GATE-2013 Test Series ...GATE-2013 Test Series ELECTRICAL ENGG. - EE ENGINEERS INSTITUTE OF INDIA...

GATE-2013 Test Series www.engineersinstitute.com ELECTRICAL ENGG. - EE

ENGINEERS INSTITUTE OF INDIA Page 1 of 2128-B/7, Jia Sarai, Near IIT, Hauz Khas, New Delhi-110016. www.engineersinstitute.com

EE : ELECTRICAL ENGINEERINGDuration: Three Hours Maximum Marks: 100

Test Booklet Series: B Test Type: 5 Paper Code: EE101

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 65 questions 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, 1/3 mark will be deducted for each wrong answer. For all 2 marks questions, 2/3 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 No.

GATE-2013 Test Series www.engineersinstitute.com

Q. 1 – Q. 25 carry one mark each.

Q. 1 Integrated output waveform for the dual slope ADC is shown in figure. The time T for an 8 bit counter with 4MHz clock will be

(a.) 0.032m sec.(b.) 0.064m sec.(c.) 0.64m sec.(d.) 0.024m sec.

Q. 2 In the given figure below the switches are in position ‘a’ or ‘b’ depending on the switch input being 0 or 1. B3 is the MSB and Bcode is (1111)

(a.) –10 volt(b.) –8 volt(c.) –9.31 volt(d.) –4.53 volt

Q. 3 For the synchronous generator shown below find the direction of current in the stator coil aa(with direction of rotation shown anticlock wise)

www.engineersinstitute.com ELECTR

Q. 25 carry one mark each.

Integrated output waveform for the dual slope ADC is shown in figure. The time T for an 8 bit counter with 4MHz clock will be

In the given figure below the switches are in position ‘a’ or ‘b’ depending on the switch input is the MSB and B0 is the LSB. Find the output voltage V0 if the input digital

For the synchronous generator shown below find the direction of current in the stator coil aa(with direction of rotation shown anticlock wise)

ELECTRICAL ENGG. - EE

Integrated output waveform for the dual slope ADC is shown in figure. The time T for an 8

In the given figure below the switches are in position ‘a’ or ‘b’ depending on the switch input if the input digital

For the synchronous generator shown below find the direction of current in the stator coil aa


(a.) & 'in a in a�

(b.) & 'in a in a �

(c.) & 'in a in a� �

(d.) In cannot be determined

Q. 4 If a series combination of a D.C source of 8V and a.c. source of 5sin3t + 4 sin5t is measured by PMMC and electrodynamometer separately. Then what will be the reading

(a.) 8V and 9.192V(b.) 17V and 17V(c.) 9.192V and 9.192V(d.) 17V and 9.192V

Q. 5 It 0

( ) sinx t c t dt

then x(t) is

(a.) 0(b.) ½(c.) 1

(d.)

Q. 6 Determine the time signal corresponding transfer function 2

2 1

4 36( )

2 9 4

z zH z

z z

when

system is stable

(a.) 1 11

8 4

n n

u n u n

(b.) 35 1. 16(2) [ 1]

112 4

nnu n u n

(c.) 1 11

4 8

n n

u n u n

(d.) 11 (2) 1

4

nnu n u n

Q. 7 For a turbo alternator of 100MVA, the inertia constant 5. The value of “H” for an alternator of 50MVA is

(a.) 15(b.) 12


(c.) 10(d.) 8

Q. 8 The non-uniformity of the current-distribution is due to

(a.) Faraday’s effect and skin affect (b.) Bundled conductor and skin effect (c.) Proximity effect and skin effect (d.) Ferranti effect and Faraday’s effect:

Q. 9 Which bridge is used as a harmonic analyzer & also used as a Notched filter

(a.) Maxwell bridge(b.) Schering bridge(c.) Heaviside campbell bridge(d.) Wein’s Bridge

Q. 10 In the system shown in the figure below, r(t) = sin .t The steady state response C(t) will exhibit a resonance peak at a frequency of

(a.) 8 rad/sec (b.) 4 2 rad/sec.

(c.) 4 rad/sec

(d.) 2 2 rad/ sec.

Q. 11 What is the Fourier Transform of given figure

(a.) 2 TAT S

2a

(b.) T

AT S2

a

(c.) 2 T2 AT S

2a

(d.) T

2 AT S2

a

Q. 12 Find the value of current 1"I " in the circuit shown below

64( + 8)s s

r t( ) ( )t+–

A

– T T


(a.) 3.5 A (b.) – 3.5 A(c.) 4 A (d.) None of above

Q. 13 In figure, the switch was closed for a long time before opening at t = 0. The voltage ‘ Rv ’ at

0t is:

(a.) It cannot be determined as the value of resistance are not given(b.) 100 volts(c.) –100 volts(d.) 0 volts

Q. 14 For the root loci of unity feedback shown in the figure below

If the gain “K” is increased by 4-times then is(a.) reduced by 0.5 times(b.) increased by 2 times(c.) reduced by 2 times(d.) none of above

Q. 15 Power consumed per phase is 3840 watts for the circuit shown below

R1

R4R3

R2

R5

R6

R7

R9

R10

R11

vR

R12

R8

10H

20+ –

5A

t = 0


Then the one possible value of PR is(a.) 29 (b.) 20 (c.) 15(d.) 19.67

Q. 16 What will be the contents of register AL after the following has been executedMOV BL, 8CMOV AL, 7EADD AL, BL(a.) 0A and carry flag is set (b.) 0A and carry flag is reset(c.) 6A and carry flag is set (d.) 6A and carry flag is reset

Q. 17 If the inductance of moving iron instrument is 2(30 5 2 )L H and spring constant 62.4 10K So what will be deflection when measuring current I = 4A

(a.) 1.162 rad(b.) 0.162 rad(c.) 2.212 rad(d.) 0.524 rad

Q. 18 The value of

1/

0

(1 )lim

x

x

x e

x

is

(a.)2

e

(b.) e(c.) 0(d.) 1

Q. 19 The particular integral of the differential equation (D2 –3D + 2) y = sin (e–x) is

(a.) 2 22 sin( )x x x xCe C e e e

(b.) 2 22 sin( )x x x xCe C e e e

(c.) 2 22 sin( )x x x xCe C e e e

(d.) 2 21 2 sin( )x x x xC e C e e e

Q. 20 The harmonic conjugate of the functions 2 21ln( )

2u x y is

(a.) Does not exist

3 – BalancedSource

Z Z

Z

IY

IB

IR

RP + 20j

RP + 20j400v RP

+20j


(b.) Since not harmonic, hence no harmonic conjugate

(c.) 1tany

x

(d.) 1siny

x

Q. 21 Find the transfer function for the control system shown below

Box shown above performs the operation same as 1 form it transfer the data in analog form

(a.)1

( 1) 1s s

(b.)1

( 1) 1s s

(c.)1

( 1) 1s s

(d.)1

( 1) 1s s

Q. 22 For the root locus plot of some open loop transfer function is shown below.

Find the value of K marked in the graph

(a.) Transfer function required

(b.) 8

(c.) 48

(d.) 2 2


Since not harmonic, hence no harmonic conjugate

function for the control system shown below

Box shown above performs the operation same as 1 2 “De-multiplexer” But not in digital form it transfer the data in analog form

For the root locus plot of some open loop transfer function is shown below.

Find the value of K marked in the graph


” But not in digital


Q. 23 If reverse current of Ge transistor at 25ºC is 2must be increased so that given transistor must come into cut off region:

(a.) 37ºC (b.) 47ºC

Q. 24 The states of diode D1 and D

(a.) Both D1 and D2 off(c.) Both D1 and D2 on

Q. 25 In the circuit shown below the impedance of circuit should be independent of the frequency of supply

The power loss will be ?

(a.)

2 C

Lv

(b.)

2v


current of Ge transistor at 25ºC is 2A. If VBB = 1 volt, then how much temperature must be increased so that given transistor must come into cut off region:

47ºC (c.) 56.7ºC (d.) 67.8ºC

and D2 in figure under extremely high negative (VS >> V) is

(b.)D1 off & D2 on (d.)D1 on & D2 off

In the circuit shown below the impedance of circuit should be independent of the frequency of

2 L

Cv

(c.)

2 L

Cv (d.) None of


= 1 volt, then how much temperature

67.8ºC

>> V) is

In the circuit shown below the impedance of circuit should be independent of the frequency of

one of these


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

Q. 26 If current coil resistance is 0.5 and pressure coil resistance is 10K and series resistor of

400 , so what will be the reading of wattmeter.

If V = 220V , I = 20A

(a.) 4400W (b.) 4396.25W (c.) 4404.65W (d.) 0W

Q. 27 The Laplace transfer of x(t) is 2

2

16( )

( 3)( 2)

sX s

s s s

Then evaluate the value of x(t) for

which Fourier transform is define

(a.) 3 215 7 12

6 10 15t t te e e

(b.) 3 27 2

10 5t t te e e

(c.) 3 215 7 12

6 10 15t t te e e

(d.) 3 21 4 4

2 10 3t t te e e

Q. 28 A 2-pole d.c. shunt generator charges a 100 volts battery, the armature circuit resistance is

0.5. The charging currents are found to be 10A and 20A for generator speed of 1055 and 1100 rpm respectively. (neglect armature reaction effect and internal resistance of battery)

The field current of the generator is (a.) If = 20A(b.) If = 20.44A(c.) If = 24.44A(d.) If = 44.44A

Q. 29 The gates 1 2 3 4 5, , , &G G G G G has propagation delay of 10 nSec, 20 nSec, 30 nSec, 40 nSec &

50 nSec respectively if the input ‘V1’ makes an abrupt change from 0 to 1 at t = to and V2

changes from 1 to 0 at t = to , then output waveform V0 is


(a.)

(b.)

(c.)

(d.) None of above

Q. 30 In the figure shown below all the FF’s are initially cleared

What is the value of Y0 after 3 clock pulse.

(a.) A B (b.) A B

Q. 31 The impulse response of the system shown below


In the figure shown below all the FF’s are initially cleared

after 3 clock pulse.

A B (c.) AB (d.) A B

The impulse response of the system shown below


A B


(a.) ( ) [ 1] 2 [ 2] [ 4]h n n n n

(b.) [ ] [ ] [ 2]h n n n

(c.) [ ] [ 3] [ 1] 2 [ 2]h n n n n

(d.) [ ] [ 2] [ 5]h n n n

Q. 32 What is the inverse Fourier transform of X()

(a.)cos sin 2

.2 2

t t

(b.)cos 2 sin 2( )

. .2 2

t td

(c.)sin sin3

.3

t t

t t

(d.)sin 2 sin 2( )

.( )

td

t

Q. 33 The steady state error for the system shown below is

Where , ( )D s Disturbance (Noise) , ( )R s unit step.

(a.) ess = 0 (b.) ess = 1 (c.) ess = –1 (d.) ess =



Q. 34 A 400MVA, 22KV, 3- salient-pole generator is operating at 300MW power output at a lagging power factor of 0.866 synchronized to 22KV bus. The generator reactance’s are

1 . . & 0.8 . .d qX p u X p u The generator gives rated a open circuit voltage at a field

current of 300A. The excitation e.m.f is

(a.) 1.72 23.99 . .p u

(b.) 1.72 43 . .p u

(c.) 1 23.99 . .p u

(d.) 1 43 . .p u

Q. 35 For y(t) shown below, at what minimum frequency signal y(t) will be sampled so that y(t) can be reconstructed from its sampled value .

( ) . 2( ).y t sinc sinc t d

(a.) 1 Hz (b.) 2 Hz (c.) 4 Hz (d.) 3Hz

Q. 36 Which one of the following will represent the impulse response of static system

(a.) 2 . ( )te u t

(b.) 2 ( 2)te u t

(c.) 2 ( 2)te u t

(d.) 2 ( )te t

Q. 37 The matrix A is defined as

1 2 3

0 3 2

0 0 2

A

The eigen value of 3 23 5 6 2A A A I are(a.) 4, 110, 105(b.) 2, 15, 18(c.) 15, 18, 21(d.) 110, 10, 105

Q. 38 3 boxes A, B, C in which A contains 2 White, 3 Red and 1 Green ball. B contains 1 White, 2 Red and 3 Green ball and C contains 3 White , 1 Red and 2 Green ball. Two balls are drawn at random and found to be 1 white and 1 Red. What is probability that they were drawn from B box.

(a.) 5/11 (b.) 1/11 (c.) 2/11 (d.) 6/11

Q. 39 In which of the following case, the order of convergence is quadratic?


(a.) Method of false position (b.) Newton-Raphson method(c.) Bisection method(d.) Iterative method

Q. 40 In how many ways 30 marks can be allotted to 8 questions if each question carries at least 2 marks:

(a.) 116280 (b.)

Q. 41 A generator operating at 50Hz delivers 1p.u. power to an infinite bus through a transmission line. A fault takes place reducing the maximum power transferable to half, whereas before fault this power was 2.0 p.u. and after the clearance of the is approximately:

(a.) 72º (b.)

Q. 42 If transistor is in active region calculate value of R

(a.) 51.19K (b.)

Q. 43 Two 22KV, 40MVA, 3, star connected genebelow:

The positive, negative and zero sequence reactances of each being, respectively, j0.2, j0.18,

j0.12 p.u. The star point of GThe single line to ground fault at the terminals of one generator.The approximate current in the grounding resistor and the voltage across grounding resistors are respectively.(a.) 5.4 KA ; 10.8 KV


Method of false position Raphson method

In how many ways 30 marks can be allotted to 8 questions if each question carries at least 2

(b.) 112801 (c.) 621180 (d.)

A generator operating at 50Hz delivers 1p.u. power to an infinite bus through a transmission line. A fault takes place reducing the maximum power transferable to half, whereas before fault this power was 2.0 p.u. and after the clearance of the fault, it is 3/2 p.u. the critical angle

(b.) 70º (c.) 59º (d.)

If transistor is in active region calculate value of R1

(b.) 40K (c.) 61.23K (d.)

, star connected generators operated in parallel as shown in figure


j0.12 p.u. The star point of G1 is earthed through a 2 resistor and that point of Gsingle line to ground fault at the terminals of one generator.

The approximate current in the grounding resistor and the voltage across grounding resistors


In how many ways 30 marks can be allotted to 8 questions if each question carries at least 2

261180

A generator operating at 50Hz delivers 1p.u. power to an infinite bus through a transmission line. A fault takes place reducing the maximum power transferable to half, whereas before

fault, it is 3/2 p.u. the critical angle

69º

80K

rators operated in parallel as shown in figure


resistor and that point of G2 is isolated .

The approximate current in the grounding resistor and the voltage across grounding resistors


(b.) 22.KA; 44KV(c.) 4.5 KA; 9KV(d.) 8.10 KA; 16.2 KV

Q. 44 For control of process through PID controller

20 1 rd

TQ sT

s

is cascaded as shown below:

dT Derivative time

When integral control action is not employed thensystem is critically damped: (a.) Td = 0.04 sec(b.) Td = 0.02 sec(c.) Td = 0.4 sec(d.) Td = 0.2 sec

Q. 45 Two J-K flip-flops are connected as synchronous counter that goes through the following Q

sequence 11 10 01 00 11

(a.) ;A A B BJ Q J Q

(b.) ( ) ;A A B B A BJ Q Q J Q Q �

(c.) ;A A B B A BJ Q Q J Q Q

(d.) 1 ;A B A BJ J Q Q

Q. 46 The value of voltage A" "v shown in the figure given below is

(a.) 20 volts

(b.) 12 volts

(c.) 45 volts

(d.) none of above


rocess through PID controller

is cascaded as shown below:

rT Rise time

When integral control action is not employed then, the value of ‘Td’ such that the overall system is critically damped:

flops are connected as synchronous counter that goes through the following Q

11 10 01 00 11 …………. the connection to the input &A BJ J

A A B B A BJ Q Q J Q Q�

A A B B A BJ Q Q J Q Q

" "shown in the figure given below is


’ such that the overall

flops are connected as synchronous counter that goes through the following QBQA

&A BJ J are



Q. 47 A 220V 60A dc series motor having combined resistance of and filed of 0.15 is controlled in regenerative braking motor dc source voltage 220V motor constant is 0.05 V-S/A-rad. The avg. motor armature current is rated and ripple free for a duty cycle of 50% determine speed during braking and power returned to supply.

(a.) 39.66 rad/sec, 6.6 kw

(b.) 32.2 rad/sec, 4.5 kw

(c.) 42.2 rad/sec, 5.4 kw

(d.) 50 rad/sec, 7.5 kw

Common Data Questions

Common Data for Questions 48 and 49:

Consider the open loop transfer function of a unity feedback system is 3( 3)

G( )( 1)

ss

s s

Q. 48 The phase crossover frequency of the system is

(a.) 3 r/s(b.) 2 r/s

(c.) 3 r/s(d.) 1 r/s

Q. 49 Which of the following for the above closed system is correct?(a.) stable system(b.) unstable system(c.) marginal stable system(d.) none of above

Common Data for Questions 50 and 51:

50Hz, 3- induction motor has a rated voltage ‘V1’. The slip at rated voltage and rated frequency at which the torque is maximum is 0.3. Now the motor runs at 80Hz supply at V2 voltage

Neglect stator impedance

Q. 50 The ratio of current and torque at starting if 1 2v v is

(a.) 1.64, 0.411(b.) 0.64, 0.411(c.) 1.84, 2.34(d.) 0.84, 2.34

Q. 51 For motor has the same value of starting current and torque at 50 & 80 Hz frequency then the ratio of v2/v1 is

(a.) 0.46(b.) 0.84


(c.) 1.55(d.) 2.55

Linked Answer Questions

Statement for Linked Answer Questions 52 and 53:

A separately exited dc motor fed from 3

rpm when firing angle is zero (0º). The armature is taking 50A at 400 V

Q. 52 Calculate supply voltage per phase

(a.) 170V

(b.) 290V

(c.) 250V

(d.) None

Q. 53 Also range of required to given speed b/w 1500 rpm to 750 rpm at full load

(a.) 86.4º

(b.) 90º

(c.) 75.4º

(d.) 0º


For the circuit shown below

Q. 54 The value of 2V is

(a.) 100 volts

(b.) 1.81 volts

(c.) 1 volts

(d.) 12 volts



A separately exited dc motor fed from 3- (phase) semi convertor develop a full load torque at 1500

rpm when firing angle is zero (0º). The armature is taking 50A at 400 Vdc having Ra = 0.5

Calculate supply voltage per phase

required to given speed b/w 1500 rpm to 750 rpm at full load



(phase) semi convertor develop a full load torque at 1500

= 0.5



Q. 55 The average power delivered to the equivalent resistance of secondary across 2V is

(a.) 1250 watts

(b.) 0.125 watts

(c.) 0.4095 watts

(d.) 0.2047 watts

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

Q. 56 Find the missing number in given number series

1, 8, 3, 16, 5, 32, 7, ……., 9

(a) 64 (b.) 55 (c.) 77 (d.) 40

Q. 57 Choose the most appropriate word from the options given below to complete the following sentence:

There are no permanent ___________in politics(a) associates (b.) allies (c.) collaborators (d.) partners

Q. 58 Choose the most appropriate alternative from the options given below to complete the following sentence:

In final conclusion, the use of final is superfluous because conclusion _____ always final.

(a) was (b.) is (c.) are (d.) has beenQ.59 Which one of the following options is the closest in meaning to the word given below?

Plethora

(a.) excess (b.) lack (c.) rarity (d.) scarcity

Q.60 One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT?

I don't think / that your friend has any illusions / about his scholarship. / No error(a) (b) (c) (d)

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

Q. 61 Shreya starts walking towards the east and, after covering a distance of 20 m, she turns left and runs for 15 m. She then turns to her right and moves 25 m. From here, she again turns right and walks for 15 m. How far is she from the starting point?

(a.) 40 m (b.) 45 m (c.) 50 m (d.) 60 m

Q. 62 Ten judges were asked to judge the relative sweetness of five compounds(A, B, C, D and E) by the method of paired comparisons. In judging each of the possible pairs they were required to state unequivocally which of the two compound was sweeter – a judgement of equality or of no difference was not permitted.



The results of their judgements are summarized in the given table. In studying the table, note that each cell entry shows the number of comparisons in which the ‘row’ compound was judged to be sweeter than the ‘column’ compound.

A B C D E

A 5 8 10 2

B 5 3 9 6

C 2 7 7 8

D 0 1 3 4

E 8 4 2 6

How many comparisons did each judge make?

(a.) 5 (b.) 10

(c.) 15 (d.) 20

Q. 63 I tried a smile-there was no response. I offered the customary gifts-he waved them aside. I tried the few words I knew-and with a gesture of dignity and scorn he handed me a present, a solitary egg; white and chilled it nestled in my palm. I smiled again but even I felt that my smiles had become mechanical. There was obviously nothing for it: I would have to put on my little act, which in my opinion is worth a whole Platoon of Assam riffles as a safety measure. I removed my dentures. There was a roar of interest and excitement from the crowd. I put them backanother roar after I had conducted this humiliating performance several times, there was at least a reaction. The chief’s lips began to twitch, and finally he broke into a hearty laugh. Pointing to his grey hair, he declared, ‘I am an old man too’ and soon he was sitting beside me very affably.

The removing of dentures by the author was intended to show that:

(a.) he was not frightened.(b.) he was old and weak in some ways.(c.) he knew a lot of tricks to amuse people.(d.) he did not wish to be treated as a friend.

Q.64 300 gram of sugar solution has 40% sugar in it. How much sugar (in gram) should be added to make it 60% in the solution?

(a.) 10 (b.) 40 (c.) 90 (d.) 60

Q. 65 Indian army can fire four shots at a time with an anti aircraft gun, If the probabilities of the 1st , 2nd , 3rd and 4th shot hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4.What is the probability that four shots aimed at an enemy aircraft will bring the aircraft down?

(a.) 0.964 (b.) 0.123

(c.) 0.166 (d.) 0.888

END OF THE QUESTION PAPER



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