE QUESTION PAPER


GATE 2014

SET-1

Electrical Engineering - EE


Given a system of equations:

Which of the following is true regarding its solutions

(A) The system has a unique solution for any given and (B) The system will have infinitely many solutions for any given (C) Whether or not a solution exists depends on the given and and (D) The system would have no solution for any values of Q.2

(A) Q.3

. The maximum value of the function in the interval (0, ∞) is

Let

and

(B)

(C)

(D)

The solution for the differential equation

, with initial conditions

and

(A) sin

(C) Q.4

Let (A) 0

Q.5

cos

, is (B) sin (D) cos

cos

be the Laplace Transform of a signal (B) 3

(C) 5

. Then,

is

(D) 21

Let

be the set of points in the complex plane corresponding to the unit circle. (That is, ∗ ∗ ∶ | | ). Consider the function where denotes the complex conjugate of . The maps to which one of the following in the complex plane

(A) (B) (C) (D)

Q.6

|

unit circle horizontal axis line segment from origin to (1, 0) the point (1, 0) the entire horizontal axis

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________. 10 A 100 V

8A 80 V 15 V


GATE 2014 Q.7

SET-1


C0 is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity , the expression for the modified capacitance is (a)

(A)

(C)

Q.8

(b)

(B)

(D)

V in series with a 100 Ω A combination of 1 µF capacitor with an initial voltage v resistor is connected to a 20 mA ideal dc current source by operating both switches at s as shown. Which of the following graphs shown in the options approximates the voltage v across the current source over the next few seconds?

+ vs -

(A)

(B)

(C)

(D)

Q.9

is nonzero only for be convolution of (A) (B) (C) (D)

′ , and similarly, is nonzero only for ′ . Let and . Which one of the following statements is TRUE?

can be nonzero over an unbounded interval. . is nonzero for is zero outside of ′ ′ . is nonzero for ′ ′ .


GATE 2014 Q.10

SET-1


For a periodic square wave, which one of the following statements is TRUE? (A) The Fourier series coefficients do not exist. (B) The Fourier series coefficients exist but the reconstruction converges at no point. (C) The Fourier series coefficients exist and the reconstruction converges at most points. (D) The Fourier series coefficients exist and the reconstruction converges at every point.

Q.11

An 8-pole, 3-phase, 50 Hz induction motor is operating at a speed of 700 rpm. The frequency of the rotor current of the motor in Hz is ____________.

Q.12

For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is (A) 1/4

Q.13

(B) 1/2

(C) 2

(D) 4

A star connected 400 V, 50 Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results: Open circuit test: Voc = 400 V (rms, line-to-line) at field current, If = 2.3 A Short circuit test: Isc = 10 A (rms, phase) at field current, If = 1.5 A The value of per phase synchronous impedance in Ω at rated voltage is __________.

Q.14

The undesirable property of an electrical insulating material is (A) high dielectric strength (C) high thermal conductivity

Q.15

(B) high relative permittivity (D) high insulation resistivity

Three-phase to ground fault takes place at locations F1 and F2 in the system shown in the figure IF1 IF2

E A

~

F1

A

F2

B

~

EB0

VF1 VF2

If the fault takes place at location F1, then the voltage and the current at bus A are VF1 and IF1 respectively. If the fault takes place at location F2, then the voltage and the current at bus A are VF2 and IF2 respectively. The correct statement about voltages and currents during faults at F1 and F2 is (A) (B) (C) (D)

VF1 leads IF1 and VF2 leads IF2 VF1 leads IF1 and VF2 lags IF2 VF1 lags IF1 and VF2 leads IF2 VF1 lags IF1 and VF2 lags IF2


GATE 2014 Q.16

SET-1


A 2-bus system and corresponding zero sequence network are shown in the figure.

The transformers T1 and T2 are connected as (A) (B) (C) (D) 

Q.17

and  and   and  and

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of (A) only one root at the origin (C) only positive real roots

Q.18

(B) imaginary roots (D) only negative real roots

The root locus of a unity feedback system is shown in the figure

The closed loop transfer function of the system is

Q.19

(A)

C (s) K  R( s) s  1s  2

(B)

C (s) K  R( s) s  1s  2  K

(C)

C (s) K  R( s) s  1s  2  K

(D)

C (s) K  R( s) s  1s  2  K

Power consumed by a balanced 3-phase, 3-wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle in radians is (A) π/12

Q.20

(B) π/8

(C) π/6

(D) π/3

In an oscilloscope screen, linear sweep is applied at the (A) vertical axis (C) origin

(B) horizontal axis (D) both horizontal and vertical axis


GATE 2014 Q.21

SET-1

A cascade of three identical modulo-5 counters has an overall modulus of (A) 5

Q.22


(B) 25

(C) 125

(D) 625

In the Wien Bridge oscillator circuit shown in figure, the bridge is balanced when C1 +Vcc

R1

R3

-Vcc C2

(A) (C)

Q.23

R4

R2

,

,

(B)

,

(D)

,

The magnitude of the mid-band voltage gain of the circuit shown in figure is (assuming transistor to be 100)

of the

+Vcc 10k C

C vo

10k hfe=100

vi

(A) 1

Q.24

(B) 10

1k

C

(C) 20

(D) 100

The figure shows the circuit of a rectifier fed from a 230-V (rms), 50-Hz sinusoidal voltage source. If we want to replace the current source with a resistor so that the rms value of the current supplied by the voltage source remains unchanged, the value of the resistance (in ohms) is __________ (Assume diodes to be ideal.)

10 A 230 V, 50 Hz


GATE 2014 Q.25

SET-1


Figure shows four electronic switches (i), (ii), (iii) and (iv). Which of the switches can block voltages of either polarity (applied between terminals ‘a’ and ‘b’) when the active device is in the OFF state? a

a

b

b (ii)

(i)

(A) (B) (C) (D)

a

a

b

b

(iii)

(iv)

(i), (ii) and (iii) (ii), (iii) and (iv) (ii) and (iii) (i) and (iv)

Q. 26 – Q. 55 carry two marks each. Q.26

Let : , ∞ ⟶ , ∞ be a function defined by , where represents the integer part of . (That is, it is the largest integer which is less than or equal to ). The value of the constant term in the Fourier series expansion of is _______

Q.27

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n-3) is (A)

Q.28

(B) 0

(C)

(D)

The line integral of function F = yzi, in the counterclockwise direction, along the circle x2+y2 = 1 at z = 1 is (A) -2π

(B) -π

(C) π

(D) 2π

Q.29

An incandescent lamp is marked 40 W, 240V. If resistance at room temperature (26°C) is 120 Ω, and temperature coefficient of resistance is 4.5x10-3/°C, then its ‘ON’ state filament temperature in °C is approximately _______

Q.30

In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ______ I 300V

R


GATE 2014 Q.31

SET-1

In an unbalanced three phase system, phase current o ∠ pu, zero sequence current ∠ in pu is

(A) 1.00

Q.32

Q.33


(B) 7.81

o

o ∠ pu, negative sequence current pu. The magnitude of phase current

(C) 11.53

(D) 13.00

The following four vector fields are given in Cartesian co-ordinate system. The vector field which does not satisfy the property of magnetic flux density is 2 2 2 (A) y a x  z a y  x a z

2 2 2 (B) z a x  x a y  y a z

2 2 2 (C) x a x  y a y  z a z

2 2 2 2 2 2 (D) y z a x  x z a y  x y a z

The function shown in the figure can be represented as

1

t 0

T

2T

(A)

(B) (C)

(D)

Q.34

Let and (A) 0 and 0

Q.35

Let

Define

be the Z-transform of a causal signal are (B) 0 and 1

(C) 1 and 0

be a continuous time signal and let

(D) 1 and 1

be its Fourier Transform defined by

by

What is the relationship between (A) (B) (C) (D)

. Then, the values of

and

?

. would always be proportional to would be proportional to if is an even function. would be proportional to only if is a sinusoidal function. . would never be proportional to


GATE 2014 Q.36

SET-1


The core loss of a single phase, 230/115 V, 50 Hz power transformer is measured from 230 V side by feeding the primary (230 V side) from a variable voltage variable frequency source while keeping the secondary open circuited. The core loss is measured to be 1050 W for 230 V, 50 Hz input. The core loss is again measured to be 500 W for 138 V, 30 Hz input. The hysteresis and eddy current losses of the transformer for 230 V, 50 Hz input are respectively, (A) 508 W and 542 W. (C) 498 W and 552 W.

(B) 468 W and 582 W. (D) 488 W and 562 W.

Q.37

A 15 kW, 230 V dc shunt motor has armature circuit resistance of 0.4 Ω and field circuit resistance of 230 Ω. At no load and rated voltage, the motor runs at 1400 rpm and the line current drawn by the motor is 5 A. At full load, the motor draws a line current of 70 A. Neglect armature reaction. The full load speed of the motor in rpm is _________.

Q.38

A 3 phase, 50 Hz, six pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is (A) 1.567

Q.39

(B) 1.712

(C) 1.948

(D) 2.134

A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The phase sequence of bus voltage is R-Y-B and that of incoming generator voltage is R-Y-B. R

Y

B R' Y' B' La

Infinite Bus

Lb

Incoming Generator

Lc

It was found that the lamps are becoming dark in the sequence La-Lb-Lc. It means that the phase sequence of incoming generator is (A) (B) (C) (D)

opposite to infinite bus and its frequency is more than infinite bus opposite to infinite bus but its frequency is less than infinite bus same as infinite bus and its frequency is more than infinite bus same as infinite bus and its frequency is less than infinite bus


GATE 2014 Q.40

SET-1


A distribution feeder of 1 km length having resistance, but negligible reactance, is fed from both the ends by 400V, 50 Hz balanced sources. Both voltage sources S1 and S2 are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.

The contributions of S1 and S2 in 100 A current supplied at location P respectively, are (A) 75 A and 25 A

Q.41

(B) 50 A and 50 A

(C) 25 A and 75 A

(D) 0 A and 100 A

A two bus power system shown in the figure supplies load of 1.0+j0.5 p.u.

The values of V1 in p.u. and δ2 respectively are (A) 0.95 and 6.00 o

Q.42

(B) 1.05 and -5.44o

(C) 1.1 and -6.00 o

(D) 1.1 and -27.12o

The fuel cost functions of two power plants are

Plant P1 :

C1  0.05Pg12  APg1  B

Plant P2 :

C2  0.10 Pg 22  3 APg 2  2 B

where, Pg1 and Pg2 are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 1000 MW load at incremental fuel cost of 100 Rs/MWh, the ratio of load shared by plants P1 and P2 is (A) 1:4

Q.43

(B) 2:3

(C) 3:2

(D) 4:1

The overcurrent relays for the line protection and loads connected at the buses are shown in the figure. A

~

B RA 300 A

C RB 200 A

100 A

The relays are IDMT in nature having the characteristic

t op 

0.14  Time Multiplier Setting Plug Setting Multiplier0.02  1

The maximum and minimum fault currents at bus B are 2000 A and 500 A respectively. Assuming the time multiplier setting and plug setting for relay RB to be 0.1 and 5A respectively, the operating time of RB (in seconds) is ____________


GATE 2014 Q.44

SET-1


For the given system, it is desired that the system be stable. The minimum value of condition is _______________.

+

R(s)

for this

C(s)

‒

.

Q.45

.

The Bode magnitude plot of the transfer function Note that ‒6 dB/octave = ‒20 dB/decade. The value of

is shown below:

is _____________.

‒ dB/Octave

dB

Q.46

dB/Octave

dB/Octave

dB/Octave

‒ dB/Octave

‒ .

dB/Octave  rad/s

.

A system matrix is given as follows.

. The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______


GATE 2014 Q.47

SET-1


The reading of the voltmeter (rms) in volts, for the circuit shown in the figure is __________ R = 0.5 

1j

1/j

100sin(t)

V 1/j

1j

Q.48

The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, the flux density in the air gap is 0.2 Wb/m2, and the area of the coil is 80 mm2. The electrodynamometer ammeter has a change in mutual inductance with respect to deflection of 0.5 mH/deg. The spring constants of both the meters are equal. The value of current, at which the deflections of the two meters are same, is ________

Q.49

Given that the op-amps in the figure are ideal, the output voltage

is

R

V2 R

R V0

2R R

R

R

V1

(A) (C)

/

(B) (D)


GATE 2014 Q.50

SET-1


Which of the following logic circuits is a realization of the function F whose Karnaugh map is shown in figure AB

0

00

01

1

1

11

10

C 1

(A)

1

1

(B)

(C)

A

A

B

B

C

C

(D)

A

A C

C B

B


GATE 2014 Q.51

SET-1


In the figure shown, assume the op-amp to be ideal. Which of the alternatives gives the correct ? Bode plots for the transfer function

(A)

(B)

(C)

(D)


GATE 2014

Q.52

SET-1


An output device is interfaced with 8-bit microprocessor 8085A. The interfacing circuit is shown in figure AB 8

BDB

8 3Lx8L Decoder A15 A14 A13 A12

0

I2 I1 I0

1 3

8

4

E1

A11

5 6

E2

Output Device

7

E3 IO/M

Output Port

2

WR

BCB

The interfacing circuit makes use of 3 Line to 8 Line decoder having 3 enable lines E1 , E 2 , E 3 . The address of the device is (A) 50 H

Q.53

(B) 5000 H

(C) A0 H

(D) A000 H

The figure shows the circuit diagram of a rectifier. The load consists of a resistance 10 Ω and an inductance 0.05 H connected in series. Assuming ideal thyristor and ideal diode, the thyristor firing angle (in degree) needed to obtain an average load voltage of 70 V is ______

+ 325 sin (314t) V

-

Load


GATE 2014 Q.54

SET-1


Figure (i) shows the circuit diagram of a chopper. The switch S in the circuit in figure (i) is switched such that the voltage across the diode has the wave shape as shown in figure (ii). The capacitance C is large so that the voltage across it is constant. If switch S and the diode are ideal, the peak to peak ripple (in A) in the inductor current is ______ S

1 mH + vD

100 V

Load

C

_

Figure (i) vD 100 V

0

0.05

0.2

0.15

0.1

t (ms)

Figure (ii)

Q.55

The figure shows one period of the output voltage of an inverter. α should be chosen such that o o α . If rms value of the fundamental component is 50 V, then α in degree is______________

0

100 V

100 V

100 V



180-

-100 V

180

180+

360-

-100 V

360

-100 V



t (degree)

GATE 2014 - Answer Keys (SET – 1) General Aptitude - GA Q. No. 1 2 3 4

Key / Range B C C 96 to 96

Q. No. 5 6 7 8

Key / Range D C B 850 to 850

Q. No. 9 10

Key / Range 48 to 48 6 to 6

Key / Range B C C D 23 to 23 C 0.5 to 0.5 B B 2470 to 2471 10 to 10 C C A B B A 1239 to 1242 C

Q. No. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

Key / Range A D B D 0.21 to 0.23 0.61 to 0.63 0.7 to 0.8 2.9 to 3.1 140 to 142 3.0 to 3.4 B C A B 69 to 70 2.49 to 2.51 76.5 to 78.0

Electrical Engineering - EE Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Key / Range B A C B C 330 to 330 A C C C 3.2 to 3.5 C 14.5 to 15.5 B C B B C C

Q. No. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38


SET - 2 GATE 2014 Solved Paper EE: Electrical Engineering Duration: 180 minutes

Maximum Marks: 100



GATE 2014

SET-2



Choose the most appropriate phrase from the options given below to complete the following sentence. India is a post-colonial country because (A) it was a former British colony (B) Indian Information Technology professionals have colonized the world (C) India does not follow any colonial practices (D) India has helped other countries gain freedom

Q.2

Who ___________ was coming to see us this evening? (A) you said (C) did you say that

Q.3

(B) did you say (D) had you said

Match the columns. Column 1 1) eradicate 2) distort 3) saturate 4) utilize

Column 2 P) misrepresent Q) soak completely R) use S) destroy utterly

(A) 1:S, 2:P, 3:Q, 4:R (C) 1:Q, 2:R, 3:S, 4:P Q.4

What is the average of all multiples of 10 from 2 to 198? (A) 90

Q.5

(B) 1:P, 2:Q, 3:R, 4:S (D) 1:S, 2:P, 3:R, 4:Q

(B) 100

The value of �12 + �12 + √12 + ⋯ is

(A) 3.464

(B) 3.932

(C) 110

(D) 120

(C) 4.000

(D) 4.444


The old city of Koenigsberg, which had a German majority population before World War 2, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively. Which of the statements below can be inferred from this passage? (A) Kaliningrad was historically Russian in its ethnic make up (B) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia (C) Koenigsberg was renamed Kaliningrad, as that was its original Russian name (D) Poland and Lithuania are on the route from Kaliningrad to the rest of Russia


GATE 2014 Q.7

SET-2


The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region. Which one of the following statements, if true, does not contradict this conclusion? (A) A high proportion of the affected population has returned from neighbouring countries where dengue is prevalent (B) More cases of dengue are now reported because of an increase in the Municipal Office’s administrative efficiency (C) Many more cases of dengue are being diagnosed this year since the introduction of a new and effective diagnostic test (D) The number of people with malarial fever (also contracted from mosquito bites) has increased this year

Q.8

If x is real and |� 2 − 2� + 3| = 11, then possible values of | − � 3 + � 2 − �| include

(A) 2, 4

(B) 2, 14

(C) 4, 52

(D) 14, 52

Q.9

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009?

Q.10

At what time between 6 �. �. and 7 �. �. will the minute hand and hour hand of a clock make an angle closest to 60°?

(A) 6: 22 �. �. (C) 6: 38 �. �.

(B) 6: 27 �. �. (D) 6: 45 �. �.



GATE 2014

SET-2



Which one of the following statements is true for all real symmetric matrices? (A) All the eigenvalues are real. (B) All the eigenvalues are positive. (C) All the eigenvalues are distinct. (D) Sum of all the eigenvalues is zero.

Q.2

Consider a dice with the property that the probability of a face with dots showing up is proportional to . The probability of the face with three dots showing up is ________.

Q.3

Minimum of the real valued function (A) ‒∞

Q.4

(B) 0

(C) 1

All the values of the multi-valued complex function (A) purely imaginary. (C) on the unit circle.

Q.5

/

(D) ∞ √

, where

, are

(B) real and non-negative. (D) equal in real and imaginary parts.

Consider the differential equation this differential equation for ? (A)

occurs at x equal to

. Which of the following is a solution to (C) ⁄

(B)

(D) ln

Q.6

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 380 µH and 240 µH. Their mutual inductance in μH is ________

Q.7

The switch SW shown in the circuit is kept at position ‘1’ for a long duration. At t = 0+, the switch is moved to position ‘2’. Assuming |Vo2| > |Vo1|, the voltage vc(t) across the capacitor is R

'2'

SW

'1' R Vo2

Vo1 C

vc

 t/2RC )  Vo1 (A) v c (t)  Vo2 (1  e  t/2RC )  Vo1 (B) v c (t)  Vo2 (1  e  t/2RC )  Vo1 (C) v c (t)  (Vo2  Vo1 )(1  e  t/2RC )  Vo1 (D) v c (t)  (Vo2  Vo1 )(1  e


GATE 2014 Q.8

SET-2


A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is placed symmetrically with respect to the plates. 10 Volt



  d/2 d

If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio ε1 : ε2 is (A) 1:4

Q.9

(B) 2:3

(A) 1/30

and the steady state output is

(B) 1/15

(C) 3/4

Consider an LTI system with impulse response then the input,

(A) (C)

Q.11

(D) 4:1

Consider an LTI system with transfer function

If the input to the system is cos of is

Q.10

(C) 3:2

sin

, then the value

(D) 4/3

. If the output of the system is , is given by (B) (D)

Assuming an ideal transformer, the Thevenin’s equivalent voltage and impedance as seen from the terminals x and y for the circuit in figure are 1 x sin(t) 1:2

(A) (C)

sin sin

, Ω , Ω

(B) (D)

sin sin

y

, Ω , . Ω


GATE 2014 Q.12

SET-2


A single phase, 50 kVA, 1000V/100 V two winding transformer is connected as an autotransformer as shown in the figure.

The kVA rating of the autotransformer is _____________. Q.13

A three-phase, 4-pole, self excited induction generator is feeding power to a load at a frequency f1. If the load is partially removed, the frequency becomes f2. If the speed of the generator is maintained at 1500 rpm in both the cases, then (A) f1, f2 > 50 Hz and f1 > f2 (C) f1, f2 < 50 Hz and f2 > f1

(B) f1 < 50 Hz and f2 > 50 Hz (D) f1 > 50 Hz and f2 < 50 Hz

Q.14

A single phase induction motor draws 12 MW power at 0.6 lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to 0.8 lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is __________.

Q.15

A three phase star-connected load is drawing power at a voltage of 0.9 pu and 0.8 power factor lagging. The three phase base power and base current are 100 MVA and 437.38 A respectively. The line-to-line load voltage in kV is ________.

Q.16

Shunt reactors are sometimes used in high voltage transmission systems to (A) limit the short circuit current through the line. (B) compensate for the series reactance of the line under heavily loaded condition. (C) limit over-voltages at the load side under lightly loaded condition. (D) compensate for the voltage drop in the line under heavily loaded condition.

Q.17

The closed-loop transfer function of a system is T

to unit step input is __________. Q.18

s

.

. The steady state error due

The state transition matrix for the system

is (A)

(B)

(C)

(D)


GATE 2014 Q.19

SET-2


The saw-tooth voltage waveform shown in the figure is fed to a moving iron voltmeter. Its reading would be close to _____________

100 V

t 20ms

40ms

Q.20

While measuring power of a three-phase balanced load by the two-wattmeter method, the readings are 100 W and 250 W. The power factor of the load is _________.

Q.21

Which of the following is an invalid state in an 8-4-2-1 Binary Coded Decimal counter (A) 1 0 0 0

(B) 1 0 0 1

(C) 0 0 1 1

(D) 1 1 0 0

Q.22

The transistor in the given circuit should always be in active region. Take .7 V. The maximum value of in Ω which can be used, is ______________.

Q.23

The sinusoidal ac source in the figure has an rms value of , the minimum value of

Q.24

√

. V,

V. Considering all possible values of

in Ω to avoid burnout of the Zener diode is _________.

A step-up chopper is used to feed a load at 400 V dc from a 250 V dc source. The inductor current is continuous. If the ‘off’ time of the switch is 20 µs, the switching frequency of the chopper in kHz is ____________.


GATE 2014 Q.25

SET-2


In a constant V/f control of induction motor, the ratio V/f is maintained constant from 0 to base frequency, where V is the voltage applied to the motor at fundamental frequency f. Which of the following statements relating to low frequency operation of the motor is TRUE? (A) At low frequency, the stator flux increases from its rated value. (B) At low frequency, the stator flux decreases from its rated value. (C) At low frequency, the motor saturates. (D) At low frequency, the stator flux remains unchanged at its rated value.


To evaluate the double integral . The integral will reduce to

and

(A) (C) Q.27

Let

⁄

, we make the substitution

(B)

(D)

be a random variable with probability density function

The probability

Q.28

⁄

. , for | | . , for | | , otherwise.

.

is ___________.

The minimum value of the function [ , ] is

in the interval

(A) 20 (C) 16

Q.29

(B) 28 (D) 32

Assuming the diodes to be ideal in the figure, for the output to be clipped, the input voltage vi must be outside the range 10k

10k vi

(A) -1 V to -2 V (C) +1 V to -2 V

1V

vo

2V

(B) -2 V to -4 V (D) +2 V to -4 V


GATE 2014 Q.30

SET-2


The voltage across the capacitor, as shown in the figure, is expressed as

vc (t)  A1 sin(ω1t  θ1 )  A 2 sin(ω2 t  θ 2 )

The values of A1 and A 2 respectively, are (A) 2.0 and 1.98

Q.31

(B) 2.0 and 4.20

(C) 2.5 and 3.50

(D) 5.0 and 6.40

The total power dissipated in the circuit, shown in the figure, is 1 kW.

10A

1

2A

XC1

XL

R Load

ac source

V

XC2

200 V

The voltmeter, across the load, reads 200 V. The value of X L is ___________.

Q.32

at a point having normal distance meters from an The magnitude of magnetic flux density (in SI units). An infinitely extended wire is infinitely extended wire carrying current of A is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. is permeability of free space. Assume ̂, ,̂ to be unit vectors along x, y and z axes respectively.

Assuming right handed coordinate system, magnetic field intensity, (A)

weber/m2

(B)

̂ A/m

(C)

A/m

at coordinate (2,1,0) will be (D) 0 A/m


GATE 2014 Q.33

SET-2


A discrete system is represented by the difference equation

a  1  X1 (k)   X1 (k  1)   a X (k  1)  a  1 a  X (k)  2   2   It has initial conditions X1(0) = 1; X2(0) = 0. The pole locations of the system for a = 1, are (A) 1 ± j0

Q.34

(B) -1 ± j0

(C) ±1 + j0

(D) 0 ± j1

An input signal x(t)  2  5sin(100π t) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by

Y(z) 1  1  z  N     X(z) N  1  z 1  where, N represents the number of samples per cycle. The output y(n) of the system under steady state is (A) 0

Q.35

(B) 1

(C) 2

(D) 5

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is (A) (B) (C) (D)

a highly attenuated square wave at 10 kHz. nearly zero. a nearly perfect cosine wave at 30 kHz. a nearly perfect sine wave at 30 kHz.

Q.36

A 250 V dc shunt machine has armature circuit resistance of 0.6 Ω and field circuit resistance of 125 Ω. The machine is connected to 250 V supply mains. The motor is operated as a generator and then as a motor separately. The line current of the machine in both the cases is 50 A. The ratio of the speed as a generator to the speed as a motor is ____________.

Q.37

A three-phase slip-ring induction motor, provided with a commutator winding, is shown in the figure. The motor rotates in clockwise direction when the rotor windings are closed. 3-phase ac, f Hz

f2 Prime Mover

Slip Ring Induction Motor

fr f1

If the rotor winding is open circuited and the system is made to run at rotational speed fr with the help of prime-mover in anti-clockwise direction, then the frequency of voltage across slip rings is f1 and frequency of voltage across commutator brushes is f2. The values of f1 and f2 respectively are (A) f + fr and f (C) f - fr and f+fr

(B) f - fr and f (D) f + fr and f-fr


GATE 2014 Q.38


A 20-pole alternator is having 180 identical stator slots with 6 conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is V1. If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is V2. Assuming full pitch, single-layer winding, the ratio V1/V2 is (A)

Q.39

SET-2

1 3

(B)

1 2

(C)

3

(D) 2

For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respectively, are (A) 10 and 21

(B)

and 21

(C) 21 and 10

(D)

and 10

Q.40

A synchronous generator is connected to an infinite bus with excitation voltage Ef = 1.3 pu. The generator has a synchronous reactance of 1.1 pu and is delivering real power (P) of 0.6 pu to the bus. Assume the infinite bus voltage to be 1.0 pu. Neglect stator resistance. The reactive power (Q) in pu supplied by the generator to the bus under this condition is _________.

Q.41

There are two generators in a power system. No-load frequencies of the generators are 51.5 Hz and 51 Hz, respectively, and both are having droop constant of 1 Hz/MW. Total load in the system is 2.5 MW. Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in Hz in the steady state is ___________.

Q.42

The horizontally placed conductors of a single phase line operating at 50 Hz are having outside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854  1012 F/m. The capacitance to ground per kilometer of each line is (A) (B) (C) (D)

4.2  109 F 8.4  109 F 4.2  1012 F 8.4  1012 F

Q.43

A three phase, 100 MVA, 25 kV generator has solidly grounded neutral. The positive, negative, and the zero sequence reactances of the generator are 0.2 pu, 0.2 pu, and 0.05 pu, respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is _________.

Q.44

A system with the open loop transfer function

is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is ______


GATE 2014

Q.45

SET-2


For the transfer function

.

The values of the constant gain term and the highest corner frequency of the Bode plot respectively are (A) 3.2, 5.0

Q.46

(B) 16.0, 4.0

(C) 3.2, 4.0

(D) 16.0, 5.0

The second order dynamic system

has the matrices P, Q and R as follows:

The system has the following controllability and observability properties: (A) (B) (C) (D)

Q.47

Controllable and observable Not controllable but observable Controllable but not observable Not controllable and not observable

and are connected in parallel to give an equivalent resistor Suppose that resistors and have tolerance of 1% each, the equivalent resistor for resistors resistors and Ω will have tolerance of (A) 0.5%

Q.48

(B) 1%

(C) 1.2%

. If Ω

(D) 2%

Two ammeters X and Y have resistances of 1.2 Ω and 1.5 Ω respectively and they give full-scale deflection with 150 mA and 250 mA respectively. The ranges have been extended by connecting shunts so as to give full scale deflection with 15 A. The ammeters along with shunts are connected in parallel and then placed in a circuit in which the total current flowing is 15A. The current in amperes indicated in ammeter X is __________.


GATE 2014 Q.49

SET-2

An oscillator circuit using ideal op-amp and diodes is shown in the figure.

The time duration for +ve part of the cycle is ∆ be _____________.

Q.50

and for –ve part is ∆ . The value of

∆

will

The SOP (sum of products) form of a Boolean function is ∑ , , ,7, , where inputs are A,B,C,D (A is MSB, and D is LSB). The equivalent minimized expression of the function is ̅

(A) ̅

(B) (C) (D)

Q.51


̅

̅

̅

̅

̅

̅ ̅

̅

̅

̅

̅

A JK flip flop can be implemented by T flip-flops. Identify the correct implementation. (A)

(B)

(C)

(D)


GATE 2014 Q.52

SET-2


In an 8085 microprocessor, the following program is executed Address location – Instruction 2000H 2001H 2003H 2005H 2006H 2007H 200AH

XRA A MVI B,04H MVI A, 03H RAR DCR B JNZ 2005 HLT

At the end of program, register A contains (A) 60H

(B) 30H

(C) 06H

(D) 03H

Q.53

A fully controlled converter bridge feeds a highly inductive load with ripple free load current. The input supply (v ) to the bridge is a sinusoidal source. Triggering angle of the bridge converter is  = 300. The input power factor of the bridge is __________.

Q.54

A single-phase SCR based ac regulator is feeding power to a load consisting of 5 Ω resistance and 16 mH inductance. The input supply is 230 V, 50 Hz ac. The maximum firing angle at which the voltage across the device becomes zero all throughout and the rms value of current through SCR, under this operating condition, are (A) 300 and 46 A (C) 450 and 23 A

Q.55

(B) 300 and 23 A (D) 450 and 32 A

The SCR in the circuit shown has a latching current of 40 mA. A gate pulse of 50 µs is applied to the SCR. The maximum value of R in Ω to ensure successful firing of the SCR is _________.

END OF THE QUESTION PAPER GATE Previous Year Solved Papers by


Key / Range A B A B

Q. No. 5 6 7 8

Key / Range C B D D

Q. No. 9 10

Key / Range 140 to 140 A

Key / Range A 0.10 to 0.12 49.9 to 50.1 B 15300 to 15500 5 to 5 A C B 9.9 to 10.3 1.2 to 1.3 A B A 0.74 to 0.82 C 6055 to 6065

Electrical Engineering - EE Q. No. 1 2 3 4 5

Key / Range A 0.13 to 0.15 C B C

Q. No. 20 21 22 23 24

Key / Range 0.78 to 0.82 D 22 to 23 299 to 301 31.0 to 31.5

Q. No. 39 40 41 42 43

6 7 8 9 10 11 12 13 14 15 16 17 18 19

35 to 35 D C B B A 545 to 555 C 6.97 to 7.03 117 to 120 C 0 to 0 C 56 to 59

25 26 27 28 29 30 31 32 33 34 35 36 37 38

B B 0.35 to 0.45 B B A 17.3 to 17.4 C A C C 1.22 to 1.32 A D

44 45 46 47 48 49 50 51 52 53 54 55


SET - 3 GATE 2014 Solved Paper Duration: 180 minutes

EE: Electrical Engineering

Maximum Marks: 100



GATE 2014

SET-3



While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I

Q.2

(B) II

(C) III

If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (C) had known, could have

Q.3

(B) well-connected

(C) rambling

(D) friendly

Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17

Q.5

(B) knew, had (D) should have known, would have

Choose the word that is opposite in meaning to the word “coherent”. (A) sticky

Q.4

(D) IV

(B) 37

(C) 64

(D) 26

The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. Q No.

Marks

1 2 3

2 3 2

Answered Correctly 21 15 23

Answered Wrongly 17 27 18

Not Attempted 6 2 3

What is the average of the marks obtained by the class in the examination? (A) 1.34

(B) 1.74

(C) 3.02

(D) 3.91


A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is (A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m. (B) Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m. (C) Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m. (D) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m.


GATE 2014 Q.7

SET-3


By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift (A) (i), (ii) and (iv)

Q.8

(B) (iii) only

(B) decreased by 13% (D) decreased by 11%

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011?

(A) 1:1 Q.10

(D) (iv) only

The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012-2013 (A) increased by 5 % (C) decreased by 20%

Q.9

(C) (i) and (iv)

(B) 2:1

(C) 1.5:1

(D) 2.5:1

Consider the equation: (7526)8 − (Y)8 = (4364)8 , where (X)N stands for X to the base N. Find Y. (A) 1634

(B) 1737

(C) 3142

(D) 3162



GATE 2014

SET-3



Two matrices A and B are given below:

 p2 + q2 B=  pr + qs

 p q A= ;  r s

pr + qs   r 2 + s2 

If the rank of matrix A is N, then the rank of matrix B is (A) N /2

Q.2

(B) N-1

(C) N

(D) 2 N

A particle, starting from origin at t = 0 s, is traveling along x-axis with velocity

v=

π

π  cos  t  m/s 2 2 

At t = 3 s, the difference between the distance covered by the particle and the magnitude of displacement from the origin is _________.

Q.3

Let ∇ ⋅ ( f v ) = x y + y z + z x , where f and v are scalar and vector fields respectively. If 2

2

2

v = yi + zj + xk , then v ⋅ ∇f is (B) 2 xy + 2 yz + 2 zx

(A) x y + y z + z x (C) x + y + z 2

2

2

(D) 0

Q.4

Lifetime of an electric bulb is a random variable with density f(x) = kx2, where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is ________.

Q.5

A function f(t) is shown in the figure. f(t) 1/2 T/2 0

-T/2

t

-1/2

The Fourier transform F(ω) of f(t) is (A) real and even function of ω. (C) imaginary and odd function of ω.

(B) real and odd function of ω. (D) imaginary and even function of ω.


GATE 2014 Q.6

SET-3

The line A to neutral voltage is 10∠15 V for a balanced three phase star-connected load with phase sequence ABC. The voltage of line B with respect to line C is given by (A) 10 3∠105 V

(B) 10∠105 V

(C) 10 3∠ − 75 V

(D) − 10 3∠90 V





Q.7



A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R ( > r) is (A) 4πε 0 r

Q.8


(B) 4πε 0 r

(C) 4πε 0 R

2

2

The driving point impedance Z(s) for the circuit shown below is 1H

1H

Z(s)

(A)

(C)

Q.9

(D) 4πε 0 R

� 4 +3� 2 +1 � 3 +2�

� 2 +1

� 4 +� 2 +1

1F

1F

(B)

� 4 +2� 2 +4

(D)

� 3 +1

A signal is represented by

1 x(t) =  0

� 2 +2

� 4 +� 2 +1

t <1 t >1

The Fourier transform of the convolved signal y(t) = x(2t) ∗ x(t/2) is

ω  sin   sin( 2ω ) ω 2 4 (C) 2 sin( 2ω ) ω (A)

4

2

ω  sin   ω 2 4 (D) 2 sin 2 ω ω (B)

4

2

Q.10

For the signal �(�) = 3 sin 8�� + 6 sin 12�� + sin 14��, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is _________.

Q.11

In a synchronous machine, hunting is predominantly damped by (A) (B) (C) (D)

mechanical losses in the rotor iron losses in the rotor copper losses in the stator copper losses in the rotor


GATE 2014 Q.12

SET-3


A single phase induction motor is provided with capacitor and centrifugal switch in series with auxiliary winding. The switch is expected to operate at a speed of 0.7 Ns, but due to malfunctioning the switch fails to operate. The torque-speed characteristic of the motor is represented by (A)

(B) Torque

Torque

0.7Ns

Ns

0.7Ns

Speed

Ns

Speed

(C)

(D) Torque

Torque

0.7Ns

0.7Ns

Ns

Ns

Speed

Speed

Q.13

The no-load speed of a 230 V separately excited dc motor is 1400 rpm. The armature resistance drop and the brush drop are neglected. The field current is kept constant at rated value. The torque of the motor in Nm for an armature current of 8 A is ____________.

Q.14

In a long transmission line with �, �, � and � are the resistance, inductance, shunt conductance and capacitance per unit length, respectively, the condition for distortionless transmission is

(A) �� = �� (C) �� = �� Q.15

For a fully transposed transmission line (A) (B) (C) (D)

Q.16

(B) � = ��/� (D) � = ��/�

positive, negative and zero sequence impedances are equal positive and negative sequence impedances are equal zero and positive sequence impedances are equal negative and zero sequence impedances are equal

A 183-bus power system has 150 PQ buses and 32 PV buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimum number of simultaneous equations to be solved is ___________.


GATE 2014

SET-3


Q.17 The signal flow graph of a system is shown below. �(�) is the input and �(�) is the output. ℎ1

ℎ0

U(s)

1 �

1

−�1

Assuming,

ℎ1 = �1

and

of the system is given by (A) � (�)

(C)

Q.18

=

� (� ) =

�0 �+�1

� 2 +� 0 �+� 1 �1 �+�0

� 2 +� 1 �+� 0

1 �

1

−�0

1

C(s)

.

ℎ0 = �0 − �1 �1 , the input-output transfer function, � (�) = (B) � (�)

(D) � (�)

= =

� 1 �+� 0 2 � +�1 �+�0 � 0 �+� 1 2 � +�0 �+�1

�(�)

�(�)

A single-input single-output feedback system has forward transfer function �(�) and feedback transfer function �(�). It is given that |�(�)�(�)| < 1. Which of the following is true about the stability of the system?

(A) The system is always stable (B) The system is stable if all zeros of �(�)�(�) are in left half of the s-plane (C) The system is stable if all poles of �(�)�(�) are in left half of the s-plane (D) It is not possible to say whether or not the system is stable from the information given Q.19

An LPF wattmeter of power factor 0.2 is having three voltage settings 300 V, 150 V and 75 V, and two current settings 5 A and 10 A. The full scale reading is 150. If the wattmeter is used with 150 V voltage setting and 10 A current setting, the multiplying factor of the wattmeter is _________.


GATE 2014

SET-3


Q.20 The two signals S1 and S2, shown in figure, are applied to Y and X deflection plates of an oscilloscope.

v

1

S1

v T

S2

1

T

2T

2T t

t

The waveform displayed on the screen is (A)

(B)

Y 1

Y 1

X

X -1

-1 (C)

(D)

Y 1

Y 1 X

X -1

-1

Q.21

A state diagram of a logic gate which exhibits a delay in the output is shown in the figure, where X is the don’t care condition, and Q is the output representing the state. 0X/1, 10/1 11/0 Q=1

Q=0

0X/1, 10/1

11/0

The logic gate represented by the state diagram is (A) XOR

(B) OR

(C) AND

(D) NAND


GATE 2014 Q.22

SET-3


An operational-amplifier circuit is shown in the figure. R +Vsat vi

+Vsat

R -

vo

+ -Vsat

+ -Vsat R2 R1

The output of the circuit for a given input vi is



R 



(C) 1 +



Q.23

R 

(B) − 1 + 2 vi R1  

(A) −  2 vi  R1 

R2  vi R1 

(D) + Vsat or -Vsat

In 8085A microprocessor, the operation performed by the instruction LHLD 2100H is (A) ( H ) ← 21H , ( L) ← 00 H (B) ( H ) ← M (2100 H ) , ( L) ← M (2101H ) (C) ( H ) ← M (2101H ) , ( L) ← M (2100 H ) (D) ( H ) ← 00 H , ( L) ← 21H

Q.24

A non-ideal voltage source �� has an internal impedance of �� . If a purely resistive load is to be chosen that maximizes the power transferred to the load, its value must be (A) 0

(B) real part of ��

(C) magnitude of �� Q.25

(D) complex conjugate of ��

The torque-speed characteristics of motor (TM) and load (TL) for two cases are shown in the figures (a) and (b). The load torque is equal to motor torque at points P, Q, R and S TM

Speed S

Torque P

TL Speed

TM Q

R

TL

Torque

(a)

(b)

The stable operating points are (A) P and R

(B) P and S

(C) Q and R

(D) Q and S


GATE 2014

SET-3



Integration of the complex function f ( z ) =

z2 , in the counterclockwise direction, around z2 −1

|z-1| = 1, is (A) -πi

Q.27

(C) πi

(B) 0

(D) 2πi

The mean thickness and variance of silicon steel laminations are 0.2 mm and 0.02 respectively. The varnish insulation is applied on both the sides of the laminations. The mean thickness of one side insulation and its variance are 0.1 mm and 0.01 respectively. If the transformer core is made using 100 such varnish coated laminations, the mean thickness and variance of the core respectively are (A) 30 mm and 0.22

(B) 30 mm and 2.44

(C) 40 mm and 2.44

(D) 40 mm and 0.24

Q.28

The function f (x) = e − 1 is to be solved using Newton-Raphson method. If the initial value of x0 is taken as 1.0, then the absolute error observed at 2nd iteration is _______.

Q.29

The Norton’s equivalent source in amperes as seen into the terminals X and Y is _______.

x

2.5V X 2.5฀ 5฀ 5฀

5฀

5V Y

Q.30

The power delivered by the current source, in the figure, is ________. 1V 1Ω 1V

1Ω

2A

1Ω


GATE 2014 Q.31

(B) −2 ��

(C) 2 ��

(D) −2√2 ��

A series �� circuit is observed at two frequencies. At ω1 = 1 krad/s, we note that source voltage �1 = 100∠0° V results in a current �1 = 0.03∠31° A. At �2 = 2 krad/s, the source voltage �2 = 100∠0° V results in a current �2 = 2∠0° A. The closest values for �, �, � out of the following options are

(A) � = 50 Ω; � = 25 mH; � = 10 µF; (C) � = 50 Ω; � = 50 mH; � = 5 µF; Q.33


A perfectly conducting metal plate is placed in x-y plane in a right handed coordinate system. A charge of +32�� √2 columbs is placed at coordinate (0, 0, 2). �� is the permittivity of free space. Assume �̂, �̂, �� to be unit vectors along x, y and z axes respectively. At the coordinate �√2 , √2, 0�, the electric field vector ��⃗ (Newtons/Columb) will be

(A) 2√2 �� Q.32

SET-3

(B) � = 50 Ω; � = 10 mH; � = 25 µF; (D) � = 50 Ω; � = 5 mH; � = 50 µF;

A continuous-time LTI system with system function �(ω) has the following pole-zero plot. For this system, which of the alternatives is TRUE?

(0,0)

(A) |�(0)| > |�(ω)|; |ω| > 0 (C) |�(0)| < |�(ω)|; |ω| > 0

Q.34

A sinusoid �(�) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that �(�) has a frequency of

(A) 10 Hz

Q.35

(B) |�(ω)| has multiple maxima, at ω1 and ω2 (D) |�(ω)| = constant; −∞ < ω < ∞

(B) 60 Hz

(C) 30 Hz

(D) 90 Hz

A differentiable non constant even function �(�) has a derivative �(�), and their respective Fourier Transforms are �(ω) and �(ω). Which of the following statements is TRUE?

(A) �(ω) and �(ω) are both real. (C) �(ω) and �(ω) are both imaginary.

(B) �(ω) is real and �(ω) is imaginary. (D) �(ω) is imaginary and �(ω) is real.


GATE 2014

SET-3


Q.36 An open circuit test is performed on 50 Hz transformer, using variable frequency source and keeping V/f ratio constant, to separate its eddy current and hysteresis losses. The variation of core loss/frequency as function of frequency is shown in the figure

15 Pc/f 10 (W/Hz) 5

50

25 f (Hz)

The hysteresis and eddy current losses of the transformer at 25 Hz respectively are (A) 250 W and 2.5 W (C) 312.5 W and 62.5 W

(B) 250 W and 62.5W (D) 312.5 W and 250 W

Q.37

A non-salient pole synchronous generator having synchronous reactance of 0.8 pu is supplying 1 pu power to a unity power factor load at a terminal voltage of 1.1 pu. Neglecting the armature resistance, the angle of the voltage behind the synchronous reactance with respect to the angle of the terminal voltage in degrees is ________.

Q.38

A separately excited 300 V DC shunt motor under no load runs at 900 rpm drawing an armature current of 2 A. The armature resistance is 0.5 Ω and leakage inductance is 0.01 H. When loaded, the armature current is 15 A. Then the speed in rpm is _____

Q.39

The load shown in the figure absorbs 4 kW at a power factor of 0.89 lagging.

1Ω 2:1 50 Hz ac source

X

110 V

ZL

Assuming the transformer to be ideal, the value of the reactance X to improve the input power factor to unity is ___________.


GATE 2014

SET-3


Q.40 The parameters measured for a 220V/110V, 50 Hz, single-phase transformer are: Self inductance of primary winding = 45 mH Self inductance of secondary winding = 30 mH Mutual inductance between primary and secondary windings = 20 mH Using the above parameters, the leakage (Ll1 , Ll2) and magnetizing (Lm) inductances as referred to primary side in the equivalent circuit respectively, are (A) 5mH, 20mH and 40mH

(B) 5mH, 80mH and 40mH

(C) 25mH, 10mH and 20mH

(D) 45mH, 30mH and 20mH

Q.41

For a 400 km long transmission line, the series impedance is (0.0 + j0.5) Ω/km and the shunt admittance is (0.0 + j5.0) µmho/km. The magnitude of the series impedance (in Ω) of the equivalent π circuit of the transmission line is ________.

Q.42

The complex power consumed by a constant-voltage load is given by (�1 + ��1 ), where, 1 kW ≤ �1 ≤ 1.5 kW and 0.5 kVAR ≤ �1 ≤ 1 kVAR. A compensating shunt capacitor is chosen such that |�| ≤ 0.25 kVAR, where Q is the net reactive power consumed by the capacitor-load combination. The reactive power (in kVAR) supplied by the capacitor is _________.

Q.43

The figure shows the single line diagram of a single machine infinite bus system.

Infinite bus

The inertia constant of the synchronous generator � = 5 MW-s/MVA. Frequency is 50 Hz. Mechanical power is 1 pu. The system is operating at the stable equilibrium point with rotor angle � equal to 30o . A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in pu is �� sin �. If the values of δ and �� ⁄�� at the instant of fault clearing are 45o and 3.762 radian/s respectively, then �� (in pu) is _______. Q.44

The block diagram of a system is shown in the figure

R(s)

+

1 -

s

+

-

G(s)

s

C(s)

If the desired transfer function of the system is C ( s) s = 2 R( s) s + s + 1

then G(s) is (A) 1

(B) s

(C) 1/s

(D)

−s s + s2 − s − 2 3


GATE 2014 Q.45

SET-3


Consider the system described by following state space equations

 x1   0 1   x1  0  x  = − 1 − 1  x  + 1 u ;   2    2 

x  y = [1 0]  1   x2 

If u is unit step input, then the steady state error of the system is (A) 0

Q.46

(B) 1/2

(C) 2/3

(D) 1

The magnitude Bode plot of a network is shown in the figure

|G(jω)| dB

0

Slope 20 dB/decade

1

log10 ω

1

3

The maximum phase angle ϕm and the corresponding gain Gm respectively, are (A) − 30° and 1.73 dB (C) + 30° and 4.77dB

Q.47

(B) − 30° and 4.77dB (D) + 30° and 1.73 dB

A periodic waveform observed across a load is represented by

 1 + sin ω t 0 ≤ ω t < 6π V (t ) =  − 1 + sin ω t 6π ≤ ω t < 12π The measured value, using moving iron voltmeter connected across the load, is (A)

Q.48

3 2

(B)

2 3

(C)

3 2

(D)

2 3

In the bridge circuit shown, the capacitors are loss free. At balance, the value of capacitance C1 in microfarad is _________.

35k฀ Vsin(฀t)

C1 G

105k฀

0.1฀F


GATE 2014 Q.49

SET-3


Two monoshot multivibrators, one positive edge triggered (M1) and another negative edge triggered (M2), are connected as shown in figure +5V 10k

M1

M2

10µF

Q1

Q2

Q1

Q2

vo

The monoshots M1 and M2 when triggered produce pulses of width T1 and T2 respectively, where T1>T2. The steady state output voltage vo of the circuit is (A)

vo T1

T2

T1

T2

T1

t

(B)

vo T1

T1

T1

T1

t

(C)

vo T2

T2

T1

T1

T2

t

(D)

vo T2

T2

T2

T2

T2

T2

t


GATE 2014

SET-3


Q.50 The transfer characteristic of the Op-amp circuit shown in figure is R

R

+Vsat

R

vi

-

+Vsat

R -

+ vo

+

-Vsat

R

R

(A)

-Vsat

(B)

v0

1

-1

v0 vi

vi

(C)

(D)

v0

v0

vi

vi

-1

1

Q.51

A 3-bit gray counter is used to control the output of the multiplexer as shown in the figure. The initial state of the counter is 0002. The output is pulled high. The output of the circuit follows the sequence A2

3-bit gray counter

CLK

(A) I0, 1, 1, I1, I3, 1, 1, I2 (C) 1, I0, 1, I1, I2, 1, I3,1

+5V

A1 A0

I0 I1 I2 I3

S0

E

S1

R

0 1 2

4X1 MUX

Output

3

(B) I0, 1, I1, 1, I2, 1, I3, 1 (D) I0, I1, I2, I3, I0, I1, I2, I3


GATE 2014

SET-3


Q.52 A hysteresis type TTL inverter is used to realize an oscillator in the circuit shown in the figure. 10k +5V

vo 0.1µF

If the lower and upper trigger level voltages are 0.9 V and 1.7 V, the period (in ms), for which output is LOW, is __________.

Q.53

A three-phase fully controlled bridge converter is fed through star-delta transformer as shown in the figure. IR R

Io

1:K

Y B

The converter is operated at a firing angle of 300. Assuming the load current (I0) to be virtually constant at 1 p.u. and transformer to be an ideal one, the input phase current waveform is (A)

(B)

2/3K

IR

1/3K

0

(C)

2K/3

IR π

2π

0

(D)

2K/3

IR

K/3

π

2π

2/3K

IR 0

π

2π

0

π


2π

GATE 2014

SET-3


Q.54 A diode circuit feeds an ideal inductor as shown in the figure. Given �� = 100 sin(ω�) V, where ω = 100π rad/s, and L = 31.83 mH. The initial value of inductor current is zero. Switch S is closed at t = 2.5 ms. The peak value of inductor current iL (in A) in the first cycle is ________.

Q.55

A single-phase voltage source inverter shown in figure is feeding power to a load. The triggering pulses of the devices are also shown in the figure.

S1

S2

C VDC

O

A C

iL

S3

S1,S4

π

π−θ

θ

B

Load

2π

S2,S3

S4

π+θ

2π−θ

If the load current is sinusoidal and is zero at 0, π, 2π…, the node voltage VAO has the waveform (A)

(B)

VDC/2 VAO

θ

π−θ π

2π

VDC/2 VAO

θ

π−θ

π

2π

-VDC/2

(C)

(D)

VDC/2 VAO

θ

π−θ

π

2π

VDC/2 VAO

θ

π−θ

π

-VDC/2



2π


Key / Range D C C C

Q. No. 5 6 7 8

Key / Range C B D D

Q. No. 9 10

Key / Range C C

Q. No. 20 21 22 23 24 25 26 27 28 29 30 31 32

Key / Range A D D C C B C D 0.05 to 0.07 2 to 2 3 to 3 B B

Q. No. 39 40 41 42 43 44 45 46 47 48 49 50 51

Key / Range 879 to 881 23 to 24 B 186 to 188 0.75 to 0.75 0.22 to 0.24 B A C A 0.3 to 0.3 C C

33 34 35 36 37 38

D C B B 32.4 to 34.0 C

52 53 54 55

A 0.62 to 0.66 B 16.6 to 17.4

Electrical Engineering - EE Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Key / Range C 2 to 2 A 0.4 to 0.5 C C A A A 14 to 14 D C 12.45 to 12.65 A B 332 to 332 C A 2 to 2


GATE 2013 Solved Paper EE : ELECTRICAL ENGINEERING Duration: Three Hours

Maximum Marks: 100

Read the following instructions carefully.

1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that either: a. The Question Booklet Code printed at the right hand top corner of this page does not match with the Question Booklet Code at the right hand top corner of the ORS or b. The Question Paper Code preceding the Registration number on the ORS is not EE, then exchange the booklet immediately with a new sealed Question Booklet. 3. On the right half hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, mark will be deducted for each wrong answer. For all 2 marks questions, mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the Question Booklet for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ballpoint pen. Name Registration Number

EE


GATE 2013


Q.1 to Q.25 carry one mark each. Q.1

In the circuit shown below what is the output voltage (Vout) in Volts if a silicon transistor Q and an ideal op-amp are used?

(A) Q.2

Q.3

15

The transfer function

(C)

0.7

0.7

(D)

15

V2 ( s ) of the circuit shown below is V1 ( s )

(A)

0.5 s + 1 s +1

(B)

3s + 6 s+2

(C)

s+2 s +1

(D)

s +1 s+2

Assuming zero initial condition, the response y (t ) of the system given below to a unit step input u (t ) is

(A) u (t )

Q.4

(B)

2 (C) t u (t )

(B) t u (t )

(D) e −t u (t )

2

The impulse response of a system is h(t ) = t u (t ) . For an input u (t − 1) , the output is 2 (A) t u (t )

2

(B)

t (t − 1) 2

u (t − 1)

(C)

(t − 1) 2 2

u (t − 1)

(D)

t2 −1 2

u (t − 1)


GATE 2013

Q.5


Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? (A) All the poles of the system must lie on the left side of the jω axis. (B) Zeros of the system can lie anywhere in the s-plane. (C) All the poles must lie within s = 1. (D) All the roots of the characteristic equation must be located on the left side of the jω axis.

Q.6

Two systems with impulse responses h1 (t ) and h2 (t ) are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) product of h1 (t ) and h2 (t ) (B) sum of h1 (t ) and h2 (t ) (C) convolution of h1 (t ) and h2 (t ) (D) subtraction of h2 (t ) from h1 (t )

Q.7

A source vs (t ) = V cos100π t has an internal impedance of (4 + j3) . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in should be (A) 3

Q.8

(D) 7

load absorbs real power and delivers reactive power. load absorbs real power and absorbs reactive power. load delivers real power and delivers reactive power. load delivers real power and absorbs reactive power.

A single-phase transformer has no-load loss of 64 W, as obtained from an open-circuit test. When a short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, the measured loss is 81 W. The transformer has maximum efficiency when operated at (A) (B) (C) (D)

Q.10

(C) 5

A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is 10∠ − 1500 A and if the voltage at the load terminals is 100∠600 V, then the (A) (B) (C) (D)

Q.9

(B) 4

50.0% of the rated current. 64.0% of the rated current. 80.0% of the rated current. 88.8% of the rated current.

The flux density at a point in space is given by B = 4 x a x + 2ky a y + 8 a z Wb/m2. The value of constant k must be equal to (A) –2

Q.11

(B) –0.5

(C) +0.5

(D) +2

A continuous random variable X has a probability density function f ( x) = e − x , 0 < x < ∞ . Then P { X > 1} is

(A) 0.368

(B) 0.5

(C) 0.632

(D) 1.0


GATE 2013

Q.12


The curl of the gradient of the scalar field defined by V = 2 x 2 y + 3 y 2 z + 4 z 2 x is (A) 4 xy a x + 6 yz a y + 8 zx a z (B) 4 a x + 6 a y + 8 a z

(

)

(

)

(

)

(C) 4 xy + 4 z 2 a x + 2 x 2 + 6 yz a y + 3 y 2 + 8 zx a z (D) 0 Q.13

In the feedback network shown below, if the feedback factor k is increased, then the

+ v in

v1

+

vf = kvout+

A0

k

+

vout

+

(A) input impedance increases and output impedance decreases. (B) input impedance increases and output impedance also increases. (C) input impedance decreases and output impedance also decreases. (D) input impedance decreases and output impedance increases. Q.14

The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is

(A) 4.46

(B) 3.15

(C) 2.23

(D) 0


GATE 2013

Q.15


The Bode plot of a transfer function G (s ) is shown in the figure below.

The gain (20 log G ( s ) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G (s) is (A)

Q.16

39.8 s

s2

32 s

(D)

32 s2

(B) an OR gate

(C) an XOR gate

(D) a NAND gate

(B) 300

(C) 500

(D) 1500

A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency in kHz which is not valid is (A) 5

Q.19

(C)

For a periodic signal v(t ) = 30 sin 100 t + 10 cos 300 t + 6 sin (500 t + π / 4) , the fundamental frequency in rad/s is (A) 100

Q.18

39.8

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles (A) an AND gate

Q.17

(B)

(B) 12

(C) 15

(D) 20

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

Ra Rb

RC

RB

Rc RA

(A) k2

(B) k

(C) 1/k

(D)

k


GATE 2013

Q.20


The angle δ in the swing equation of a synchronous generator is the (A) angle between stator voltage and current. (B) angular displacement of the rotor with respect to the stator. (C) angular displacement of the stator mmf with respect to a synchronously rotating axis. (D) angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis.

Q.21

Leakage flux in an induction motor is (A) flux that leaks through the machine (B) flux that links both stator and rotor windings (C) flux that links none of the windings (D) flux that links the stator winding or the rotor winding but not both

Q.22

Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V , V1 and V2 , as indicated. The correct relation among the voltmeter readings is

(A) V = Q.23

V1 V2 + 2 2

(B) V = V1 + V2

(C) V = VV 1 2

(D) V = V2 − V1

Square roots of −i , where i = −1 , are (A) i, –i

π 3π 3π ) + i sin( − ), cos( ) + i sin( ) 4 4 4 4 π 3π 3π π (C) cos( ) + i sin( ), cos( ) + i sin( ) 4 4 4 4 3π 3π 3π 3π (D) cos( ) + i sin( − ), cos( − ) + i sin( ) 4 4 4 4

(B) cos( −

Q.24

π

2 2 Given a vector field F = y x a x − yz a y − x a z , the line integral

∫ F ⋅ d l evaluated along a segment

on the x-axis from x = 1 to x = 2 is (A) –2.33 Q.25

(B) 0

(C) 2.33

(D) 7

2 − 2  x1  0 The equation     =   has 1 − 1   x2  0 (A) no solution  x  0 (B) only one solution  1  =    x2  0 (C) non-zero unique solution (D) multiple solutions


GATE 2013


Q.26 to Q.55 carry two marks each. Q.26

A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as Rs = 300 . Other bridge resistances are R1 = R2 = R3 = 300 . The maximum permissible current through the strain gauge is 20 mA. During certain measurement when the bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by 1% over the nominal value, the output voltage V0 in mV is

Rs

R1 V0

Vi R3 (A) 56.02 Q.27

(B) 40.83

(C) 29.85

(D) 10.02

In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V across RL, the minimum value of RL in and the minimum power rating of the Zener diode in mW respectively are

(A) 125 and 125 Q.28

R2

(B) 125 and 250

(C) 250 and 125

(D) 250 and 250

ω (s) 10 . When connected in = Va ( s) 1 + 10 s feedback as shown below, the approximate value of K a that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is The open-loop transfer function of a dc motor is given as

R(s)

(A) 1

Ka

(B) 5

Va(s)

10

ω(s)

1+10s

(C) 10

(D) 100


GATE 2013

Q.29


In the circuit shown below, if the source voltage VS = 100∠53.13° V then the Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is j4 Ω

3Ω

j6 Ω

5Ω

VL1 j40I2

VS

10VL1

I1

(A) 100∠90° Q.30

RL=10 Ω I2

(B) 800∠0°

(C) 800∠90°

(D) 100∠60°

Three capacitors C1, C2, and C3, whose values are 10µF, 5µF, and 2µF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum safe voltage in Volts that can be applied across the combination and the corresponding total charge in µC stored in the effective capacitance across the terminals are respectively

C2

C3

C1 (A) 2.8 and 36 (C) 2.8 and 32 Q.31

A voltage ω across WX in Volts is

(B) 7 and 119 (D) 7 and 80 Volts is applied across YZ. Assuming ideal diodes, the voltage measured

1kΩ

W

Y

X

Z +

(A)

ω

(C) (sin ω t − sin ω t ) / 2

1kΩ

_

(B) (sin ω t + sin ω t ) / 2 (D) 0 for all t


GATE 2013

Q.32


The separately excited dc motor in the figure below has a rated armature current of 20 A and a rated armature voltage of 150 V. An ideal chopper switching at 5 kHz is used to control the armature voltage. If La= 0.1 mH, Ra= 1 , neglecting armature reaction, the duty ratio of the chopper to obtain 50% of the rated torque at the rated speed and the rated field current is

La ,Ra

200 V

(A) 0.4 Q.33

(C) 0.6

(D) 0.7

For a power system network with n nodes, Z33 of its bus impedance matrix is j0.5 per unit. The voltage at node 3 is 1.3 ∠–10° per unit. If a capacitor having reactance of –j3.5 per unit is now added to the network between node 3 and the reference node, the current drawn by the capacitor per unit is (A) 0.325 ∠–100°

Q.34

(B) 0.5

(B) 0.325 ∠80°

(C) 0.371 ∠–100°

(D) 0.433 ∠80°

A dielectric slab with 500 mm × 500 mm cross-section is 0.4 m long. The slab is subjected to a uniform electric field of E = 6 a x + 8 a y kV/mm. The relative permittivity of the dielectric material is equal to 2. The value of constant ε 0 is 8.85 × 10−12 F/m. The energy stored in the dielectric in Joules is (A) 8.85 × 10–11

Q.35

(C) 88.5

(D) 885

1 1  A matrix has eigenvalues –1 and –2. The corresponding eigenvectors are   and   −1 − 2 respectively. The matrix is 1  1 (A)   − 1 − 2

Q.36

(B) 8.85 × 10–5

∫

2 1 (B)   − 2 − 4

− 1 0  (C)    0 − 2

1 0 (D)   − 2 − 3

z2 − 4 dz evaluated anticlockwise around the circle z − i = 2 , where i = −1 , is z2 + 4

(A) −4π

(B) 0

(C) 2 + π

(D) 2 + 2i


GATE 2013

Q.37


The clock frequency applied to the digital circuit shown in the figure below is 1 kHz. If the initial state of the output Q of the flip-flop is ‘0’, then the frequency of the output waveform Q in kHz is

(A) 0.25 Q.38

(C) 1

(D) 2

In the circuit shown below, Q1 has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If Vcc is +5 V, X and Y are digital signals with 0 V as logic 0 and Vcc as logic 1, then the Boolean expression for Z is

(A) X Y Q.39

(B) 0.5

(B)

(C) X Y

(D) XY

In the circuit shown below the op-amps are ideal. Then Vout in Volts is

(A) 4

(B) 6

(C) 8

(D) 10


GATE 2013

Q.40


The signal flow graph for a system is given below. The transfer function

(A) (C)

Q.41

s +1 5s + 6s + 2 s +1

Q.43

(D)

2

s + 4s + 2

s +1 2

s + 6s + 2 1 2

5s + 6s + 2

The impulse response of a continuous time system is given by h(t ) = δ (t − 1) + δ (t − 3) . The value of the step response at t = 2 is (A) 0

Q.42

(B)

2

Y (s) for this system is U ( s)

(B) 1

(C) 2

(D) 3

Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the chosen operating frequency. Their respective resistances are R1 and R2. When connected in series, their effective Q factor at the same operating frequency is (A) q1 R1 + q2 R2

(B) q1 / R1 + q2 / R2

(C) (q1R1 + q2 R2 ) / ( R1 + R2 )

(D) q1R2 + q2 R1

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage VWX 1 = 100V is applied across WX to get an open circuit voltage

VYZ 1 across YZ. Next, an ac voltage VYZ 2 = 100V is applied across YZ to get an open circuit voltage VWX 2 across WX. Then, VYZ 1 / VWX 1 , VWX 2 / VYZ 2 are respectively, W

1:1.25

Y

X

(A) 125/100 and 80/100 (C) 100/100 and 100/100

Z

(B) 100/100 and 80/100 (D) 80/100 and 80/100


GATE 2013

Q.44


Thyristor T in the figure below is initially off and is triggered with a single pulse of width 10 µs. It is given that L = (100 ) µ H and C = (100π )µ F. Assuming latching and holding currents of the π thyristor are both zero and the initial charge on C is zero, T conducts for

T

L C

15 V

(A) 10 µs Q.45

(B) 50 µs

(B) 98

(C) 52

(D) 48

A function y = 5 x 2 + 10 x is defined over an open interval x = (1, 2) . At least at one point in this dy is exactly interval, dx

(A) 20 Q.47

(D) 200 µs

A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50 Hz source, is rotating at 1440 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is (A) 100

Q.46

(C) 100 µs

(B) 25

(C) 30

(D) 35

3 When the Newton-Raphson method is applied to solve the equation f ( x ) = x + 2 x − 1 = 0, the

solution at the end of the first iteration with the initial guess value as x0 = 1.2 is (A) –0.82

(B) 0.49

(C) 0.705

(D) 1.69

Common Data Questions Common Data for Questions 48 and 49:

In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is switched at 250 kHz, with a duty ratio of 0.4. All elements of the circuit are assumed to be ideal.

100 µH 12 V

Q.48

470 µF

20 Ω

The average source current in Amps in steady-state is (A) 3/2

Q.49

Q

(B) 5/3

(C) 5/2

(D) 15/4

The PEAK-TO-PEAK source current ripple in Amps is (A) 0.96

(B) 0.144

(C) 0.192

(D) 0.288


GATE 2013


Common Data for Questions 50 and 51:

The state variable formulation of a system is given as  x1  − 2 0   x1  1  x1   x  =  0 − 1  x  + 1 u , x1 (0) = 0, x 2 (0) = 0 and y = [1 0]  x    2    2   2 Q.50

The system is (A) controllable but not observable (B) not controllable but observable (C) both controllable and observable (D) both not controllable and not observable

Q.51

The response y (t ) to a unit step input is (A)

1 1 −2 t − e 2 2

(B) 1 −

(C) e −2 t − e − t

1 −2 t 1 − t e − e 2 2

(D) 1 − e − t

Linked Answer Questions Statement for Linked Answer Questions 52 and 53: In the following network, the voltage magnitudes at all buses are equal to 1 p.u., the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1 .

" 1 "#

%$"2

1Ω

2

01

1Ω

1Ω

"! !

Q.52

02

The voltage phase angles in rad at buses 2 and 3 are (A) θ 2 = −0.1, θ3 = −0.2 (B) θ 2 = 0, θ3 = −0.1 (C) θ 2 = 0.1, θ3 = 0.1 (D) θ 2 = 0.1, θ3 = 0.2

Q.53

If the base impedance and the line-to-line base voltage are 100 and 100 kV, respectively, then the real power in MW delivered by the generator connected at the slack bus is (A) −10

(B) 0

(C) 10

(D) 20


GATE 2013


Statement for Linked Answer Questions 54 and 55: The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50 Hz, square-wave ac output voltage (vo) across an R-L load. Reference polarity of vo and reference direction of the output current io are indicated in the figure. It is given that R = 3 Ω , L = 9.55 mH .

Q1

Q3 D1

D3

V dc

vo Q4

D2

In the interval when v 0 < 0 and i0 > 0 the pair of devices which conducts the load current is (A) Q1, Q2

Q.55

io R

Q2 D4

Q.54

L

(B) Q3, Q4

(C) D1, D2

(D) D3, D4

Appropriate transition i.e., Zero Voltage Switching (ZVS)/Zero Current Switching (ZCS) of the IGBTs during turn-on/turn-off is (A) ZVS during turn-off (C) ZCS during turn-off

(B) ZVS during turn-on (D) ZCS during turn-on


GATE 2013


General Aptitude (GA) Questions Q.56 to Q.60 carry one mark each. Q.56

They were requested not to quarrel with others. Which one of the following options is the closest in meaning to the word quarrel? (A) make out

Q.57

(C) dig out

(D) fall out

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43°C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was (A) 40

Q.58

(B) call out

(B) 43

(C) 46

(D) 49

(C) committed

(D) committing

Complete the sentence: Dare _______________ mistakes. (A) commit

Q.59

(B) to commit

Choose the grammatically CORRECT sentence: (A) Two and two add four. (B) Two and two become four. (C) Two and two are four. (D) Two and two make four.

Q.60

Statement: You can always give me a ring whenever you need.

Which one of the following is the best inference from the above statement? (A) Because I have a nice caller tune. (B) Because I have a better telephone facility. (C) Because a friend in need is a friend indeed. (D) Because you need not pay towards the telephone bills when you give me a ring.

Q.61 to Q.65 carry two marks each. Q.61

What is the chance that a leap year, selected at random, will contain 53 Saturdays? (A) 2/7

Q.62

(B) 3/7

(C) 1/7

(D) 5/7

Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on.

Which one of the following is the best inference from the above statement? (A) The emergence of nationalism in colonial India led to our Independence. (B) Nationalism in India emerged in the context of colonialism. (C) Nationalism in India is homogeneous. (D) Nationalism in India is heterogeneous. Q.63

The set of values of p for which the roots of the equation 3x2+2x+p(p–1) = 0 are of opposite sign is (A) (–∞, 0)

(B) (0, 1)

(C) (1, ∞)

(D) (0, ∞)


GATE 2013

Q.64


A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is (A) 30

Q.65

(B) 36

(C) 40

(D) 24

Find the sum to n terms of the series 10+84+ 734 + .....

(

) +1

(

) +1

(

)+n

(

)+ n

9 9n + 1 10 9 9n − 1 (B) 8 n 9 9 −1 (C) 8 9 9n − 1 (D) 8 (A)

2



GATE 2013 - Answer Keys Electrical Engineering - EE Q. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Key/Range B D B C C C C B C A A D A A B C A A B D D D

Q. No 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Key/Range B B D C B C C C D D D C D A B B C A B C B C

Q. No 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Key/Range B B C B C A A Marks to All Marks to All D Marks to All D C A D C A D B C D


GATE 2012 Solved Paper EE : ELECTRICAL ENGINEERING Duration: Three Hours

Maximum Marks: 100

Read the following instructions carefully.

1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal and read the instructions printed on the ORS carefully. If you find that the Question Booklet Code printed at the right hand top corner of this page does not match with the Booklet Code on the ORS, exchange the booklet immediately with a new sealed Question Booklet. 3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble corresponding to your test paper code and the appropriate bubble under each digit of your registration number and (ii) write your registration number, your name and name of the examination centre and put your signature at the specified location. 4. This Question Booklet contains 20 pages including blank pages for rough work. After you are permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator. 5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each question has only one correct answer. Questions must be answered on the left hand side of the ORS by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen against the question number. For each question darken the bubble of the correct answer. More than one answer bubbled against a question will be treated as an incorrect response. 6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken the bubbles in the ORS very carefully. 7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks questions include two pairs of common data questions and two pairs of linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then the answer to the second question in the pair will not be evaluated. 8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks. For all 1 mark questions, ̃ mark will be deducted for each wrong answer. For all 2 marks questions, ̄ mark will be deducted for each wrong answer. However, in the case of the linked answer question pair, there will be negative marks only for wrong answer to the first question and no negative marks for wrong answer to the second question. 10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the question paper for rough work. 12. Before the start of the examination, write your name and registration number in the space provided below using a black ink ball point pen. Name Registration Number

EE


GATE 2012



Two independent random variables X and Y are uniformly distributed in the interval [–1,1]. The probability that max[X, Y] is less than 1 2 is (A) 3 4

Q.2

Q.3

(B) 9 16

(C) 1 4

(D) 2 3

If x   1 , then the value of x is x

(C) x (D) 1 (A) e  / 2 (B) e / 2 Given 1 2 . If C is a counterclockwise path in the z-plane such that z  1  1 , the value f ( z)   z 1 z  3 1 of f ( z ) dz is 2 j C



Q.4

(A) –2 (B) –1 (C) 1 In the circuit shown below, the current through the inductor is

(D) 2

j1 W

1W 1 1

0V

-

0A 1 +

+ 1

0V -

0A 1W

- j1 W

2 1 1 A A A (B) (C) 1 j 1 j 1 j The impedance looking into nodes 1 and 2 in the given circuit is

(A) Q.5

(D) 0 A

ib 1kW

99ib

9kW 1 100W 2

Q.6

(A) 50 W (B) 100 W A system with transfer function

(C) 5 kW

(D) 10.1 kW

( s 2  9 ) ( s  2) ( s  1) ( s  3) ( s  4) is excited by sin ( t ) . The steady-state output of the system is zero at G( s) 

(A)   1 rad/s (C)   3 rad/s

(B)   2 rad/s (D)   4 rad/s


GATE 2012

Q.7

Q.8

In the sum of products function f ( X , Y , Z ) 

(2, 3, 4, 5) , the prime implicants are

(A) X Y , X Y

(B) X Y , X Y Z , X Y Z

(C) X Y Z , X Y Z , X Y

(D) X Y Z , X Y Z , X Y Z , X Y Z

If x [n]  (1 / 3) Z-plane will be (A)

Q.9


1 3

n

 z 3

 (1 / 2) n u[n] , then the region of convergence (ROC) of its Z-transform in the

(B)

1 3

 z 

1 2

(C)

1 2

 z 3

(D)

1 3

 z

The bus admittance matrix of a three-bus three-line system is 5   13 10  Y  j 10  18 10    10  13  5

If each transmission line between the two buses is represented by an equivalent network, the magnitude of the shunt susceptance of the line connecting bus 1 and 2 is (A) 4 Q.10

(B) 2

(C) 1

The slip of an induction motor normally does not depend on (A) rotor speed (C) shaft torque

Q.11

(B) synchronous speed (D) core-loss component

A two-phase load draws the following phase currents: i2 (t )  I m cos( t  2 ) . These currents are balanced if 1 is equal to (A)  2

Q.12

(D) 0

(D) ( / 2  2 )

(C) ( / 2  2 )

(B) 2

i1 (t )  I m sin( t  1 ) ,

A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent magnet moving coil (PMMC) meter connected across the same load reads v(t)

10V 5V 0

10

12

20

time (ms)

-5V (A) 4 V Q.13

(B) 5 V

(C) 8 V

(D) 10 V

The bridge method commonly used for finding mutual inductance is (A) Heaviside Campbell bridge (C) De Sauty bridge

(B) Schering bridge (D) Wien bridge


GATE 2012

Q.14


With initial condition x(1)  0.5 , the solution of the differential equation dx t  x  t is dt (A) x  t 

Q.15

1 2

(B) x  t 2 

1 2

The unilateral Laplace transform of f (t) is

(C) x 

Q.16

t 2

1 . The unilateral Laplace transform of t f (t ) is s  s 1 2s  1 ( s  s  1) 2 2s  1 (D) 2 ( s  s  1) 2

(B) 

2

2

The average power delivered to an impedance (4  j3) Wby a current 5cos(100 t  100) A is (A) 44.2 W

Q.17

(D) x 

2

s ( s  s  1) 2 s (C) 2 ( s  s  1) 2

(A) 

t2 2

(B) 50 W

(C)

62.5 W

(D) 125 W

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

t =0

S

C2

C1 i(t)

(A) zero (C) an exponentially decaying function Q.18

(B) a step function (D) an impulse function

The i-v characteristics of the diode in the circuit given below are  v  0.7 A, v  0.7 V  i   500  0 A, v  0.7 V 

The current in the circuit is

1kW i +

+

- 10V

(A) 10 mA Q.19

(B) 9.3 mA

v

-

(C) 6.67 mA

(D) 6.2 mA

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is (A) 4

(B) 6

(C) 8

(D) 10


GATE 2012

Q.20


Consider the given circuit. A CLK

B

In this circuit, the race around (A) does not occur (C) occurs when CLK = 1 and A = B = 1 Q.21

(B) occurs when CLK = 0 (D) occurs when CLK = 1 and A = B = 0

The figure shows a two-generator system supplying a load of PD = 40 MW, connected at bus 2. G1

Bus 1

Bus 2

G2

PG2 PG1 PD = 40 MW

The fuel cost of generators G1 and G2 are : C1 ( PG1 )  10,000 Rs / MWh and C2 ( PG 2 )  12,500 Rs / MWh and the loss in the line is Ploss( pu)  0.5 PG21 ( pu) , where the loss coefficient is specified in pu on a 100 MVA base. The most economic power generation schedule in MW is (A) PG1 = 20, PG2 = 22 (C) PG1 = 20, PG2 = 20 Q.22

The sequence components of the fault current are as follows: Ipositive = j1.5 pu, Inegative = –j0.5 pu, Izero = –j1 pu. The type of fault in the system is (A) LG

Q.23

(B) LL

(C) LLG

(D) LLLG

A half-controlled single-phase bridge rectifier is supplying an R-L load. It is operated at a firing angle α and the load current is continuous. The fraction of cycle that the freewheeling diode conducts is (A) 1

Q.24

(B) PG1 = 22, PG2 = 20 (D) PG1 = 0, PG2 = 40

2



(B) 1  





(C) 

2

(D) 



The typical ratio of latching current to holding current in a 20 A thyristor is (A) (B) (C) (D)

5.0 2.0 1.0 0.5


GATE 2012

Q.25


For the circuit shown in the figure, the voltage and current expressions are v(t )  E1 sin ( t )  E3 sin (3 t ) and i (t )  I1 sin ( t  1 )  I 3 sin (3 t  3 )  I 5 sin (5 t ) . The average power measured by the Wattmeter is

i(t) Wattmeter Load

+

v(t)

(A) (C)

1 E1 I 1 cos1 2 1 [ E1 I 1 cos1  E3 I 3 cos3 ] 2

(B)

1 [ E1 I 1 cos1  E1 I 3 cos3  E1 I 5 ] 2

(D)

1 [ E1 I 1 cos1  E3 I 1 cos1 ] 2

Q. 26 to Q. 55 carry two marks each. Q.26

Given that  5  3 1 0 and I   A , the value of A 3 is   0 2 0 1 

(A) 15 A + 12 I (C) 17 A + 15 I

The maximum value of f ( x)  x 3  9 x 2  24 x  5 in the interval [1, 6] is

Q.28

(B) 25

(C) 41

If VA  VB  6 V, then VC  VD is VA

R R

2W

(D) 46

VB R

R

R R

1W

R

10 V

+

(A) 21

-

Q.27

(B) 19 A + 30 I (D) 17 A + 21 I

R + 5V

(A) –5 V

(B) 2 V

VC

2A

VD

(C) 3 V

(D) 6 V


GATE 2012

Q.29


The voltage gain Av of the circuit shown below is 13.7 Volts 12kW C

100kW

vo

C

(A) Q.30

Av  200

(B)

b=100

10kW

vi

Av  100

Av  20

(C)

(D)

Av  10

The state transition diagram for the logic circuit shown is 2-1 MUX D CLK

Q

X1 Y X0 Select

Q

A

A=1 A=1

(A) Q=0

A=0

A=0

Q=0

Q.31

Q=0

Q=1

A=1

A=1

A=1

A=1

A=0 A=1

(B)

A=0

(C)

A=0

A=0

A=1 A=0

(D) Q=1

Q=1

Q=0

A=0

Q=1

Let y[n] denote the convolution of h[n] and g[n], where h [n]  (1 / 2) n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals (A) 0

(B) 1/2

(C) 1

(D) 3/2


GATE 2012

Q.32


The circuit shown is a R2 C Input

+5V

R1

+

+ Output -

+

-

-5V

1 rad/s ( R1  R2 ) C 1 (B) high pass filter with f3dB = rad/s R1C

(A) low pass filter with f3dB =

1 rad/s R1C 1 (D) high pass filter with f3dB = rad/s ( R1  R2 ) C

(C) low pass filter with f3dB =

Q.33

For the system shown below, SD1 and SD2 are complex power demands at bus 1 and bus 2 respectively. If V2  1 pu , the VAR rating of the capacitor (QG2) connected at bus 2 is

SG1

Bus 1 V1=1 0 pu

Bus 2 V2

Z = j 0.5 p.u pu

SD1 = 1 pu (A) 0.2 pu Q.34

SD2 = 1 pu (C) 0.312 pu

(D) 0.4 pu

A cylindrical rotor generator delivers 0.5 pu power in the steady-state to an infinite bus through a transmission line of reactance 0.5 pu. The generator no-load voltage is 1.5 pu and the infinite bus voltage is 1 pu. The inertia constant of the generator is 5 MW-s/MVA and the generator reactance is 1 pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is (A) 53.5

Q.35

(B) 0.268 pu

QG2

(B) 60.2

(C) 70.8

(D) 79.6

In the circuit shown, an ideal switch S is operated at 100 kHz with a duty ratio of 50 %. Given that Δic is 1.6 A peak-to-peak and I0 is 5 A dc, the peak current in S is

S L + - 24 V (A) 6.6 A

(B) 5.0 A

∆ic

D

I0

v0

C R

(C) 5.8 A

+

(D) 4.2 A


GATE 2012

Q.36

A 220 V, 15 kW, 1000 rpm shunt motor with armature resistance of 0.25 W has a rated line current of 68 A and a rated field current of 2.2 A. The change in field flux required to obtain a speed of 1600 rpm while drawing a line current of 52.8 A and a field current of 1.8 A is (A) 18.18 % increase

Q.37

(B) 18.18 % decrease

(C) 36.36 % increase

(D) 36.36 % decrease

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is (A) 1/3

Q.38


(B) 1/2

(C) 2/3

(D) 3/4

The direction of vector A is radially outward from the origin, with

A  k r n where

r 2  x 2  y 2  z 2 and k is a constant. The value of n for which   A  0 is

(A) –2 Q.39

(B) 2

(C) 1

Consider the differential equation d 2 y (t ) dy(t ) 2  y (t )   (t ) with y (t ) 2 dt dt

The numerical value of (A) –2 Q.40

(D) 0

t 0 

 2 and

dy  0. dt t 0

dy is dt t 0

(B) –1

(C) 0

(D) 1

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is 2W

R

+

- j1 W

+

10 V

3V

-

Circuit A

(A) 0.8 W Q.41

(B) 1.4 W

Circuit B

(C) 2 W

(D) 2.8 W

The state variable description of an LTI system is given by  x1   0 a1 0   x1   0          x 2    0 0 a 2   x2    0  u  x   a      3   3 0 0   x3   1   x1    y  1 0 0  x2  x   3 where y is the output and u is the input. The system is controllable for

(A) a1  0 , a 2  0 , a3  0 (C) a1  0 , a 2  0 , a3  0

(B) a1  0 , a 2  0 , a3  0 (D) a1  0 , a 2  0 , a3  0


GATE 2012

Q.42


The Fourier transform of a signal h(t) is H ( j )  (2 cos) (sin 2) /  . The value of h(0) is (A) 1/4

Q.43

(B) 1/2

(C) 1

(D) 2

The feedback system shown below oscillates at 2 rad/s when

R(s) +

K ( s  1) s  as 2  2 s  1

Y(s)

3

-

(A) K = 2 and a = 0.75 (C) K = 4 and a = 0.5

(B) K = 3 and a = 0.75 (D) K = 2 and a = 0.5 t

Q.44

The input x(t) and output y(t) of a system are related as y (t ) 

 x( ) cos(3 ) d .

The system is



(A) time-invariant and stable (C) time-invariant and not stable Q.45

An analog voltmeter uses external multiplier settings. With a multiplier setting of 20 kWit reads 440 V and with a multiplier setting of 80 kWit reads 352 V. For a multiplier setting of 40 kW the voltmeter reads (A) 371 V

Q.46

(B) 383 V

(C) 394 V

(D) 406 V

The locked rotor current in a 3-phase, star connected 15 kW, 4-pole, 230 V, 50 Hz induction motor at rated conditions is 50 A. Neglecting losses and magnetizing current, the approximate locked rotor line current drawn when the motor is connected to a 236 V, 57 Hz supply is (A) 58.5 A

Q.47

(B) stable and not time-invariant (D) not time-invariant and not stable

(B) 45.0 A

(C) 42.7 A

(D) 55.6 A

A single phase 10 kVA, 50 Hz transformer with 1 kV primary winding draws 0.5 A and 55 W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions 2 times the corresponding dimensions of the first transformer. The core material and lamination thickness are the same in both transformers. The primary windings of both the transformers have the same number of turns. If a rated voltage of 2 kV at 50 Hz is applied to the primary of the second transformer, then the no load current and power, respectively, are (A) 0.7 A, 77.8 W

(B) 0.7 A, 155.6 W

(C) 1 A, 110 W

(D) 1 A, 220 W


GATE 2012


Common Data Questions Common Data for Questions 48 and 49: In the 3-phase inverter circuit shown, the load is balanced and the gating scheme is 1800-conduction mode. All the switching devices are ideal.

S1

S3

S5

vph

+ - Vd S4

S6

Q.48

R 3-phase balanced load

The rms value of load phase voltage is (A) 106.1 V

Q.49

R

S2

3-phase inverter

R=20 Ω

(B) 141.4 V

(C) 212.2 V

(D) 282.8 V

If the dc bus voltage Vd =300 V, the power consumed by 3-phase load is (A) 1.5 kW

(B) 2.0 kW

(C) 2.5 kW

(D) 3.0 kW

Common Data for Questions 50 and 51: With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: (i) 1 W connected at port B draws a current of 3 A (ii) 2.5 W connected at port B draws a current of 2 A

+ B

A

Q.50

For the same network, with 6 V dc connected at port A, 1 W connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is (A) 6 V

Q.51

(B) 7 V

(C) 8 V

(D) 9 V

With 10 V dc connected at port A, the current drawn by 7 W connected at port B is (A) 3/7 A

(B) 5/7 A

(C) 1 A

(D) 9/7 A


GATE 2012


Linked Answer Questions Statement for Linked Answer Questions 52 and 53: In the circuit shown, the three voltmeter readings are V1  220 V , V2  122 V , V3  136 V .

R V2

RL

V1

V3

Load

I

X

Q.52

The power factor of the load is (A) 0.45

Q.53

(B) 0.50

(C) 0.55

(D) 0.60

If RL  5 W , the approximate power consumption in the load is (A) 700 W

(B) 750 W

(C) 800 W

(D) 850 W

Statement for Linked Answer Questions 54 and 55: The transfer function of a compensator is given as

Gc ( s )  Q.54

Gc (s) is a lead compensator if (A) a =1, b = 2 (C) a = –3, b = –1

Q.55

sa . sb

(B) a = 3, b = 2 (D) a = 3, b = 1

The phase of the above lead compensator is maximum at (A)

2 rad/s

(B)

3 rad/s

(C)

6 rad/s

(D) 1 / 3 rad/s


GATE 2012


General Aptitude (GA) Questions (Compulsory) Q. 56 – Q. 60 carry one mark each. Q.56

One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow. (A) (B) (C) (D)

Q.57

requested that should be given the driving test instead of tomorrow

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 = (A) 2.23

Q.58

(C) 11.37

(D) 27.64

Choose the most appropriate alternative from the options given below to complete the following sentence: If the tired soldier wanted to lie down, he ___ the mattress out on the balcony. (A) (B) (C) (D)

Q.59

(B) 4.33

should take shall take should have taken will have taken

Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ___ was impressive. (A) beggary

Q.60

(B) nomenclature

(C) jealousy

(D) nonchalance

Which one of the following options is the closest in meaning to the word given below? Latitude (A) Eligibility

(B) Freedom

(C) Coercion

(D) Meticulousness

Q. 61 - Q. 65 carry two marks each. Q.61

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is (A) 1/4

(B) 1/16

(C) 7/16

(D) 9/16


GATE 2012

Q.62


One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them. Which one of the following statements best sums up the meaning of the above passage? (A) Thorough regimentation was the main reason for the efficiency of the Roman legions even in adverse circumstances. (B) The legions were treated inhumanly as if the men were animals. (C) Discipline was the armies’ inheritance from their seniors. (D) The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.

Q.63

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is (A) 5

Q.64

(C) 9

(D) 10

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is (A) 2

Q.65

(B) 6

(B) 3

(C) 4

(D) 8

The data given in the following table summarizes the monthly budget of an average household. Category Food Clothing Rent Savings Other expenses

Amount (Rs.) 4000 1200 2000 1500 1800

The approximate percentage of the monthly budget NOT spent on savings is (A) 10%

(B) 14%

(C) 81%

(D) 86%



GATE 2012 - Answer Keys Electrical Engineering – EE Q. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Key / Range B A C C A C A C B D B A A D D B D D B A A C

Q. No. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Key / Range D Marks to All C 8 C A D D A B B D C D C Marks to All D A D C A D

Q. No. 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Key / Range Marks to All Marks to All B B D C C A B A A B D A D B C A A A D


GATE Solved Question Papers for Electrical Engineering [EE] by AglaSem.Com

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