GATE Previous Year Solved Paper Electrical Engineering (Fully Solved)

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General Aptitude Q. No. 1 – 5 Carry One Mark Each 1.

Which of the following combinations is incorrect? (A) Acquiescence – Submission (B) Wheedle – Roundabout (C) Flippancy – Lightness (D) Profligate – Extravagant

Answer: 2.

(B)

Given set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is probability that the sum of the two numbers equals 16? (A) 0.20

Answer: Exp:

(B) 0.25

(C) 0.30

(D) 0.33

(A)

4 5 20 Total mass

5,11 4,12 4 favorable 3,13 2,14

3.

4 1 0.2 20 5

Which of the following options is the closest in meaning to the sentence below? She enjoyed herself immensely at the party. (A) She had a terrible time at the party. (B) She had a horrible time at the party. (C) She had a terrific time at the party (D) She had a terrifying time at the party

Answer: 4.

(C)

Based on the given statements, select the most appropriate option to solve the given question.

If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? Statements: (I) Each step is ¾ foot high. (II) Each step is 1 foot wide. (A) Statement I alone is sufficient, but statement II alone is not sufficient. (B) Statement II alone is sufficient, but statement I alone is not sufficient. (C) Both statements together are sufficient, but neither statement alone is sufficient. (D) Statement I and II together are not sufficient. Answer: (D) Exp:

Though we know height of each step, and of strains is not mentioned.

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Didn’t you buy _________ when you went shopping? (A) any paper

Answer:

(B) much paper

(C) no paper

(D) a few paper

(A) Q. No. 6 – 10 Carry Two Marks Each

6.

The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option. Statement: There has been a significant drop in the water level in the lakes supplying water to the city. Course of action: (I) The water supply authority should impose a partial cut in supply to tackle the situation. (II) The government should appeal to all the residents through mass media for minimal use of water. (III) The government should ban the water supply in lower areas. (A) Statements I and II follow. (B) Statements I and III follow (C) Statements II and III follow. (D) All statements follow. Answer: (A) 7.

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

Q No

Marks

Answered Correctly

Answered Wrongly

Not Attempted

1

2

21

17

6

2

3

15

27

2

3

1

11

29

4

4

2

23

18

3

5

5

31

12

1

What is the average of the marks obtained by the class in the examination? (A) 2.290 Answer: Exp:

(B) 2.970

(C) 6.795

(D) 8.795

(B)

21 2 15 3 11 11 1 23 2 31 5 2.970 21 15 11 23 31

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The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between numbers of female students in the Civil department and the female students in the Mechanical department?

Electrical 20% Computer Mechanical

science

10%

20% Civil 30%

Answer:

16 Electrical malestudents 40

Exp:

Electrical Femalestudents

4 40 32 5

Total no.of Student 72. % Female 20 32 30 48 Difference is 16.

9.

Select the alternative meaning of the underlined part of the sentence. The chain snatchers took to their heels when the police party arrived. (A) took shelter in a thick jungle (B) open indiscriminate fire (C) took to flight (D) unconditionally surrendered

Answer:

(C)

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The probabilities that a student passes in Mathmatics, Physics and Chemistry are m,p, and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p, c: (I) p + m + c = 27/20 (II) p + m + c = 13/20 (III) (p) (m) (c) = 1/10 (A) Only relation I is true (B) Only relation II is true (C) Relations II and III are true. (D) Relations I and III are true.

Answer: Exp:

(A)

P(atleast two) p(exat 2) 0.5 0.4 0.1 0.75 p m c 0.1 (0.5 0.11 2) p mc 0.65 0.7 1.35 27 20

Electrical Engineering Q. No. 1 – 25 Carry One Mark Each

1.

A moving average function is given by y t signal of frequency

1 t u dt. If the input u is a sinusoidal T t T

1 Hz, then in steady state, the output y will lag u (in degree) by 2T

________. Answer: Exp:

90

u(τ) = sin (ωτ) 2f 2.

1 2T T

T t T

cos 1 y t sin d T t T T t t

1 cos t T cos t

1 cos t cos T sin t sin T cos t 2 2 y t cos t sin 90 t x t sin t

90

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Consider a one-turn rectangular loop of wire place in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is 0.4, and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B t 0.25sin t, where 2 50 radian/second. The power absorbed (in Watt) by the loop from the magnetic field is __________. 10 cm

5 cm

Answer: Exp:

0.192

2 Vemf R d Vemf dt

P

1

B.dS B.S. 800 sin t S

d 1 cos t dt 8 2 1 p cos 2 t 64 R 2 1 cos 2t p 0.4 64 2 Vemf

2 2 cos 2t 20 0.4 64 0.4 64 2 2 0.192W 20 0.4 64

pavg pavg

3.

If the sum of the diagonal elements of a 2 × 2 matrix is 6, then the maximum possible value of determinant of the matrix is ________.

Answer: Exp:

9

Sum of the diagonals elements is -6 for 2×2 matrix The possible eigen value are 1, 5 5, 1, 8, 2 2, 3 4, 2 9,3 3, 1 3, 3 10, 4

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When the Wheatstone bridge shown is used to find value of resistance Rx, the Galvanometer G indicates zero current when R1 50 , R 2 65 & R 3 100 . If R3 is known with 5% tolerance on its nominal value of 100 , what is range of Rx in ohms? R2

R1 G

R3

Rx V

(A) [123.5, 136.5] (C) [117, 143] Answer: Exp:

(B) [125.898, 134.12] (D) [120.25, 139.75]

(A)

Weinbridge is balanced, R1, Rx = R2R3 50×Rx = 65×100 Rx = 130 Now R3 = 100±100×0.05 = 100±5 = 95/105 Rx

R 2 R 3 65 105 136.5 R1 50

65 95 123.5 50 Rangeof R x is123.5 to136.5 Rx

5.

For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage, VTh (in volt), seen from terminal AB is _________. 20i

1

2V

1

i

A

2

B

Answer: Exp:

3.36

Vth = 2i1 2 = 1[i+i1]+i = 2i+i1 i(1) = -20i + 2i1 ∴ 21i = 2i1

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2 i i1 21 25 2 4 2 2i i1 2 i1 i1 1 i1 i1 21 21 21 42 1.68 25 Vth 2i1 3.36V

i1

6.

The impulse response g(t) of a system, G, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of G as shown in Figure (b)?

gt

1 G 0

(A)

Answer: Exp:

t

1 a

2 3

G

b (B)

3 4

(C)

4 5

(D) 1

(D)

Overall impulse response = g(f)*g(t) h(f) = g(f)*g(f) ht 1

m 1

m 1

1

7.

Base load power plants are P: wind farms. Q: run-of-river plants. R: nuclear power plants. S: diesel power plants. (A) P, Q and S only (B) P, R and S only

Answer:

(C) P, Q and R only (D) Q and R only

(D)

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Of the four characteristic given below, which are the major requirements for an instrumentation amplifier? P: High common mode rejection ratio Q: High input impedance R: High linearity S: High output impedance (A) P, Q and R only (B) P and R only

Answer: Exp:

(C) P, Q and S only (D) Q, R and S only

(A)

Additional characteristics include very low DC offset, low drift, low noise, very high open-loop gain, very high common-mode rejection ratio, and very high input impedances. Instrumentation amplifiers are used where great accuracy and stability of the circuit both short and long-term are required.

9.

A random variable X has probability density function f(x) as given below: a bx for 0 x 1 f x otherwise 0

If the expected value E X 2 3, then Pr X 0.5 is __________. Answer: Exp:

0.25

f x dx 1 so a bx dx 1

1

b 1 2 2a b 2 ____ 1

a

given E X 2 3

x a bx dx 1

2 a b 3 2 3 3a 2b 4 ____ 2 from 1 and 2 a0 b2 p r X 0.5 f x dx 2 x dx 0.25 0.5

0.5

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10.

1 ˆ where r is the distance from the origin and rˆ is the unit r, r2 vector in the radial direction. The divergence of the function over a sphere of radius R, which includes the origin, is

Consider a function f

(A) 0 Answer: Exp:

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F

(B) 2

(C) 4

(D) R

(A) 1 ar r2

.F

1 2 1 1 F r Fr sin F 2 r r r sin r sin

1 2 1 r 2 0 0 r 2 r r .F 0 .F

11.

A separately excited DC generator has an armature resistance of 0.1 and negligible armature inductance. At rated field current and rated rotor speed, its open-circuit voltage is 200 V. When this generator is operated at half the rated speed, with half the rated field current, an un-charged 1000 F capacitor is suddenly connected across the armature terminals. Assume that the speed remains unchanged during the transient. At what time (in microsecond) after the capacitor is connected will the voltage across it reach 25V? (A) 62.25

Answer: Exp:

(B) 69.3

(C) 73.25

(D) 77.3

(B)

E b2 N2 2 0.5N1 0.51 E b2 0.25 E b1 0.25 200 50 E b1 N12 N1 51 R C 0.1 1000 6

50 2000e t 10010 t 69.3 sec

12.

In the following chopper, the duty ratio of switch S is 0.4. If the inductor and capacitor are sufficiently large to ensure continuous inductor current and ripple free capacitor voltage, the charging current (in Ampere) of the 5 V battery, under steady-state, is ________.

S

20V

Answer: Exp:

L 3 C

5V

1

V0 DVS 0.4 20 8V I0

V0 E 8 5 3 1A R 3 3

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If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE? (A) f a .f b 0 (B) f a .f b 0 (C) f a .f b 0 (D) f a f b 0

Answer: (C) Exp: We know that, (Intermediate value theorem) If f a f b 0 then f x has at least one root in (a, b) f(x) does not have root is (a, b) means f a f b 0 14.

The primary mmf is least affected by the secondary terminal conditions in a (A) power transformer

(B) potential transformer

(C) current transformer Answer: (B) Q15.

(D) distribution transformer

Consider a HVDC link which uses thyristor based line-commutated converters as shown in the figure. For a power flow of 750 MW from System 1 to System 2, the voltages at the two ends, and the current, are given by: V1 =500 kV, V2 =485 kV and I=1.5 kA. If the direction of power flow is to be reversed (that is, from System 2 to System 1) without changing the electrical connections, then which one of the following combinations id feasible? System1

System 2

I

V1

V2

If power is to be reversed (A) V1 500kV, V2 485kV and I 1.5kA (B) V1 485kV, V2 500kV and I 1.5 kA (C) V1 500kV, V2 485kV and O 1.5kA (D) V1 500kV, V2 485kV, I 1.5kA Answer: Exp:

(A)

V V2 I 1 R For power to be reversed I

V2 V1 Ve R

I

V1

V2

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An inductor is connected in parallel with a capacitor as shown in the figure.

i

L C

Z

As the frequency of current i is increased, the impedance (Z) of the network varies as

Inductive

(A)

Inductive

(B)

z

z

f

f Capacitive

Capacitive (C)

Inductive

(D)

Capacitive

z

z

Inductive

f

f

Answer: Exp:

(B)

Z = ZL//ZC jL Z

Z

Capacitive

Inductive

1 jC

1 jL jC jL

1 1 LC

z

f Capacitive

L Z j 2 1 LC

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For the signal-flow graph shown in the figure, which one of the following expressions is Y(s) equal to the transfer function ? X 2 (s) X (s) 0 1

X 2 (s)

X1 (s)

1

G2

G1

1

1

(A)

Answer: Exp:

G1 1 G 2 (1 G1 )

(B)

Y(s)

G2 1 G1 (1 G 2 )

(C)

G1 1 G1G 2

(D)

G2 1 G1G 2

(A)

P1 G 2

1 G1G 2 G1 1 G1 1 G 2 TF

18.

P11 G2 1 G1 1 G 2

The voltages developed across the 3 and 2 resistors shown in the figure are 6V and 2V respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5V voltage source?

6v

3

2v

Network 1

Network 2

5

(A) 5 Answer: 5 6V 2A Exp: I 3

(B) 7

5v

(C) 10

(D) 14

2V 1A 2 I 1 2 I 1A I

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The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source? (A) 416

Answer:

(A)

Exp:

I1

(B) 440 R1

(C) 200 R2

(D) 920

I2

M

x1

V1

x2

ZL

V1 2 M 2 R1 jX1 I1 R 2 jX 2 ZL Given, L1 = 800 mH L2 = 600 mH M = 480 mH W = 314 rad/sec ZL = 0 R1 R2 neglected 2 M 2 2 M 2 Zin jX1 j X1 jX 2 X2 Zin

3142 0.482 j 314 0.8 j 251.32 120.576 0.6 314 j130.744 jw Leff j314.Leff Leff 0.416 416 mH

20.

A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant? 20log G(j2f )

20 0 20

0.1 1 10 100 1k 10k 100k

f (Hz)

Capacitive

(A)

1000(s 10) s 1000

(B)

10(s 10) s(s 1000)

(C)

s 1000 10s(s 10)

(D)

s 1000 10(s 10)

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Answer:

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(D)

Exp: 1 K.1 .S 1000 G S 1 1 S 10

0dB

20dB 0dB

MdB = 20dB @ initial frequency 20 log M = 20

10

1k

1p 1z

20 log K = 20 K = 10

G S

21.

10 S 1000 10 1000 S 10 1

S 1000 10 S 10

In the 4×1 multiplexer, the output F is given by F A B. Find the required input 'I3I2 I1I0 '. I0

I1

4 1 MUX

I2

F

I3

S1

A

(A) 1010 Answer: Exp:

(B) 0110

S0

B

(C) 1000

(D) 1110

(B)

F A B AB' A'B

00 01 10 11

AB S1S0 A 'B' I0 0 A 'B I1 1 AB' I 2 1 AB I3 0

I0 0 I1 1 I2 1 I3 0

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In the given circuit, the silicon transistor has 75 and collector voltage Vc 9V. Then the ratio of RB and RC is _______. 15V

RB

RC VC

Answer: Exp:

105.1

IC I B

6 RC

8.3 , RB

IB

75, IC I B

76 IB 76

6 8.3 , IB RC RB

8.3 6 RB RC

R B 76 8.3 105.1 RC 6

23.

A (0-50A) moving coil ammeter has a voltage drop of 0.1 V across its terminals at full scale deflection. The external shunt resistance (in milliohms) needed to extend its range to (0-500A) is ________.

Answer: Exp:

0.22

I2 500, I1 500 I2 I1 450 450 R sh 0.1 R sh 0.1 / 450 0.22m

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Consider the circuit shown in the figure,. In this circuit R 1k, and C 1F. The input voltage is sinusoidal with a frequency of 50 Hz, represented as phasor with magnitude Vi and phase angle 0 radian as shown in the figure. The output voltage is represented as a phasor with magnitude V0 and phase angle radian. What is the value of output phase angle (in radian) relative to the phase angle of the input voltage? R C

vo Vo

vi Vi 0 C

R

(A)

Answer: Exp:

(B)

(C)

2

(D)

2

Vt SCR SCR Vt Vin Vn 1 SCR 1 SCR

VCn V V Vo 1 R SC SCR SCR Vin SCR Vin Vin Vo 1 SCR 1 SCR Vo 0; 0

25.

A steady current I is flowing in the –x direction through each of two infinitely long wires L at y as shown in the figure. z 2 The permeability of the medium is 0 . The B field at (0,L,0) is (A)

40 I zˆ 3L

4 I (B) 0 zˆ 3L (C) 0 30 I zˆ 4L (A)

(D) Answer: Exp:

y L / 2

Current I

yL/2 0

Current I

x

H = H1+H2

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I a z 2 L 2

z

I a z 3L 2 2

I 2 2 a z 2 L 3L 4I a z 3L

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y

x L ,0 0, 2

L 0, ,0 2

Q. No. 26 – 55 Carry Two Marks Each 26.

Consider a discrete time signal given by x[n] (0.25)n u[n] (0.5)n u[n 1]

The region of convergence of its Z-transform would be (A) the region inside the circle of radius 0.5 and centered at origin. (B) the region outside the circle of radius 0.25 and centered at origin. (C) the annular region between the two circles, both centered at origin and having radii 0.25 and 0.5. (D) the entire Z plane. Answer: (C) Exp:

x n 0.25 u n 0.5 u n 1 n

ROC1 : Z 0.25

n

ROC2 : Z 0.5

ROC ROC1 ROC2 0.25 Z 0.5

27.

Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is (A) 5/11 (B) 1/2 (C) 7/13 (D) 6/11 Answer: (D) 6 1 Exp: Probability of getting 6 is 36 6 1 i.e,. Probability of A wins the game 6 Probability of A not wins the game 1 Probability of B wins the game

1 5 6 6

1 6

5 6 If a starts the game, Probability A win the game

Probability of B not win the game

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P A P A P B P A P A P B P A P B P A ..... 1 551 55551 .......... 6 666 66666 1 55 5555 1 ..... 6 66 6666

2 4 1 5 5 1 ..... 6 6 6

1 1 13 6 6 5 2 6 6 11 1 6

28.

The circuit shown in meant to supply a resistive load R L from two separate DC voltage sources. The switches S1 and S2 are controlled so that only one of them is ON at any instant. S1 is turned on for 0.2 ms and S2 is turned on for 0.3 ms in a 0.5 ms switching cycle time period. Assuming continuous conduction of the inductor current and negligible ripple on the capacitor voltage, the output voltage V0 (in Volt) across RL is ________.

S1

L

RL

S2 10V Answer:

Vo

C

5V

(7)

Exp:

V0 10V 5V

t msec 0.2 V0

0.5

10 0.2 5 0.3 7V 0.5

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Determine the correctness or otherwise of the following Assertion [a] and the Reason p[r]. Assertion: Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions. Reason: Accuracy depends on the power mismatch vector tolerance. (A) Both [a] and [r] are true and [r] is the correct reason for [a]. (B) Both [a] and [r] are true and [r] is not the correct reason for [a]. (C) Both [a] and [r] are false. (D) [a] is false and [r] is true.

Answer: 30.

(A)

In the given circuit, the parameter k is positive, and the power dissipated in the 2 resistor is 12.5 W. The value of k is 4V ________.

5

2

Vo

10

5A

kV0

Answer: Exp:

0.5

P2 12.5 W 12.5 2.5 2 V0 2 2.5 5V

i 2

2.5 KV0 5 KV0 2.5

K

31.

2.5 1 0.5 5 2 5

In the signal flow diagram given in the figure, u1 and u2 are possible inputs whereas y1 and y2 are possible outputs. When would the SISO system derived from this diagram u1 be controllable and observable? (A) When u1 is the only input and y1 is the only output. (B) When u2 is the only input and y1 is the only output. (C) When u1 is the only input and y2 is the only output. (D) When u2 is the only input and y2 is the only output.

Answer:

(B)

y1

x1 1/ s

1

1

1 2

u2

1/ s

1

x2

1

1

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y2

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32.

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5V is applied to Port1, a current of 1.25 A flows through a 1 resistance connected across Port 2. When 3V is applied to Port 1, then current (in Ampere) through a 2 resistance connected across Port 2 is _________.

Answer: Exp:

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0.545 I2 0.4 3 0.6 2I 2

I1 y11v1 y12 v1 I2 y 21v1 y 22 v 2

1.2 1.2I 2

4 10y 21 y 21 0.4 I2 0.545A.

1.25 0.4v1 1.25y22 0.4 y 22 0.6

33.

A self commutating switch SW, operated at duty cycle is used to control the load voltage as shown in the figure. D VL L

SW

Vdc

VC

C

RL

Under steady state operating conditions, the average voltage across the inductor and the capacitor respectively, are (A) VL 0 and VC

1 Vdc 1

1 (B) VL Vdc and Vc Vdc 2 1

(C) VL 0 and VC

Vdc 1

(D) VL

Answer: 34.

(A)

The figure shown a digital circuit constructed using negative edge triggered J-K flip flops. Assume a starting state of Q2Q1Q0 000. This state Q2Q1Q0 000 will repeat after ________ number of cycles of the clock CLK.

J0

1 CLK

1

Answer: Exp:

Vdc and VC Vdc 2 1

J1

Q0

Q0

1

K1

Q2

Clock

Clock

Clock

K0

J2

Q1

Q0

1

K2

Q2

6

First flip flop acts as mod-2 counter Second 2 flip flops from mod (2n-1) Johnson counter = mod counter ∴ overall modulus = mod – 6 counter

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35.

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The signum function is given by x ;x 0 sgn(x) x 0; x 0

The Fourier series expansion of sgn(cos(t)) has (A) only sine terms with all harmonics. (B) only cosine terms with all harmonics (C) only sine terms with even numbered harmonics. (D) only cosine terms with odd numbered harmonics. Answer: (D) Exp: sgn(cos t) 1; cos t 0 1;cos t 0 cos t

t

sign(cos t)

t 1

it represents square wave, which is even and half wave symmetry function, it contains cosine terms for all odd harmonics. 36.

A DC motor has the following specifications: 10 hp, 37.5 A, 230V; flux/pole = 0.01 Wb, number of poles = 4, number of conductors = 666, number of parallel paths = 2. Armature resistance = 0.267. The armature reaction is negligible and rotational losses are 600W. The motor operates from a 230V DC supply. If the motor runs at 1000 rpm, the output torque produced in (in Nm) is __________.

Answer: Exp:

E

14.14 2Np 0.01 666 4 1000 55.5 60A 60 2

Internal power =EI=55.5×37.5=2081.25 Pout=2081.25-600=1481.25 T

Pout 1481.25 14.14 Nm 1000 w 2 60

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37.

Find the transfer function

Y s X s

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of the system given below.

G1

X S

H

Y S

Y S

G2

(A)

G1 G2 1 HG1 1 HG 2

(B)

G1 G2 1 HG1 1 HG 2

(C)

G1 G 2 1 H G1 G 2

(D)

G1 G 2 1 H G1 G 2

Answer: Exp:

(C)

From the block diagram Y G1 X HY G 2 X HY

Y X G1 G 2 HY G1 G 2 Y 1 H G1 G 2 X G1 G 2

38.

G1 G 2 Y X 1 H G1 G 2

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at (2-j3). List all the poles and zeroes. (A) Poles at (2±j3), no zeroes (B) Poles at (±2-j3), one zero at origin (C) Poles at (2-j3), (-2+j3), zeroes at (-2-j3), (2+j3) (D) Poles at (2±j3), zeroes at (-2±j3)

Answer: Exp:

(D)

This is an APF 2 3j

Im

2 3j

0 Re

2 3j

2 3j

39.

Two single-phase transformers T1 and T2 each rated at 500 kVA are operated in parallel. Percentage impedances of T1 and T2 are (1+j6) and (0.8+j4.8), respectively. To share a load of 1000 kVA at 0.8 lagging power factor, the contribution of T 2 (in kVA) is _________. Answer: 555 Exp:

ST2 S

6.0880.53 z1 1000 555KVA 10.9480.53 z1 z 2

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40.

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A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is _______. Air, r 1.0

5mm

10mm

Glass, εr = 4.0 Answer: Exp:

18.75 A 0 C1 d 4A 0 C2 d 4A 0 CC Ceq 1 2 C1 C2 5d

air 0

30kV cm

1

5mm

2

5mm

C1 C2

glass 40

30kV cm

Q CV Ceqv A A A 4A 0 Dn V 5dA 4 Dn 0 V 5d D 4 E1 n V 0 5d D n s

4V 30 5 5 103 105 V 4d 4 V 18.75kV

30 105

41.

A sustained three-phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located? I3

I1 Transmission line

V1

P

V2

S

Q

Transmission line

R

I4

I2

V2 V1

I3

I2

I1 I4

(A) Location P

(B) Location Q

(C) Location R

(D) Location S

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Answer: Exp:

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(D) V2 I3

Since V2 leads I3

42.

3 0 2 The maximum value of “a” such that the matrix 1 1 0 has three linearly 0 a 2 independent real eigenvectors is

(A) Answer: Exp:

2

(B)

3 3

1

(C)

3 3

1 2 3 3 3

(D)

1 3 3 3

(B)

The characteristic equation of A is |A-XI| = 0 f(x) = x3+6x2+11x+6+2a = (x+1)(x+2)(x+3)+2a = 0 f(x) cannot have all 3 real roots (if any) equal for if f(x) = (x-k)3, then comparing coefficients, we get 6 = -3k, 3k2 = 11 No such k exists (a) Thus f(x) = 0 has repeated (2) roots (say) α,α,β or (b) f(x) = 0 has real roots (distance)(say) α,β,δ Now f ' x 0 x1

6 3 2.577a; 3

x2

6 3 1.422 3

At x1, f(x) has relative max. At x2, f(x) has relative min. The graph of f(x) will be as below y

y

Max. x1 Max.

Min.

x

x2

x x1

x1 is repeated root

x2 Min. x 2 is repeated root

Case (a) repeated roots (α,α,β)

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y

Max.

x

x2

x1

Min.

Case (b)

distinct roots

Note that the graph of f(x) cannot be like the one given below y 3realroots not possible

x

x1

x2

Thus in all possible cares we have 3 1 f(x2)≤0 2 a 0 a 9 3 3 43.

The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region? (A) It corresponds to a frequency greater than K (B) It corresponds to a frequency less than K (C) It corresponds to a frequency K (D) Root locus of modified system never transits to unstable region

Answer:

(D)

44.

A 200/400V, 50 Hz, two-winding transformer is rated at 20 kVA. Its windings are connected as an auto-transformer of rating 200/600V. A resistive load of 12 is connected to the high voltage (600V) side of the auto-transformer. The value of equivalent load resistance (in Ohm) as seen from low voltage side is _________. Answer: (4)8 V1 200 K K 0.5 Exp: V2 400 2

1 R L1 R L2 R 4 12 4 48 1 0.5

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45.

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Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below: C1 P1 0.01P12 30P1 10; 100MW P1 150MW C2 P2 0.05P22 10P2 10; 100MW P2 180MW

The incremental cost (in Rs/MWh) of the power plant when it supplies 200 MW is _____. Answer: (30) dC1 Exp: 2 0.01P1 30 0.02 P1 30 dP1 dC2 2 0.05P2 10 0.1P2 10 dP2

dC1 dC2 dP1 dP2 0.02P1 30 30 0.1P2 10 2P1 3000 10P2 1000 2P1 2000 10P2 P1 P2 200 P2 200; P1 0 dC1 30Rs / Mwh dP1

46.

An unbalanced DC Wheatstone bridge is shown in the figure. At what value of p will the magnitude of V0 be maximum?

1 x

(A)

(B) (1+x)

(D)

Answer:

V0

1 x

(C) 1

R 1 x

pR

pR

1 x (A)

R

E

Exp: R 1 x

PR V0 PR

PR

PR E

V0

R R

R 1 x Ry

E

Let1 x y

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RE E R PR 1 P y R.y V0 .E E Ry PR py y 1 V0 V0 V0 E p y 1 p dV0 y 1 E 0 dp p y 2 1 p 2 1 y 1 P 2 p y 2 V0

y 1 py y p y 1 p p y

p 1 y y y y 1 y p y 1 x

47.

A separately excited DC motor runs at 1000 rpm on no load when its armature terminals are connected to a 200V DC source and the rated voltage is applied to the field winding. The armature resistance of this motor is 1. The no-load armature current is negligible. With the motor developing its full load torque, the armature voltage is set so that the rotor speed is 500 rpm. When the load torque is reduced to 50% of the full load value under the same armature voltage conditions, the speed rises to 520 rpm. Neglecting the rotational losses, the full load armature current (in Ampere) is _______.

Answer:

(100)

Exp: N 0 1000 rpm E N E 0 200V 200 1000 N full 500 rpm E full 500 E full 100V V Ia ra 200 Ia Ia 100A

48.

A solution of the ordinary differential equation and y 1

Answer: Exp:

d2 y dy 5 6y 0 is such that y(0) = 2 2 dt dt

1 3e dy . The value of 0 is ___________. 3 e dt

(-3)

Roots, 3, 2 y t C1e 3t C2 e 2t y 0 C1 C2 2 1 3e y 1 3 e 3 3e 2 C1e 3 C2 e 2 e

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y t e3t 3e 2t dy t dt

49.

3e3t 6e2t ,

dy 0 dt

3 6 3 C

The op-amp shown in the figure has a finite gain A = 1000 and an infinite input R resistance. A step-voltage Vi = 1 mV is applied at the input at time t = 0 as 1k vi shown. Assuming that the operational 1mV amplifier is not saturated, the time constant (in millisecond) of the output t 0s voltage V0 is (A) 1001

(B) 101

(C) 11

(D) 1

Answer:

1F

A 1000

Vo

(D)

Exp:

Time constant = RC= 1103 1106 1ms

50.

A 3-phase 50 Hz square wave (6-step) VSI feeds a 3-phase, 4 pole induction motor. The VSI line voltage has a dominant 5th harmonic component. If the operating slip of the motor with respect to fundamental component voltage is 0.04, the slip of the motor with respect to 5th harmonic component of voltage is ________.

Answer: 5.8 Exp: Slip of motor w.r.t. 5th harmonic = 6-5s = 6-5×0.04= 5.8 51.

An 8 bit unipolar Successive Approximation Register type ADC is used to convert 3.5V to digital equal output. The reference voltage is +5V. The output of ADC at end of 3 rd clock pulse after the start of conversion is ________. (A) 1010 0000

(B) 1000 0000

(C) 0000 0001

(D) 0000 0011

Answer: (A) Exp: The block diagram of SAR type ADC is as follows Vin

VDAC

Control logic

Start of conversion CLOCK

1st CP 2.56 V 2nd CP 3.84 V

Output Register

3rd CP 3.2 V

8bit DAC

Unipolar means all the voltages will be +ve i.e. nothing is –ve. The functionality of SAR type DAC is, it will load a value to output register with MSB=1 and remaining bit=0, and it will cross check a logic as follows. India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 28

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if Vin VDAC ma int ain the loaded bit Vin VDAC clear the loaded bit.

This process continues upto 8 number of clock pulses The output of DAC=(Resolution)×(Decimal equivalent of applied binary). From the given information Resolution

5 20 mV. 2 1 8

when SOC is applied on 1st clock the value located to output register is ' 10000000 2 ' (128)10 then VDAC 128 20mv 2.56V So 3.5>2.56V maintain the bit

So at the end of 1st clock pulse the output is 10000000. On second clock pulse the value loaded to output register is (10100000)2 (192)10 then VDAC 195 20mv 3.84V So 3.5 3.84V clear the loaded bit So at the end of 2nd clock pulse output is (10000000)2 . On third clock pulse the value loaded to output register is (10100000)2 (160)10 then VDAC 160 20mv 3.2V So 3.5 3.2V ma int ain the loaded bit So at the end of 3rd clock pulse output is (10100000)2 . 52.

The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of 50 Hz. It uses unipolar pulse width modulation with switching frequency of 50 kHz and modulation index of 0.7. For V m = 100 V DC, L = 9.55 mH, C = 63.66 μF, and R = 5, the amplitude of the fundamental component in the output voltage V0 (in volt) under steady-state is __________.

Vin Answer:

Full bridge V n VSI

L

C

R

Vo

(56.72V)

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Exp:

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pulse width 0.7 180 126

2Vdc sin 2 2 100 126 sin 56.72V 2

The amplitude of fundamental component in V0

53.

f(A,B,C,D) = Πm (0,1,3,4,5,7,9,11,12,13,14,15) is a maxterm representation of a Boolean function f(A,B,C,D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function is

(A) A C D A B D

(B) ACD ABD

(C) ACD ABCD ABCD

(D) B C D A B C D A B C D Answer: Exp:

(C)

f A,B,C,D ACD ABD In option (C)

f A, B,C, D ACD ABCD ABCD

ACD ABD C C

ACD ABD.1 ACD ABD

CD 00

01

11

10

00

1

01

1

11

10

1

1

AB

ACD

ABD

54.

A 50Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous speed, and producing 1 pu of real power. The initial value of the rotor angle δ is 5o , when a bolted three phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of δ in degrees, 0.02 second after the fault is ________. Answer: (0.9) Exp:

M Pavg

2 1 1 PU 180 50 4500 0.5

0.5 2250 1 4500

45deg sec 1 t 45o 0.2 45o 0.9o

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The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt) is given by (t) = 12 sin t. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______. Answer: (10) 1 1 Exp: Y S Z S 1 j

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55.

Y S

1 1

2

vt

8V

1

1H

tan 1 u

in t 8 12sin t 1 tan 1 0 1 0 12 1 it 8 cos t sin t. 2 2 i t 8 6sin t 6cos t i t 8.

2

1.2 sin t 45 11 1 2

2

6 6 I rms 82 10 2 2

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General Aptitude Q. No. 1 – 5 Carry One Mark Each

1.

A generic term that includes various items of clothing such as a skirt, a pair of trousers and a shirt as (A) fabric (B) textile (C) fibre (D) apparel

Answer: 2.

(D)

Choose the statement where underlined word is used correctly. (A) The industrialist had a personnel jet. (B) I write my experience in my personnel diary. (C) All personnel are being given the day off. (D) Being religious is a personnel aspect.

Answer: 3.

(C)

Based on the given statements, select the most appropriate option to solve the given question. What will be the total weight of 10 poles each of same weight? Statements: (I) One fourth of the weight of a pole is 5 kg (II) The total weight of these poles is 160 kg more than the total weight of two poles. (A) Statement II alone is not sufficient (B) Statement II alone is not sufficient (C) Either I or II alone is sufficient

(D) Both statements I and II together are not sufficient. Answer: (C) 4.

Consider a function f x 1 x on 1 x 1. The value of x at which the function attains a maximum, and the maximum value of function are: (A) 0, 1

Answer: Exp:

(B) 1,0

(C) 0, 1

(D) -1, 2

(C)

f x 1 x on 1 x 1

f 1 1 1 1 1 0 f 0.5 1 0.5 1 0.5 0.5 f 0 1 0 1 f 0.5 1 0.5 0.5 f 1 1 1 1 1 0

maximum value occurs at x = 0 and maximum value is 1.

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5.

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We ____________ our friend’s birthday and we ___________ how to make it up to him. (A) completely forgot --- don’t just known (B) forget completely --- don’t just know (C) completely forget --- just don’t know (D) forgot completely --- just don’t know

Answer:

(C) Q. No. 6 – 10 Carry Two Marks Each

6.

In a triangle PQR, PS is the angle bisector of QPR and QPS 60o. What is the length of PS? P

r

q

s Q

R

p (A) Answer: 7.

q r

(B)

qr

qr q r

(C)

q2 r 2

(D)

q r

2

qr

(B)

Four branches of a company are located at M,N,O, and P. M is north of N at a distance of 4 km; P is south of O at a distance of 2 km; N is southeast of O by 1 km. What is the distance between M and P in km? (A) 5.34

Answer:

(B) 6.74

(C) 28.5

(D) 45.49

(A)

Exp:

N

M 0 45 2

4

1

E

W

N

S

P

8.

If p, q, r, s are distinct integers such that: f (p, q, r, s) = max (p, q, r, s) g (p, q, r, s) = min (p, q, r, s) h (p, q, r, s) = remainder of (p × q)/(r × s) if (p × q) > (r × s) or remainder of (r × s)/(p × q) if (r × s) > (p × q) Also a function fgh (p, q, r, s) = f(p, q, r, s) × g(p, q, r, s) × h(p, q, r, s)

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Also the same operations are valid with two variable function of the form f(p, q). What is the value of fg (h(2, 5, 7, 3), 4, 6, 8)? Answer: Exp:

8

f g (h(2,5,7,3),4,6,8) =fg(1,4,6,8) =f(1,4,6,8)xg(1,4,6,8)=8x1=8

9.

If the list of letters, P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence? I.

2P,2R,2S,2T,2U

II.

P 3,R 3,S 3,T 3, U 3

III. P2 ,R 2 ,S2 ,T2 , U2 (A) I only (B) I and II (C) II and III (D) I and III Answer: 10.

(B)

Out of the following four sentences, select the most suitable sentence with respect to grammer and usage: (A) Since the report lacked needed information, it was of no use to them. (B) The report was useless to them because there were no needed information in it. (C) Since the report did not contain the needed information, it was not real useful to them

(D) Since the report lacked needed information, it would not had been useful to them. Answer: (A)

Electrical Engineering Q. No. 1 – 25 Carry One Mark Each 1.

Find the transformer ratios a and b that the impedance (Zin) is resistive and equal 2.5 when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s. C 10F

L 1mH

R 2.5

1: b

1: a

(A) a = 0.5, b = 2.0

(B) a = 2.0, b = 0.5

(C) a = 1.0, b = 1.0

(D) a = 4.0, b = 0.5

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Answer: Exp:

(B)

j20

X c j20

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j5

X L j 5 2.5 a2

1: b Zin

2.5 a 2 j5 j20

1 b2

5 0 b2 b 0.5

20

2.5 2.5 a 2 a 2 b2

2.

The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t1 by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle shows the transient correctly? Line1

Synchronous generator Xs

~

Infinte Bus 10

E

(A)

Line 2

(B)

0

0

t1

0

Answer: Exp:

time

time

(C)

t1

(D)

t1 time

0

t1 time

(A)

For generator is +Ve. After fault increases

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3.

In the following circuit, the input voltage Vin is 100 sin 100t . For 100RC 50, the average voltages across R (in volts) under steady-state is nearest to

C

Vin

R C

(A) 100 Answer: Exp:

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(B) 31.8

(C) 200

(D) 63.6

(D)

Given circuit is voltage doubler Vm = Voltage across each capacitor = 100V Voltage across two capacitors (in steady state) = 2Vm = 200V Average voltageacross'R'

4.

A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for 230 V and 5 kW at a speed of 1200 rpm. If the same armature coils are reconnected to forms a lap winding, what is the rated voltage (in volts) and power (in kW) respectively at 1200 rpm of the reconnected machine if the field circuit is left unchanged? (A) 230 and 5 (B) 115 and 5 (C) 115 and 2.5 (D) 230 and 2.5

Answer: Exp

200 63.6V

E

(C) 1 no. of parallel paths

230 4 E 2 E 115V PE P 2.5kW

5.

Given f z g z h z , where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE? (A) If f(z) is differential at z0, then g(z) and h(z) are also differentiable at z0. (B) If g(z) and h(z) are differentiable at z0, then f(z) is also differentiable at z0. (C) If f(z) is continuous at z0, then it is differentiable at z0. (D) If f(z) is differentiable at z0, then so are its real and imaginary parts.

Answer: Exp:

(B)

Given f z g z h z

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f z ,g z ,h z are complex variable functions

(c) is not correct, since every continuous function need not be differentiable (D) is also not correct Let g(z) = x h(z) = iy

g z x i0 ux v0 x x 1 0 x x 0 0

h z 0 iy u0 vy y 0 0 x x x 0 1 y y

Cauchy – rieman equation as of g(z), h(z) are failed. f(z) and g(z) are not differentiable

But f z x iy ux u 1 x u u x y

vy v 0 x u v y x

f(z) in differentiable i.e, f(z) is differential need not imply g(z) and h(z) are differentiable Ans (B)

i.e, g(z) and h(z) are differentiable then f(z) = g(z) + h(z) is differentiable.

6.

A 3-bus power system network consists of 3 transmission lines. The bus admittance matrix of the uncompensated system is j4 j6 j3 j3 j7 j5 pu. j4 j j8

If the shunt capacitance of all transmission line is 50% compensated, the imaginary part of the 3rd row 3rd column element (in pu) of the bus admittance matrix after compensation is (A) j 7.0 Answer:

(B)

Exp:

y10 y12 y13 y12 y13

y Bus

(B) j 8.5 y12 y 20 y 21 y 23 y 23

(C) j 7.5 y13 y 23 y30 y31 y32

(d) j 9.0

y31 y13 j4 y32 y 23 j5

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after compensating, y30

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j1 2

y30 y31 y32 (new) j0.5 j4 j5 j8.5

7.

A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radians/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to directly drive a load whose load torque T L depends on its rotational speed (in radians/second), such that TL 2.78 T . Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load is _________.

Answer: Exp:

179.86

Under steady state load torque = motor torque 500 2.78 T T 178.88 rad/sec

8.

A circular turn of radius 1 m revolves at 60 rpm about its diameter aligned with the x-axis as shown in the figure. The value of 0 is 4107 in SI unit. If a uniform magnetic field intensity H 107 zˆ A/m is applied, then the peak value of the inducted voltage, Vturn in volts , is __________. Z

H

Vturn X

Answer: Exp:

39.45

V B .dl

Vemf E m .dl Vemf

V r 1 6.28a B 0 107 a z Vemf

6.28a

107 0 a z .dl

4 107 6.28 107. Vemf

1 2

78.91 39.45V 2

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0.1 F

9.

The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is Vi 2sin 2 2000t . The amplitude of the output voltage Vi Vo in Volt is _________.

Answer:

1k

1 k

Vo

1.96

Exp: 1 103 0.1 106 s Z1 1k; Z2 1 j0.1 103 1 103 6 0.1 10 s 1 103

2000 rad / sec Z2

103 103 1 j0.1 2000 103 1 j0.2

V0

Z2 Vi 103 2sin(2 2000t) 2sin(2 2000t) Z1 (1 j0.2) 103 1.0198

V0 1.96sin 22000t

Amplitude of the output voltage =1.96V 10.

In the following circuit, the transistor is in active mode and VC 2V. To get VC 2V. To get VC 4V, we replace RC with R C . Then the ratio R C R C is _________.

10V

RC RB

Answer: Exp:

VC

0.75

we have Vc 2V; Ic R c 10 2 8

… (i)

We have Vc=4V Ic R 'c 10 2 8

… (ii)

(2) Ic R c' 6 R c' 3 ; 0.75 (1) Ic R c 8 R c 4

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11.

The Laplace transform of f t 2 t is s 3 2 . The Laplace transform of g t 1 t is (B) s 1 2

(A) 3s5 2 2 Answer: Exp:

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(C) s1 2

(D) s3 2

(B)

Given that laplace transform of f t 2 Given as g f gt

t is s 3 2 .

1 t

2 t f t 2t 2t

f t 1 L g t L 2t 2

f t ds 0

s

3 1 1 3 2 1 s 2 s ds 2 s 2 3 1 2 s 1 1 2 0 s 1 2 s 1 2 2 s

12.

A capacitive voltage divider is used to measure the bus voltage V bus in a high-voltage 50 Hz AC system as shown in the figure. The measurement capacitor C1 and C2 have tolerances of 10% on their normal capacitance values. If the bus voltage Vbus is 100 kV rms, the maximum rms output voltage Vout (in kV), considering the capacitor tolerance, is __________.

C1

1F 10%

v bus C2

Answer: Exp:

9F 10%

vout

10

Xc2 Vout Vbus Xc1 Xc2 1 C 2 1 1 C C 2 1

C 1 Vbus 1 1 C C 2 1

1.1 Vbus 10kV 1.1 9.9

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13.

Match the following P. Stokes’s Theorem

1.

D.ds Q

Q. Gauss’s Theorem

2.

f z dx 0

R. Divergence Theorem

3.

.A dv A.ds

S. Cauchy’s Integral Theorem

4.

A .ds A.dl

(A) P-2, Q-1, R-4, S-3

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

(C) P-4, Q-3, R-1, S-2

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

Answer: 14.

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(B)

Consider the following Sum of Products expression, F. F ABC ABC ABC ABC ABC

The equivalent Product of Sums expression is (A) F A B C A B C A B C (B) F A B C A B C A B C (C) F A B C A B C A B C (D) F A B C A B C A B C Answer: (A) Exp: Given minterm is F m 0,1,3,5,7 F m 2, 4,6

So product of sum expression is F A B C A B C A B C

15.

A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. d 2i Assuming zero initial conditions, the value of 2 at t = 0+ is dt R

V

(A)

Answer:

V L

L

(B)

V R

(C) 0

(D)

RV L2

(C)

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Exp:

i L (0 ) 0 i L (0 ) at t 0

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P

L (0 ) V

di L (0 ) V dt L 2 d i L (0 ) 0 dt 2

16.

L (0 )

V

We have a set of 3 linear equations in 3 unknowns. 'X Y' means X and Y are equivalent statements and 'X Y' means X and Y are not equivalent statements. P: There is a unique solution. Q: The equations are linearly independent. R: All eigenvalues of the coefficient matrix are nonzero. S: The determinant of the coefficient matrix is nonzero. Which one of the following is TRUE? (A) P R Q S (C) P Q R S

Answer: 17.

(B) P R Q S (D) P Q R S

(A)

Match the following: Instrument Type

Used for

P. Permanent magnet moving coil

1. DC only

Q. Moving iron connected through current R. Rectifier

transformer

2. AC only 3.AC and DC

S. Electrodynamometer P 1

(A)

Answer: 18.

Q2 R 1

P 1

(B)

S3 (C)

Q3 R 1

P 1

(C)

S2

Q2 R 3

P3

(D)

S3

Q 1 R 2 S 1

Two semi-infinite dielectric regions are separated by a plane boundary at y=0. The dielectric constant of region 1 (y0) are 2 and 5, Region 1 has uniform electric field E 3aˆ x 4aˆ y 2aˆ z , where aˆ x ,aˆ y , and aˆ z are unit vectors along the x, y and z axes, respectively. The electric field region 2 is (A) 3aˆ x 1.6aˆ y 2aˆ z

(B) 1.2 aˆ x 4 aˆ y 2aˆ z

(C) 1.2aˆ x 4aˆ y 0.8aˆ z

(D) 3aˆ x 10aˆ y 0.8aˆ z

Answer: Exp:

(A)

(1)

(2)

y0

y>0

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E1 3ax 4ay

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Ez= y=0

+2az 2 E 2 3a x (4a y ) 2a z 5 E z 3a x 1.6a y 2a z

19.

The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown in Figure (c). F1

Vo / Vi

F1

Vo / Vi V0

Vi

V0

Vi f2

f1

f

f

(b)

(a) R/2

R

F1

Vsat

Vi

V0

Vsat

R F2 (c)

The cut-off frequencies of F1 and F2 are f1 and f 2 respectively. If f1 f 2 , the resultant circuit exhibits the characteristics of a (A) Band-pass filter (B) Band-stop filter (C) All pass filter (D) High-Q filter Answer: 20.

The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The “air-gap” voltage, Vg across the magnetizing inductance, is 210 V rms, and the slip, is 0.005. The torque (in Nm) produced by the motor is ______.

Answer: Exp:

(B)

333.27

Voc across j6.28 Vg 210V

0.0375

j0.2127

j0.22

j6.28 (0.4 j0.22) (0.04 j0.22) j6.28 0.21680.04

R th

0.0375 j0.2127

Rotor circuit is

Vg

I2

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Vg

I2

z

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210 (0.0375 1) j(0.2127 j0.22)

I2 186.81A Te

3 r2 3 I 22 . 186.812 1 s s 314.15

333.27 Nm

21.

Nyquist plot of two functions G1 (s) and G 2 (s) are shown in figure. Im

Im

0

G 2 (s)

G1 (s)

Re

Re

0 Nyquist plot of the product of G1 (s) and G 2 (s) is

(A)

(B) Im

Im 0

(C)

1

Re

(D)

Im

Im

Re

Re

Re

0

Answer: Exp:

(B)

Im

1 G1 (s) ; G 2 (s) 5 s G1G 2 (s) 1

Re

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22.

A 3-phase balanced load which has a power factor of 0.707 is connected to balanced supply. The power consumed by the load is 5kW. The power is measured by the twowattmeter method. The readings of the two wattmeters are (A) 3.94 kW and 1.06 kW

(B) 2.50 kW and 2.50 kW

(C) 5.00 kW and 0.00 kW

(D) 2.96 kW and 2.04 kW

Answer: Exp:

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(A)

P1 VL IL cos(30 ) P2 VL IL cos(30 )

3 p1 p 2 cos cos tan 1 p1 p 2 3.94 1.06 o cos tan1 3 45 5 satisfiying only for(A)

An open loop control system results in a response of e2t sin 5t cos5t for a unit impulse input. The DC gain of the control system is _________. Answer: 0.241 23.

Exp:

g(t) e2 sin 5t cos5t

G(s)

5 s2 2 2 (s 2) 5 s 2 52

DC gain means G(s) s 0 G(0)

24.

5 2 7 2 2 2 2 5 2 5 29 2

When a bipolar junction transistor is operating in the saturation mode, which one of the following statement is TRUE about the state of its collector-base (CB) and the baseemitter (BE) junctions? (A) The CB junction is forward biased and the BE junction is reverse biased. (B) The CB junction is reversed and the BE junction is forward biased. (C) Both the CB and BE junctions are forward biased. (D) Both the CB and BE junctions are reverse biased.

Answer: 25.

(C)

The current i (in Ampere) in the 2 resistor of the given network is ____ . 1 i 5V

1

1

2

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Answer: Exp:

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The Network is balanced Wheatstone bridge. i 0 Amp

Q. No. 26 – 55 Carry Two Marks Each 26.

A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225% of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03 / phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is ________.

Answer: Exp:

0.17

Smt

r2 x2

0.15

r2 0.03 x 2 0.2 x2 x2

For Test=Temax, Test 2 1 SmT 1 1 Tem SmT s mT 1

r2 ' r2' x 2 0.2 x2

Extra resistance 0.2 0.03 0.17 / p4 27.

Two three-phase transformers are realized using single-phase transformers as shown in the figure. A2 B2

C2

A2

A1

a1

B1

b1

C1

c1

A1

a1

B2

B1 C2

C1

a2 b2

V1

c2

b1 c1

b2

V2

c2

The phase different (in degree) between voltage V1 and V2 is ________. India’s No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 15

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Answer: Exp:

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30

Upper transformer secondary is connected in Bottom transformer secondary is connected in Y Phase angle between delta voltage & star voltage is 30o.

28.

A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, start connected through a star-delta transformer as shown in the figure. The line-to-line voltage rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected and Is 1000o A, then what is the value of I p in Ampere? Ip

Is

a

A

R

B

R

R

C

b C

(A) 5030o Answer: Exp:

(B) 50 30o

(C) 50 330o

(D) 200300

(B)

kVA is constant (per phase)

230 100 30 I p 115 0 3 3 Ip 50 30 29.

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is Q2 K , where K is given by 40 d 2 (A) 0

1 1 (B) ˆi ˆj 4 4

1 1 (C) ˆi ˆj 8 8

(D)

y

d

Q

d

1 2 2 ˆ 1 2 2 ˆ i j 8 2 8 2

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Answer: Exp:

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(D)

F F1 F2 F3

1 2da x 2da y 2da x 2da y 2 2

F

1 Q2 40 (2d)3

F

1 Q 2 1 2 2 1 2 2 ax ay 2 40 d 8 2 8 2

y

Q

Q(d,d,0)

X

X

So, Ans : (D)

Q

Q

y

30.

The volume enclosed by the surface f (x, y) ex over the triangle bounded by the line x=y; x=0; y=1 in the xy plane is _____.

Answer: Exp:

Triangle is banded by x = y, x = 0, y = 1 is xy plane. yx

Required volume

f x, y dxdy

0,1

0AB 1

1

1,1

y 1

x0

e dxdy

A B

x

x 0 y x 1

0,0

e x . y x dx 1

1,0

x 0

1

e x 1 x dx

x 0

e

x

xe x dx

x 0

e

ex

1

1

x

x 1 0 1

e1 1 0 1 e 2

31.

For the system governed by the set of equations: dx1 / dt 2x1 x 2 u dx 2 / dt 2x1 u y 3x1

the transfer function Y(s)/U(s) is given by (A) 3(s 1) / (s2 2s 2)

(B) 3(2s 1)(s2 2s 1)

(C) (s 1) / (s2 2s 1)

(D) 3(2s 1)(s2 2s 2)

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Answer: Exp:

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(A)

dx1 2x1 x 2 4 dt dx 2 2x1 4 dt y 3x1

Considering the standard equation x i Ax BU y Cx DU x 1 2 1 x1 1 x 2 0 x 1 [4] 2 2 x y [3 0] 1 x2

Transform function C SI A B 1

1

s 0 2 1 1 G(s) 3 0 0 s 2 0 1 1 s 2 1 1 [3 0] s 1 2

s

3 0 2

1 1 s 2 1

s2 2s 2

32.

s 1 1 3 0 2 s s 2 2 s 2

s 1 1 3 0 s 2 2s 2 s 4

3(s 1) s 2s 2 2

For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE? (A) The impulse response will be integral, but may not be absolutely integrable. (B) The unit impulse response will have finite support. (C) The unit step response will be absolutely integrable. (D) The unit step response will be bounded.

Answer:

(B)

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33.

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In the following sequential circuit, the initial state (before the first clock pulse ) of the circuit is Q1Q0 00. The state (Q1Q0 ), immediately after the 333rd clock pulse is Q1

Q0

J0

Q0

J1

Q1

K0

Q0

K1

Q1

CLK

(A) 00 Answer:

(B) 01

(C) 10

(D) 11

(B)

Exp: J1 Q0 K1 Q0 J 0 Q1 K 0 Q1 Q1 Q0 0

1

1

0

0 0

0 1

1 1 0

0 0 1

1 0 0

0 1 1

1 1 0

1 0 0

If is a Johnson (MOD-4) counter. Divide 333 by 4, so it will complete 83 cycle and remainder clock is 1, at the completion of cycles output’s in at Q1Q0 00 so, next at 333rd clock pulse output is at Q1Q0 01. 34.

A three-phase, 11 kV, 50 Hz, 2 pole, star connected, cylindrical rotor synchronous motor is connected to an 11 kV, 50 Hz source, Its synchronous reactance is 50 per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is 100A at unity power factor. If the load torque is increased so that the stator current is 120 A, then the load angle (in degrees) at this node is ____.

Answer: 47.27 Exp: Ef = Vt - Ia×S

11

kV j100 50 6350 j5000 3 E f 8082.23

Ia S E f 2 Vt2 2E f Vt cos 120 50 2 8082.232 63502 2 8082.23 6350 cos 2

47.27

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35.

Two coins R and S are tossed. The 4 joint events HR HS ,TR TS ,HR TS ,TR HS have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE? (A) The coin tosses are independent (B) R is fair, R it not. (C) S is fair, R is not

Answer: Exp:

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(D) The coin tosses are dependent

(D)

Given events HRHS, TRTS, HRTS, TRHS If coins are independent Corresponding probabilities will be 1 1 1 1 1 1 1 1 . , . , . , . 2 2 2 2 2 2 2 2 1 1 1 1 , , , respectively 4 4 4 4

But given probabilities are 0.28, 0.18, 0.3, 0.24 respectively we can decide whether R is fair or S is fair The coin tosses are dependent. 36.

A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is ___________. 3R

R

60

60

Answer: Exp:

1.193

GMR 0.7788R 3R 3R

13

1.9137R kR k 1.913

37.

The z-Transform of a sequence x[n] is given as X(z) = 2z+4-4/z+3/z2. If y[n] is the first difference of x[n], then Y(z) is given by (A) 2z+2-8/z+7/z2-3/z3

(B) -2z+2-6/z+1/z2-3/z3

(C) -2z-2+8/z-7/z2+3/z3

(D) 4z-2-8/z-1/z2+3/z3

Answer: Exp:

(A)

y(n) is first difference of x(n) So

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g(n) x(n) x(n 1) Y(z) x(Z)(1 z 1 ) X(z) z 1X(z) Y(z) 2z 4 4z 1 3z 2 2 4z 1 4z 2 2z 4 4z 1 3z 2 2 4z 1 4z 2 3z 3 2z 2 8z 1 7z 2 3z 3

38.

An open loop transfer function G(s) of a system is G s

K s s 1 s 2

For a unity feedback system, the breakaway point of the root loci on the real axis occurs at, (A) -0.42 (C) -0.42 and -1.58 Answer: Exp:

(B) -1.58 (D) None of the above

(A)

1 G(s) 0

s s 2 3s 2 12 0 k s3 3s 2 2s dK 0 ds 3s 2 6s s 0

S=-0.42 is the solution makes k>0

39.

In the given rectifier, the delay angle of the thyristor T 1 measured from the positive going zero crossing of Vs is 30°. If the input voltage Vs is 100 sin(100πt)V, the average voltage across R (in Volt) under steady-state is _______.

Vs D3

T1 D4

Answer: Exp:

D2

R

V0

61.52

30 Vin 100sin 100t Vm 3 cos 2 100 3 cos30 61.52V 2

V0

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40.

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of αL is obtained by interconnecting these two coils, the minimum value of α is ________.

Answer: 41.

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In the given network V1 = 100∠0°V, V2 = 100∠-120°V, V3 = 100∠+120°V. The phasor current i (in Ampere) is j1

V1

j1

V2 V3

(A) 173.2∠-60° Answer:

(A)

Exp:

i

(B) 173.2∠-120°

i

(C) 100.0∠-60°

(D) 100.0∠-120°

V1 V3 V2 V3 j

j

1000o 100120o 100 120o 100120o 1 90o 190o i 173.2 60o i

42.

A differential equation

di 0.2i 0 is applicable over -10< t 0 (B) The system is stable for h

1

(C) The system is stable for 0 h (D) The system is stable for Answer:

1 2

1 1 h 2

(A)

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General Aptitude Q. No. 1 – 5 Carry One Mark Each 1.

The man who is now Municipal Commissioner worked as _____________. (A) the security guard at a university (B) a security guard at the university (C) a security guard at university (D) the security guard at the university

Key:

(B)

2.

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia. Choose the option which is closest in meaning to the underlined phase in the above sentence. (A) put up with (B) put in with (C) put down to (D) put up against

Key:

(D)

3.

Find the odd one in the following group of words. Mock, deride, praise, jeer (A) mock (B) deride

(C) praise

(D) jeer

Key:

(C)

4.

Pick the odd one from the following options. (A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ (D) In a quadratic function, the value of the product of the roots , is 4. Find the value of

Key: 5.

n n n n

(A) n 4

(B) 4 n

Key:

(B)

Exp:

Given 4

(C) 2 2n 1

(D) 4n 1

n n n n 1 1 n n n n

n

n n n

n

n

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Q. No. 6 – 10 Carry Two Mark Each 6.

Key: Exp:

Among 150 faculty members in an institute, 55 are connected with each other through Facebook and 85 are connected through WhatsApp. 30 faculty members do not have Facebook or WhatsApp accounts. The number of faculty members connected only through Facebook accounts is ______. (A) 35 (B) 45 (C) 65 (D) 90 (A) F Facebook, W WhatsApp, E Total faculties given E, n(E) 150 n(E) 150, n F W 30

n F W n(E) N F W 150 30

85

55

n F W 120 n f w n f n(w) n(F w 120 n(F) 85

F n(F) 35

n(F) 120 85 35 55 n(F) n F W n F w 55 n(F) 55 35 20 n(w) 85 20 65

7.

Key: 8.

Key:

Fw n F w 20

W n(w) 60 30

F W

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention with the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or more importantly, required. Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph? (i) The author believes that computers are not good for us (ii) Mobile computers and the internet are both intended inventions (A) (i) (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii) (D) All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences? (i) Ooty is not a hill-station (ii) No hill-station can have more than one lake. (A) (i) Only (B) (ii) Only (C) both (i) and (ii) (D) neither (i) nor (ii) (D)

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9.

In a 2 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? (A) 21 (B) 27 (C) 30 (D) 36

Key:

(C)

Exp:

1: (AEOK) 2: (AEJF), (FJOK) 4: (ABLK), (BCML), (CDNM), (DEON)

A

B

C

D

E

2: ACMK, ADNK 2: ECMD,EBLO 2: ACHF,ADIF F

G

H

I

J

2: ECHJ, EBGJ 2: FHMK,FINK 2: JHMD,JGLO 1: BDNL 2 : BDIG,GINL

8: ABGF, BCHJ, CDIH, EDI, FGLK, GHML, HINM Total = 1+2+4+2+2+2+2+2+2+1+2+8=30

10.

25

K

L

M

N

O

f x

2 1.5 1 0.5 0

4

3

2

1

0.5

1

2

3

X4

1 1.5

2 25

Chose the correct expression for f(x) given in the graph. (A) f x 1 x 1 (B) f x 1 x 1 (C) f x 2 x 1 Key: Exp:

(D) f x 2 x 1

(C) Substituting the coordinates of the straight lines and checking all the four options given, we get the correct option as C which is f(x)= 2 x 1

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Electrical Engineering Q. No. 1 –25 Carry One Mark Each 1.

The maximum value attained by the function f x x x 1 x 2 in the interval 1, 2 is ____.

Key:

Exp:

f ( x) x( x 1)( x 2) x 1

f ( x) x 3 3 x 2 2 x f 1 ( x) 0 3 x 2 6 x 2 0

1 3

But x 1

1 only lies on the interval [1,2] 3

1 11 1 ;f ( x) 6 x 6 6 1 6 0 3 3 1 x 1 is a point of minimum 3 f(x) = x(x-1)(x-2) = 0 at either ends x =1 & x =2 At x 1

Max value = 0 2. Key: Exp:

Consider a 3 3 matrix with every element being equal to 1. Its only non-zero eigenvalue is ____. 3 Consider A 33

1 1 1 1 1 1 1 1 1

It’s only non-zero Eigen value λ = 1 order of the matrix = 1 3 3 The Laplace Transform of f t e2t sin 5t u t is

3.

(A) Key: Exp:

5 s 2 4s 29

(A) Consider

(B)

5 s 5 2

(C)

s2 s 2 4s 29

(D)

5 s5

5 X(S) s +25 By frequency shifting property, 1 X(S-S0 ) x(t)eS0t

x(t) = sin5t u(t)

thus at S0 2 2t

f(t) = e sin5tu(t) 5 F(s) 2 s 4s 29

2

5 F(s) (s-2)2 +25

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A function y t , such that y 0 1 and y 1 3e1 , is a solution of the differential equation

4.

d2 y dy 2 y 0 . Then y 2 is 2 dt dt

Key:

(A) 5e1 (B)

(B) 5e2

(C) 7e1

Exp:

2 The operator function of given D.E is (D +2D+1)y = 0

(D) 7e2

A.E is D2 +2D+1 = 0 D = -1,-1 y = e-x C1 + C2 (1)

Given y(0)=1 & y(1) =3e-1 From ; y(0) = 1 i.e , y = 1 at x = 0 1 = C1

y(1) = 3e-1 i.e, y = 3/e at x=1

3 -1 e 1 C2 (1) 3 1 C2 C2 2 e y = e-x [1+2x] y(2) = e-2 [1+4] = 5e-2 5.

The value of the integral

2z 5 dz over the contour z 1. taken in the anti1 2 z z 4z 5 2

C

clockwise direction, would be (A) Key: Exp:

24i 13

(B)

48i 13

(C)

24 13

(D)

12 13

(B) Singular points are obtained by

1 2 1 z z -4z+5 0 z = & z =2 i 2 2 1 Out of these z = only lies inside C. z =1 2 By Cauchy’s integrated formula,

C

2z+5

1 2 z - z -4z+5 0 2

dz =

C

1 2 5 2z+5 2 48πi dz = 2πi 2 2 1 z -4z+5 1 13 4 5 1 2 2 z2

5

|EE| 6.

GATE-2016-PAPER-01

The transfer function of a system is

Y s R s

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s , The steady state output x(t) is A cos 2t for s2

the input cos 2t . The value of A and , respectively are (A)

1 2

Key:

(B)

Exp:

H(s) = H( ) =

, 45O

(B)

1 2

, 45O

(C)

2, 45O

(D)

2, 45O

S S+2

900 tan 1 2 2 +4

If input is COS 2t i.e., = 2

1 450 2 1 y(t) = cos(2t 450 ) 2 1 by comparision A= & 450 2 H( ) =

7.

The phase cross-over frequency of the transfer function G(s) = (A)

3

(B)

1 3

100

s 1

(C) 3

Key:

(A)

Exp:

Phase Crossover frequency PC : GH =PC 1800

3

in rad/s is

(D) 3 3

GH 3tan-1 1800 3tan -1w PC WPC tan 600 3 8.

Consider a continuous-time system with input x(t) and output y(t) given by y t x t cos t . This system is

Key: Exp:

(A) linear and time-invariant (C) linear and time-varying (C) Linearity

y1 (t)= x1 (t)cost;

(B) Non-linear and time-invariant (D) Non-linear and time-varying

y 2 (t)= x 2 (t)cost

y1 (t) + y2 (t) = x1 (t)cost + x 2 (t)cost y1 (t) + y2 (t) = [x1 (t) + x 2 (t)]cost If x1 (t) + x 2 (t) = x(t) then y1 (t) + y 2 (t) = y(t) ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Thus the system is linear Time-invariance consider y1 (t) x1 (t) cost ; If x1 (t) x(t - τ)

y1 (t) x(t - τ) cost Define y(t - τ) x(t - τ)cos(t - τ)

y1 (t) y(t - τ) system is time-varient 9.

The value of

A

e t 2t 2 dt. where t is the Dirac delta function, is

1 2e

B

2 e

C

1 e2

D

1 2e 2

Key:

(A)

10.

Key:

A temperature in the range of -40OC to 55OC is to be measured with a resolution of 0.1OC. The minimum number of ADC bits required to get a matching dynamic range of the temperature sensor is (A) 8 (B) 10 (C) 12 (D) 14 (B)

Exp:

Usually when voltage information is given we use the formula R =

Vmax -Vmin 2n

Here based on the given information we can think the systems as following block diagram

Temp

Temperature to voltage converter

analog voltage

nbit ADC

. . .

Here the Vmax and Vmin will be the equivalent of Tmax and Tmin respectively So we can still use the above relation

Tmax -Tmin 5-(-40) 2n = 2n = 950 n 2 0.1 n log 2 (950) 9.89 10 Resolution =

So minimum requirement is 10 bits 11.

Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The Boolean expression for output F in terms of A and B is (A) A B

(B) A B

(C) A B

(D) A B

F

Y

1 S A

B

7

|EE| Key: Exp:

GATE-2016-PAPER-01

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(D) We can redraw the max circuit as follows

A

A

1

F

B

So the Boolean expression of F(A, B)=BA BA=A B=A B 12.

A transistor circuit is given below. The Zener diode breakdown voltage is 53 V as shown The base to emitter voltage droop to be 0.6V. The value of the current gain is ________. 10V

4.7k

220

0.5mA 5.3V

Key:

19

Exp:

5.3 = 0.6 + 470 IE

470

I E 0.01A

10 - 5.3 1mA 4.7 103 I B =1 0.5 0.5mA IX =

IE (1 β)IB 0.01 (1 β) 0.5 103 (1 β)

0.01 20 β 19 0.5 103

13.

In cylindrical coordinate system, the potential produced by a uniform ring charge is given

Key:

(A) increases with r (C) is 3 (B)

Exp:

Since the charge is not varying with time the field E is static So E 0

f r, z , where f is a continuous function of r and z. Let E be the resulting electric field. Then the magnitude of E

(B) is 0 (D) decreases with z

8

|EE| 14.

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A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability r of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent

Key: Exp:

points located just inside and just outside the toroid, is ________. 100 The field inside and outside the toroid is due to long straight conductor only Let the two points almost at same distance

μ 0μ r I 2πr μI The flux density outside toroid = 0 T 2πr μ 0μ r I 2πr μ 100 Ratio = r μ0I 2πr The flux density inside toroid =

15.

R A and R B are the input resistances of circuits as shown below. The circuits extend infinitely in

the direction shown. Which one of the following statements is TRUE? 2 RA

2

1

2 RB

(A) R A R B Key: Exp:

1

1

1

2 1

(B) R A R B 0

1

2 1

(C) R A R B

(D) R B R A 1 R A

(D) By comparing 2 network on the input side we can say that R B =1//R A R B =

16.

2

RA 1 RA

In a constant V/f induction motor drive, the slip at the maximum torque (A) is directly proportional to the synchronous speed (B) remains constant with respect to the synchronous speed (C) has an inverse relation with the synchronous speed (D) has no relation with the synchronous speed ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Key:

(C)

Exp:

SmT

r2 r r2 2 x2 j L 2 j2L 2 .f

SmT

1 f

NS

120f P

SMT

17.

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1 NS

In the portion of a circuit shown, if the heat generated in 5 resistance is 10 calories per second then heat generated by the 4 resistance, the calories per second, is ______. 4

6

5

Key: Exp:

2 Here the power information regarding the resistor is given because

E Calorie =watt t sec P5 = 10 P=

V5Ω = 10 V5Ω = 50 5 P4Ω is asked

V4Ω

2

1 4 P4Ω = 50 4 4 4 6 1 16 calorie 50 2 4 100 sec 18.

2

In the given circuit, the current supplied by the battery, in ampere, is ________. l1

`

1

1

1

l2

1V

Key: Exp:

l2

0.5 If we write KCL at node × then

10

|EE| I1 = 2 I2 I 2

GATE-2016-PAPER-01 I1 2

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1

X

1

Write KVL in the outer boundary of network

1 (1 I1 ) (2 I 2 ) 0 1 I1 2 I 2 1 I 1 =I1 2 1 1 2J1 I1 0.5A 2 2 19.

Key: Exp:

20.

Key: Exp:

1V

I1

I2 I2

1

In a 100bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates). Two of the PV buses are converted to PQ type. In this iteration. (A) The number of unknown voltage angles increases by two and the number of unknown voltage magnitudes increases by two. (B) The number of unknown voltage angles remain unchanged and the number of unknown voltage magnitudes increases by two (C) The number of unknown voltage angles increases by two and the number of unknown voltage magnitudes decreases by two (D) The number of unknown voltage angles remains unchanged and the number of unknown voltage magnitudes decreases by two (B) Total no of Buses = 100 Generator Buses = 10 Load Buses = 100-10=90 Slack Bus = 1 If 2 of the PV buses are converted to PQ type the no of on voltage magnitudes increases by 2 with constant unknown voltage angles The magnitude of three-phase fault current at buses A and B of a power system are 10 pu and 8 pu, respectively. Neglect all resistance in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is 1.0 pu. The voltage magnitude at bus B during a three-phase fault as but. A is 0.8pu. The voltage magnitude at bus A during a threephase fault at bus B, in pu, is _____. 0.84 Voltage at ith bus when fault is at kth bus is zik Vi E 1 z kk z f

If

Vproduct X p.u

1 10 X A 0.1P.U xn 1 8 B 0.125P.U XB

Z VB E 1 AB ZAA ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Z 0.8 1 1 AB ZAB 0.02 0.1 2AB 0.02 VA 1 1 1 0.84 P.U 2 0.125 BB

21.

Key: 22.

Consider a system consisting of a synchronous generator working at a lagging power factor, a synchronous motor working at an overexcited condition and a directly grid-connected induction generator. Consider capacitive VAr to be a source and inductive VAr to be a sink of reactive power. Which one of the following statements is TRUE? (A) Synchronous motor and synchronous generator are sources and induction generator is a sink of reactive power. (B) Synchronous motor and induction generator are sources and synchronous generator is a sink of reactive power. (C) Synchronous motor is a source and induction generator and synchronous generator are sinks of reactive power (D) All are sources of reactive power (A) A buck converter, as shown in figure (a) below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage VL during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is ______ VL 30V

M

Vg

TOFF

TON

VL

D

C

V0

R

t

20V

a

Key: Exp:

Ta

b

0.4 When M is ON, VS VL V0 VL 30 VS V0

When M is OFF,

VL V0 20 V0 V0 20

30 VS 20 Vs 50V D

V0 2 0.4 VS 5

12

|EE| 23.

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A steady dc current of 100A is flowing through a power module (S.D) as shown in Figure (a). The V-I characteristics of the IGBT (S) and the diode (D) are shown in Figures (b) and (c), respectively. The conduction power loss in the power module (S, D), in watts, is _____ Is A

I0 A

V0 0.7V

S

D

dV dl 0.02

V0 1V

VS Volt

VS Volt

100 A

V l characteristic of diode c

V l characteristic of 1GBT

a

dV dl 0.01

b

Key:

169 to 171

24.

A 4pole, lap-connected, separately excited dc motor is drawing a steady current of 40 A while running at 600 rpm. A good approximation for the waveshape of the current in armature conductor of the motor is given by 40A I (A) I (B) 10A

t

t

(C)

(D)

I 10A

T 25ms

Key: Exp:

10A

I

T 25ms

T 25ms T 25ms

10A

10A

(C) no of parallel paths = 4 Armature current/conductor =

40 10A 4

For linear commutation, the change from 10A to 10A is straight line N = 600rpm Time for 1 revolution =- 0.1 sec. For 1 pole-pitch, t

0.1 25m sec 4 poles

13

|EE| 25.

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If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the equivalent inductance at port 1 is n :1

` L

Port 1

(A) nL

Port 2

(B) n2L

(C)

n L

(D)

n2 L

Key:

(B)

Exp:

The property of an ideal transformer is of port2 is terminated by an impedance

Z L then the

ZL

impedance seen from port is

NZ / NL

In the given problem Zin

L

1/n

2

2

n 2L

Q. No. 26 – 50 Carry Two Mark Each 26.

Key: Exp:

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is ______. 0.06 Total possible options = 43 Favorable choices {BBB, BlBlBl, GGG, RRR} = 4 4 1 Probability = 3 0.06 4 16

27.

Let S n n where 1. The value of in the range 0 1 . Such that S 2 is ______.

n 0

Key:

0.293

Exp:

S = n αn

n=0

2α α 2α 2 + 3α3 ] \ 2α α[1 2α 3α 2 ] 2α α[1 α]2 if α 1

(1 α) 2 2 α 1

1 α 0.293 2

14

|EE| 28.

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Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x 2 respectively. Then the eigenvalues and eigenvectors of the matrix A2 3A 4l would, respectively, be (A) 2,14; x1 , x 2 (B) 2,14; x1 x2 , x1 x2 (D) 2,0; x1 x 2 , x1 x 2

(C) 2,0; x1 , x 2 Key: Exp:

(A) Matrix A Eigen values 1 , -2 Matrix A 2 -3A+4I

12 3(1) 4, (2) 2 3(2) 4 Eigen values 2 , 14 respectively

A & P(A) = a 0 I + a1A + a 2 A 2 have same eigen vectors

Key:

Let A be a 4 3 real matrix with rank 2. Which one of the following statement is TRUE? (A) Rank of ATA is less than 2 (B) Rank of ATA is equal 2 (C) Rank of ATA is greater than 2 (D) Rank of ATA can be any number between 1 and 3 (B)

Exp:

Given that ρ A43 2

29.

From the properties of Rank; we have ρ AAT = ρ(A)

Rank of AAT = Rank of AT A = Rank of A 2 30.

Consider the following asymptotic Bode magnitude plot is in rad s . magnitude dB

12dB 20dB dec 0.dB

8

0.5

Which one of the following transfer function is best represented by the above Bode magnitude plot? 2s

(A)

1 0.5s 1 0.25s

(C)

1 2s 1 4s

2s

2

(B) (D)

4 1 0.5s

s 1 0.25s

4s

1 2s 1 4s

2

15

|EE| Key: Exp:

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(A) By looking to the plot we can say that since the initial slope is +20 there must be a zero on the origin If we find 2 we can get the answer by eliminating options

Slope =

M 2 - M1 log2 - log1

magnitude

dB

0 12 40 log 8 - log2

12 40 12 log2 = log 840

12dB

20dB dec 0.dB

log 8- log2

0.5

1

2

8

2 =4

So one of the corner frequency is 2 = 4s at this frequency 2 poles should exist because the change in slope is -40db From this we can say option A satisfies the condition (i) A zero at origin

(ii) one of corner frequency 4H term will be 1+ 31.

s having 2 poles 4

Consider the following state-space representation of a linear time-invariant system 1 0 1 1 x t x t , y t cT x t , c and x 0 0 2 1 1

The value of y(t) for t loge 2 is _________. Key:

6

32.

Loop transfer function of a feedback system is G s H s

s3 .Take the Nyquist contour in s 2 s 3

the clockwise direction. Then the Nyquist plot of G(s) H(s) encircles – 1 + j0

Key:

(A) Once in clockwise direction (C) Once in anticlockwise direction (A)

Exp:

GH =

S+3 S(S-3)

GH

( 2 +a)1/2 1 2 2 2 1/2 ( +a)

(B) Twice in clockwise direction (D) Twice in anticlockwise direction

GH tan 1 1800 1800 tan 1 2 tan 1 3 3 3 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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|EE| GH =

1

2

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3

at 0, GH = 0 0 at , GH = 0 180

1 0 90 9 So the plot start at 00 and goes to 1800 through 900 Since there are 2 poles on origin we will get 2 radius semicircle those will start where the mirror image ends and will terminate where the at 3, GH =

actual plot started in clockwise direction. So the plot will be

-1+io

w=0

w= So the Nyquist plot of G(s) H(s) encircles – 1 + j0 once in clockwise direction

M= -1

33.

Given the following polynomial equation s3 5.5s2 8.5s 3 0 , the number of roots of the

Key:

polynomial, which have real parts strictly less than – 1, is _______ 2

Exp:

The polynomial is S3 +5.5S2 +8.5S+3=0 , since we are interested to see the roots wrt S = -1 so in the above equation replace S by z-1 then the equation is

(Z-1)3 +5.5(Z-1)2 +8.5(Z-1)+3=0 Z3 -3Z2 +3Z-1+5.5(Z2 +1-2Z)+8.5Z-8.5+3=0 Z3 +Z2 (3 5.5)+Z(3+8.5-11)+(-1+5.5-8.5+3)=0

Z3 +2.5Z2 0.52 1 0 Using RH table

Z3 1 2

Z 2.5

0.5 1

1

Z 0.9 Z0 1 The single sign change in 1st column indicate that out of 3 roots 1 root lie on the right half of S = 1 plane if memory remaining 2 lies on left half of S = -1 plane. ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Suppose x1 t and x 2 t have the Fourier transforms as shown below.

34.

X1

X 2

1

1 0.5

0.5

0.3

1

0.3 0

1

2

2

1

1

Which one of the following statements is TRUE? (A) x1 t and x 2 t are complex and x1 t x 2 t is also complex with nonzero imaginary part (B) x1 t and x 2 t are real and x1 t x 2 t is also real (C) x1 t and x 2 t are complex but x1 t x 2 t is real (D) x1 t and x 2 t are imaginary but x1 t x 2 t is real Key:

(C)

Exp:

x1 (t) & x 2 (t) are complex functions x 2 ( ) = x1 (- ) , x 2 (t) = x1 (-t) x1 (t) x 2 (t)will be real The output of a continuous-time, linear time-invariant system is denoted by T{x(t)} where x t is

35.

the input signal. A signal z(t) is called eigen-signal of the system T, when T z t z t , , where is a complex number, in general, and is called an eigen value of T. suppose the impulse

Key: Exp:

response of the system T is real and even. Which of the following statements is TRUE? (A) cos(t) is and eigen-signal but sin(t) is not (B) cos(t) is and sin(t) are both eigen-signal but with different eigenvalues (C) sin(t) is an eigen-signal but cos(t) is not (D) cos(t) and sin(t) are both eigen-signal with identical eigenvalues (D) Consider the Eigen signal Z(t) = Cos t For Cost, y(t)

cos(t-τ)h(τ)dτ

(cos t cos τ +sin t sin τ)h(τ)dτ

= cos t cos τh(τ)dτ sin t sin τh(τ)dτ

h(τ)is an even signal

sinτh(τ)dτ = 0

18

|EE|

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y(t) = cos t cos τh(τ)dτ

Thus the integration value will be an Eigen value γ . Similarly consider the Eigen signal Z(t) = sin t For sint, y(t)

sin(t-τ)h(τ)dτ =sin t cos τh(τ)dτ cos t sin τh(τ)dτ

Thus y(t)= sin t

cos τh(τ)dτ

Eigen value ‘ γ ’is same for both the Eigen functions sint & cost 36.

The current state QA QB of a two JK flip-flop system is 00. Assume that the clock rise-time is much smaller than the delay of the JK flip-flop. The next state of the system is 5V J

K

QA

QO

J

QV

K

CLK

Key: Exp:

(A) 00 (C)

(B) 01

(C) 11

(D) 10

Logic 1 JA

QA

KA

QA

JB

QB

KB

QB

J A = K A =1 J B = K B =QA

It is given initially QA QB = 0 Since it is a synchronous counter, when clock is applied both flipflop will change there state simultaneously based on JK FF state table

JA =1, KA =1 , QA =0 QA = 1

JB =1, KB =1, QB =0 QB = 1 So next state Q A Q B is 11

19

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A 2-bit flash Analog to Digital Converter (ADC) is given below. The input is 0 VIN 3 Volts.

37.

The expression for the LSB of the output B0 as a Boolean function of X2 , X1 , and X0 is 3V

100

X2

200

X1

X0

B1

Digital circuit

B0

200

100 VIN

Key: 38.

(A) X0 X2 X1

(B) X0 X2 X1

(C) X0 X2 X1

(D) X 0 X 2 X1

(A) Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is (A) x 2

(C) x 2 y2 2

(B) y 2

Key:

(D)

Exp:

The potential due to Q 4-2Q at (x, y) is

q 2

k x +y If potential at (x, y) = 0 where k=

q 2

k x +y

2

2q 2

k (x-6) + y

2

2

(D) x 2 y 2 16 2

2q k (x-6) 2 + y 2

1 4πε

0 (x-6)2 + y2 2 x 2 + y2 0

(x-6) 2 + y 2 4(x 2 + y 2 ) x 2 +36 -12x + y 2 = 4x 2 4y 2 x 2 y 2 - 4x-12 = 0 2 2 2 2 2 2 Option:D (x+2) + y 16 x +4x +4+ y = 16 x y + 4x-12 = 0

20

|EE| 39.

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In the circuit shown, switch S2 has been closed for a long time. A time t = 0 switch S1 is closed At t 0 , the rate of change of current through the inductor, in amperes per second, is _______. S1

1

S2

2 1H

3V

3V

Key:

2

Exp:

At t = 0- Network is in steady state with S1 opens S 2 (closed) So we can say i L (0- )=

3 1.5A 2 At t = 0+ indicator behaves as ideal current source of 1.5A if we draw the network at t = 0+ , both switch closed

VL (0 + )

Writing Nodes equation at VL (0 ) node

1 1 3 3 VL (0 )= 1.5 1 2 1 2 VL (0 ) = 2

1 3V

2

1.5

3V

di L (0+ ) di(0+ ) L 2 2A/sec dt dt

at t = 0+ 40.

Key: 41.

A three-phase cable is supplying 800kW and 600kVAr to an inductive load, It is intended to supply an additional resistive load of 100kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3kV, 50Hz, the capacitance per phase of the bank, expressed in microfarads, is _________. 47 to 49 A 30MVA, 3-phase, 50Hz 13.8kV, star-connected synchronous generator has positive, negative and zero sequence reactance, 15%,15% and 5% respectively. A reactance Xn is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phases ‘b’ and ‘c’, with a fault impedance of j0.1 p.u. The value of X n in p.u. that will

Key: Exp:

limit the positive sequence generator current to 4270 A is ________. 1.108 X1 0.15 P.U

21

|EE| Ibase

30 106 3 13.8 103

GATE-2016-PAPER-01

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1255.109

X2 0.15P.U X0 0.05P.U Xf 0.1P.U I P.U

I actual 4270 3.4 P.U I base 1255.109

Ia1

Ea Z1 Z2 || ZO 3zf 3zn

3.4

1 0.15 Z2 || Z0 3zf 3z n

Z2 || 20 3z f 3z n 0.144 1 1 1 Z2 20 3z f 3zln 0.144

20 3zf 3zn 3.675 3zn 3.675 0.05 3 0.1 Zn 1.108P.U

42.

If the star side of the star-delta transformer shown in the figure is excited by a negative sequence voltage, then A a (A) VAB leads Vab by 60O (B) VAB lags Vab by 60O (C) VAB leads Vab by 30O (D) VAB lags Vab by 30O

B

N

c b

C

Key:

(D)

43.

A single-phase thyristor-bridge rectifier is fed from a 230V, 50Hz, single-phase, AC mains. If it is delivering a constant DC current 10A, at firing angle of 30O, then value of the power factor at AC mains is (A) 0.87 (B) 0.9 (C) 0.78 (D) 0.45

Key:

(C)

Exp:

IPF = 0.9cos 0.9 cos30 0.78

22

|EE| 44.

GATE-2016-PAPER-01

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The switches T1 and T2 are shown in Figure (a).

C

T1

Vdc 2 250V iL

1

0.8

Vdc

R 12

XL 16 at 100Hz 2 250V

t

T2

Vm

b a

They are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage m t 0.8sin 200t V and the triangular carrier voltage c are as shown in Figure (b). The carrier frequency is 5kHz. The peak value of the 100Hz component of the load current i L , in ampere, is ______. Key:

10

Exp:

ma

Vm 0.8 Vcarrier

V0l max ma.

Vds 0.8 250 200V 2

2L 162 122 20 I L max

45.

200 10A 20

The voltage s across and the current lg through a semiconductor switch during a turn-ON transition are shown in figure. The energy dissipated during the turn – ON transition, in mJ, is _________. vs

600V 0 t

is

50A 100A 0

T1 1s

T2 1s

t

23

|EE|

GATE-2016-PAPER-01

Key:

75

Exp:

1 E Pdt V t tdt 600 150 106 + 100 2

46.

www.gateforum.com

1 6 2 600 10 75mJ

Key:

A single-phase 400V, 50Hz transformer has an iron loss of 5000W at the condition. When operated at 200V, 25Hz, the iron loss is 2000W. When operated at 416V, 52Hz, the value of the hysteresis loss divided by the eddy current loss is 1.4423

Exp:

Since

V 400 200 8 is constant, Bm is constant f 50 2.5

Pcore Ph Pe k1f k 2 f 2

Ph k1f

5000 50k1 502. k 2 50k1 2500k 2

Pe K 2 f 2

2000 25k1 25k1 252 k 2 25k1 625k 2

k1 50k 2 100 k 2 0.8 k1 25k 2 80 k1 60

∴ Pcore = 60f 0.8 f 2 Ph 60f Pe 0.8f 2

When f 52Hz, Ph 60 52 3120 Pe 0.8 522 2163.2 Ph 3120 1.4423 Pe 2163.2

47.

ADC shunt generator delivers 45 A at a terminal voltage of 220V. The armature and the shunt field resistance are 0.01 and 44 respectively. The stray losses are 375W. The percentage

Key: Exp:

efficiency of the DC generator is ______. 86.84 Pout 220 45 990W

IL 45A

If

220 If 5A 44 Ia IL If 45 5 50A

44

Armature losses = Ia 2 ra 502 0.01 25W

ra 0.01 220V

Field losses = If 2 R f 52 44 1100W Stray losses = 375W Total losses = 1500W 1 losses 1 Pout ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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1 1500 1 9900 86.84%

A three-phase, 50Hz salient-pole synchronous motor has a per-phase direct-axis reactance Xd

48.

of 0.8pu and a per-phase quadrature-axis reactance X q of 0.6pu . Resistance of the machine is

Key: Exp:

negligible. It is drawing full-load current at 0.8pf (leading)j. When the terminal voltage is 1pu, per-phase induced voltage, in pu, is ______. 1.608 Xd 0.8P.U P.f 0.8 leading Ra 0 Xq 0.6PU

Vt 1P.U

cos 0.8 36..86 Ia 136.86 tan

I a q cos I a R a sin Ia q cos 1 0.6 0.8 0.3529 Vt I a q sin I a R a cos Vt Ia q sin 1 1 0.6 0.6

19.44O 36.86 19.44 56.3 Id Ia sin 1 sin56.4 0.832 Iq Ia cos 1 0.5547 0.5547 Ef V cos Id d Iq R a 0 Vcos Id d 1.cos19.44 0.832 0.8 1.608pu

EF 1.608PU

49.

Key:

A single-phase, 22kVA, 2200V/220, 50Hz, distribution transformer is to be connected as an autotransformer to get an output voltage of 2420 V. Its maximum kVA rating as an auto-transformer is (A) 22 (B) 24.2 (C) 242 (D) 2420 (C)

Exp:

Rated LV current = KVA max

2200 10 242kVA 1000

Or 2420 100 242kVA 1000

50.

Key:

100A

22kVA 100A 220

110A

2200VLOV

220V 10A 2200V

2420V

A single-phase full-bridge voltage source inverter (VSI) is fed from a 300 V battery. A pulse of 120O duration is used to trigger the appropriate devices in each half-cycle. The rms value of the fundamental component of the output voltage, in volts, is (A) 234 (B) 245 (C) 300 (D) 331 (A)

25

|EE| Exp:

VO t

V01

51.

Key: Exp:

GATE-2016-PAPER-01

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n 4Vs sin n t cos n 6 n 1,3,s

1 4VS cos 6 233.9 234V 2

A single-phase transmission line has two conductors each of 10mm radius. These are fixed a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three-phase system is to be 5% more than that of the inductance per conductor of the single-phase system. The distance D, in meters, is _______. 1.439 For single phase L1

1m

1 D 0.2n m 0.2n Ds Ds

For three phase L3 0.2n

DM 0.2n DS

D23 Ds

D

D

L3 1.05L1

D m 3 D.D.1 D

D2/3 1 0.2 1.05 0.2 n D DS S

2

3

1m

D 1.439 mts

In the circuit shown below, the supply voltage is 10sin 1000t volts. The peak value of the steady

52.

state current through the 1 resistor, in amperes, is _________. 2F 4

240F

500mH

1

5 4mH ~

10sin 1000t

Key: Exp:

1 W =1000, the various impedance at this frequency are

26

|EE|

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-j Z250μf Z4mH ( j 1000 4 103 ) 6 1000 250 10

( j4) (j4) open circuit -j Z24f Z500mH ( j 1000 500 103 ) 6 1000 250 10

( j500) (j500) open circuit Since both LC pair parallel combination becomes open then the circuit can be redrawn as

10sin1000t sin1000t 4+1+5 So peak value of I1Ω 1A

I1Ω

4

1

5

V 10sin1000t A dc voltage with ripple is given by t 100 sin t 5sin 3t volts. Measurements of

53.

this voltage t , made by moving-coil and moving-iron voltmeters, show readings of V1 and V2 respectively. The value of V2 V1 , in volts, is _______. Key: Exp:

0.312 V1 100V 2

2

10 5 V2 100 100.312V 2 2 2

V2 V1 0.312V

The circuit below is excited by a sinusoidal source. The value of R, in , for which the admittance of the circuit becomes a pure conductance at all frequencies is ________.

54.

100F

R

R

0.02H

Key: Exp:

~

14.14 Admittance becomes pure conductance means the imaginary part of Y must be zero which imply resonance condition. Let first get Y expression interms of L,C then by equalising imaginary part we will

C

L

R

R

27

|EE|

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get the answer.

j R+ 1 1 R-j L C mg[Y ] 0 Y 2 eq 2 2 1 R+j L RR +( L) 2 1 R + C C

1 L C 2 2 R +( L) 2 1 R2 + C Cross multiplying 2

1 1 2 2 1 (L)R L R +(L) C C C 1 1 1 R 2 L 0 L C C C 2

L 1 R 2 L0 C C Now by looking into above equation we can say that if

L then it will have no depending on frequency C L for resonance R 2 C R2

So R

55.

L 0.02 10 2 14.14 C 100 106

In the circuit shown below, the node voltage VA is _________V. A

I1

5 5

5A

10I1

5

5 10V

Key:

11.42

Exp:

All the branch currents are expressed interval of VA now writing KCL at node A

VA V 10I1 VA 10 5 A 0 5 5 5

28

|EE|

GATE-2016-PAPER-01

1 1 1 VA 2I1 5 1 5 5 10

VA

2 1 V 10 VA 2 A 6 5 10 10 2 1 2 VA 6 2 5 10 10

80 7 VA 8 VA 11.42V 7 10

5A 5 VA 5

www.gateforum.com

I1

5 5

5 VA 10I1 5

10I1

10 VA -10 10

29

|EE|

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General Aptitude Q. No. 1 – 5 Carry One Mark Each 1. Key: 2. Key: 3.

Key: Exp:

4.

The chairman requested the aggrieved shareholders to ___________him. (A) bare with (B) bore with (C) bear with (D) bare (C) Identify the correct spelling out of the given options: (A) Managable (B) Manageable (C) Manageble (B) Pick the odd one out in the following 13, 23, 33, 43, 53 (A) 23 (B) 33 (C) 43 (B) Given numbers are 13, 23, 33, 43, 53. All the numbers have second digits as 3. If We sum of the digits of each number we get 4, 5, 6, 7, 8. All given numbers are irrational numbers except 33 which is rotation. So odd one out is 33.

(D) Managible

(D) 53

Key:

R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes. Which of the following can be logically inferred from the above statements? (A) R2D2 is a robot which can only repair aeroplanes. (B) R2D2is the only robot which can repair aeroplanes. (C) R2D2 is a robot which can repair only aeroplanes. (D) Only R2D2 is a robot. (B)

5.

If 9y 6 3, then y2 4y 3 is _________. (A) 0

Key: Exp:

(B) 1 3

(C) 1 3

(D) undefined

(C) 9Y 6 3 Possibility (A): 9y 9 y 1 Possibility (B): 9y 3 y

1 3

When y=1 4y 2 4(1) 3 4 1 y2 1 3 3 3 3 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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1 3 1 4 2 1 3 1 4 3 1 3 9 9 9 3 3

When y

Q. No. 6 – 10 Carry Two Mark Each 6.

The following graph represents the installed capacity for cement production (in tones) and the actual production (in tones) of nine cement plants of a cement company Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tones is

300 250

Installed Capacity

Actual Pr oduction 250 230

220

190

180

200

160

Capacity production 150 tonnes 100

200

200 190

190 150

160

160

150

140

120

100

5

6

120

50 0

1

2

3

4

7

8

9

Plant Number

Key: Exp:

120 Largent plant Installed Capacity Actual production Plant number

220 160 1

200 190 4

250 230 8

200 190 9

Total production of larger plants = 160+190+230+190=770 tonnes Smaller Plants Installed Capacity Actual production Plant number

180 150

190 160

160 120

150 100

140 120

Total production of smallest plants = 150+160+120+100+120= 650tonnes Difference = 770-650 = 120 tonnes ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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A poll of students appearing for masters in engineering indicated that 60% of the students believed that mechanical engineering is a profession unsuitable for women. A research study on women with master or higher degrees in mechanical engineering found that 99% of such women were successful in their professions. Which of the following can be logically inferred from the above paragraph? (A) Many students have isconceptions regarding various engineering disciplines (B) Men with advanced degrees in mechanical engineering believe women are well suited to be mechanical engineers. (C) Mechanical engineering is a profession well suited for women with masters or higher degrees in mechanical engineering. (D) The number of women pursuing high degrees in mechanical engineering is small.

Key:

(C)

8.

Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a developing country. Which of the following can be logically inferred from the above sentence? Based on the proposal, (i) In the initial years, SIT students will get degrees from IIT. (ii) SITs will have a distinct national objective (iii) SIT like institutions can only be established in consultation with IIT. (iv) SITs will serve technological needs of a developing country. (A) (iii) and (iv) only (B) (i) and (iv) only (C) (ii) and (iv) only (D) (ii) and (iii) only

Key:

(C)

9.

Key:

Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts? (A) 0.2508 (B) 0.2816 (C) 0.2934 (D) 0.6000 (A)

10.

The numeral in the units position of 211870 146127 3424 is _____.

Key:

(7)

3

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Electrical Engineering Q. No. 1 –25 Carry One Mark Each 1.

The output expression for the Karnaugh map shown below is (A) A B

BC 00

A

(B) A C

(C) A C

1

11

10

1

1

1

1

01

1 1

(D) A C Key: Exp:

(B) A

BC

BC

1

1

1

1

BC

BC F A, B, C A C

1 1

A

R2

2.

The circuit shown below is an example of a C

(A) low pass filter

15V

(B) band pass filter Vin

(C) high pass filter

Vout

(D) notch filter Key:

R1

15V

(A) 1 R2 cs Z1 R i , Z2 1 1 R 2 CS R2 cs Z R2 TF 2 Z1 1 R 2CS R1 R2

Exp:

When S 0 ; TF

R2 non zero value R1

When S ; TF 0 Given circuit is an example of low pass filter

4

|EE| 3.

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The following figure shows the connection of an ideal transformer with primary to secondary turns ratio of 1:100. The applied primary voltage is 100V (rms), 50Hz, AC. The rms value of the current I, in ampere, is _____. XL 10

(10)

Exp:

Where ZL

I

R 80k

XC 40k

I

100V ~

Key:

I :100

80 j40 3 10 8 4i 2 100 1

Zsec ondary n2

100 100 100 10 36.86 j10 ZL J10 8 j4 8 j6

Since all the calculation done with respect to RMS, I also in RMS

4.

dy t

Consider a causal LTI system characterized by differential equation

dt

1 y t 3x t . The 6

1 3

response of the system to input x t 3e u t , where u(t) denotes the unit step function, is (A) 9e (C) 9e Key: Exp:

t 3

t 3

ut

(B) 9e t 6

u t 6e u t

t 6

ut

(D) 54e

t 6

t 3

u t 54e u t

(D) 1 S y s 3 s 6 3 H s 1 s 6

Similarly X s

y s

3 1 s 3

9 54 54 1 1 1 1 s s s s 6 6 3 3

Thus y t 54 e

t

6

u t 54e t 3 u t 0

5

|EE| 5.

GATE-2016-PAPER-02

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Suppose the maximum frequency in a band-limited signal x(t) is 5kHz. Then, the maximum frequency in x(t) cos 2000t , in kHz, is ______.

Key:

6

Exp:

Maximum frequency of x t 5kHz Maximum frequency of cos 2000t 1kHz x t cos 2000t Gives convolution between their respective spectrums in frequency domain

max frequency of x t cos 2000t 6kHz 6.

Consider the function f (z) z z * where z is a complex variable and z* denotes its complex

Key:

conjugate. Which one of the following is TRUE? (A) f(z) is both continuous and analytic (B) f(z) is both continuous but not analytic (C) f(z) is not continuous but is analytic (D) f(z) is neither continuous not analytic (B)

Exp:

f z z z

x iy x iy z is conjugate of z 2x i 0 f z 2x is continues but not analytic, since

C – R equations will not satisfy A 3 3 matrix P is such that, P3 P. Then the eigenvalues of P are

7.

(A) 1, 1, - 1 (B) 1,0.5 j0.866,0.5 j0.866 (C) 1, 0.5 j0.866,0.5 j0.866 Key: Exp:

(D) 0, 1, - 1 (D) If is an Eigen value of p then 3 is an Eigen value of p3. p3 p

3

3 0 2 1 0 0; 2 1

0; 1

6

|EE|

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The solution of the differential equation, for t 0, y" t 2y ' t y t 0 with initial

8.

conditions y 0 = 0 and y ' 0 1, is u t denotes the unit step function), (A) te t u t

(B) e t te t u t

(C) e t te t u t

(D) e t u t

Key: (A) Exp: The operator form of the of given D.E is

D2 2D 1 y 0 The A.E is D2 2D 1 0 D 1 0 D 1, 1. 2

y t e t C1 C2 t

Given y 0 0 & y ' 0 1 i.e, t 0; y 0 from (s); 0 C1 C1 0 y ' 0 1

dy e t C1 C2 t e t C2 dt dy At t 0; y' 1 dt

From (1),

1 0 C2 0 1C2 1 C2 C2 1

From (1) y(t) e t (t) te t u(t) 9.

2xy dx 2x ydy dz along a path joining the origin (0,0,0) and 2

The value of the line integral

2

c

the point (1,1,1) is (A) 0 Key: (B) Exp:

(B) 2

(C) 4

(D) 6

Let f 2xy 2 i 2x 2 y j k

i curl f f x 2xy 2

j

y

2x 2 y

k 0 z 1

f is irrotational

Consider a straight line passing through 0,0,0 & 1,1,1 i.e,

x y z t x y z t dx dy dz dt 1 1 1

2xy dx 2x 2

C

2

ydy dz

1

t 0

2t 3 dt 2t 3 dt dt

1

t 0

4t

3

1 dt t 4 t 2 1

7

|EE|

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Let f(x) be a real, periodic function satisfying f x f x . The general form of its Fourier

10.

series representation would be (A) f x a 0 k 1 a k cos kx

(B) f x k 1 bk sin kx

(C) f x a 0 k 1 a 2k cos kx

Key: Exp:

(D) f x k 1 a 2k 1 sin 2k 1x

(B) We know that a periodic function f(x) defined in (-c, c) can be represented by the poisoins series a nx nx f x o a n cos bn sin 2 n 1 c c n 1 If a periodic function f(x) is odd, its Fourier expression contains only sine terms

11.

A resistance and a coil are connected in series and supplied from a single phase, 100V, 50Hz ac source as shown in the figure below. The rms values of plausible voltage across the resistance

VR and coil VC

respectively, in volts, are VR ~

VC

VS

Key:

(A) 65, 35 (C)

(B) 50, 50

12.

The voltage (v) and current (A) across a load are as follows.

(C) 60, 90

(D) 60, 80

v t 100 sin t , i t 10sin t 60O 2sin 3t sin 5t

Key: Exp:

The average power consumed by the load, in W, is ________. 250 The instantaneous power of load is p t V i t 100sin t 10sin(t 60 100sin t 2sin3t 100sin t 5sin5t T

since Pavg

P t dt , in the above expression 0

st

Only 1 term will result non zero answer Remaining 2 terms will be 0. so directly consider P t 100sin t 10 sin t 60 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Pavg Vrms I rms cos V I

13.

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100 10 1000 1 cos 60 250 watt 2 2 2 2

A power system with two generators is shown in the figure below. The system (generators, buses and transmission lines) is protected by six overcurrent relays R1 to R 6 . Assuming a mix of directional and nondirectional relays at appropriate locations, the remote backup relays for R 4 are R1

R2

S1 ~

(A) R1 , R 2

R5 R3

R6

~

R4

(B) R 2 , R 6

S2

(C) R 2 , R 5

(D) R1 , R 6

Key:

(D)

14.

A power system has 100 buses including 10 generator buses. For the load flow analysis using Newton-Raphson method in polar coordinates, the size of the Jacobian is (A) 189 189 (B) 100 100 (C) 90 90 (D) 180 180

Key: Exp:

(A) Total no of Buses = 100 generator buses = 10 – 1 = 9 (n) load buses = 100 -10 = 90(m) Jacobeam matrix size = 2m n 2m n 2 90 9 2 90 9 189 189

15.

The inductance and capacitance of a 400kV. Three-phase. 50Hz lossless transmission line are 1.6 mH/km/phase and 10nF km phase respectively. The sending end voltage is maintained at 400kV.

Key: Exp:

To maintain a voltage of 400kV at the receiving end, when the line is delivering 300MW load, the shunt compensation required is (A) Capacitive (B) Inductive (C) Resistive (D) Zero (B) XL jL j314 1.6 103 j0.5024 XC

j j j31847.3376 C 314 10 109

Since XC XL , the shunt compensation is inductive 16.

A parallel plate capacitor field with two dielectrics is shown in the figure below. If the electric field in the region A is 4kV/cm, the electric field in the region B, in kV/cm, is A r 1

B r 4

2cm

9

|EE|

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Key:

(A) 1 (C)

Exp:

Since the voltage & distance b w the two plates are same for both the regions. The electric field is same for both the regions E

(C) 4

(D) 16

V d

Electric field in region B = 4kV cm 17.

Key: Exp:

A 50MVA, 10kV, 50Hz, star-connected, unloaded three-phase alternator has a synchronous reactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to the generator terminals, the ratio of initial and final values of the sinusoidal component of the short circuit current is _________. 5 Vprefault ISC X P.U ISC initial IScfinal

1 5 0.2

Consider a liner time-invariant system transfer function H s

18.

Key: Exp:

1 . If the input is cos(t) and s 1

the steady state output is Acos t , then the value of A is _________. 0.707 1 H tan 1 2 1 1 H 45O 2 So when input is cost then O/P 1 yt cos t 45O 2 1 0.707 So A 2

19.

A three-phase diode bridge rectifier is feeding a constant DC current of 100A to a highly inductive load. If three-phase, 415V, 50Hz AC source is supplying to this bridge rectifier then the rms value of the current in each diode, in ampere, is _________. Key: 57.73 Exp: IO 100A RMS, diode current =

100 57.73A 3

10

|EE| 20.

GATE-2016-PAPER-02

A buck-bost DC-DC converter shown in the figure below, is used to convert 24 V battery voltage to 36 V DC voltage to feed a load of 72 W. It is operated at 20kHz with an inductor of 2 mH and output capacitor of 1000 F. All devices are considered to be ideal.

24V

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Load 36V

S

2mH

The peak voltage across the solid-state switch (S), in volt, is _________. Key: 60 For the network shown in the figure below, the frequency in rad s at which the maximum

21.

9

phase lag occurs is.______.

1

in

0

1F

Key: Exp:

0.316 The given circuit is standard lag compensator Whose Transfer function 1 1 s s 1 1 s G s 1 1 10s 1 s a 1 s So 1, 10 the frequency at which maximum phase lag happen 1 1 m 0.316 rad sec 10

22.

The direction of rotation of a single-phase capacitor run induction motor is reversed by (A) interchanging the terminals of the AC supply (B) interchanging the terminals of the capacitor (C) interchanging the terminals of the auxiliary winding. (D) interchanging the terminals of both the windings

Key: (C) 23.

In the circuit shown below, the voltage and current are ideal. The voltage (Vout) across the current source, in volts, is 2 10V

5A

Vouts

11

|EE| (A) 0

GATE-2016-PAPER-02 (B) 5

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(C) 10

(D) 20

Key: (D) Exp:

10V

Writing KVL VO 10 10 0

10V

5A

VO 20V

VO

24.

The graph associated with an electrical network has 7 branches and 5 nodes. The number of independent KCL equations and the number of independent KVL equations, respectively, are (A) 2 and 5 (B) 5 and 2 (C) 3 and 4 (D) 4 and 3

Key:

(D)

Exp:

No of branches = 7 Nodes = 5 No of KCL equations = No of Modal equations = n – 1 = 5 – 1 = 4 No of KVL equations = No of Mesh equations = b-(n – 1) = 7-4 = 3 Since no information given regarding how many simple & principal node, if we assume all principal nodes then the answer for nodal is 5 – 1 = 4

25.

The electrodes, whose cross-sectional view is shown in the figure below, are at the same potential The maximum electric field will be at the point

A

D

C

B

(A) A Key:

(A)

Exp:

At A

(B) B

(C) C

(D) D

Fields are additive F1 F2 At C C Fields are subtractive F1 F2

At D field is due to one electrode F2 At B field make an angle

F12 F22 2F1F2 cos So maximum electric field is at ‘A’ ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Q. No. 26 – 50 Carry Two Mark Each

26.

The Boolean expression a b c d b c simplifies to

Key:

(A) 1 (D)

Exp:

F

27.

For the circuit shown below, taking the opamp is ideal, the output voltage Vout in terms of the

=

(C) a.b

(B) a.b

a b c d b c

= a d bb cc

input voltages V1 , V2 and V3 is

1

V3 V1

1

(D) 0

= a d 1 1 = 1 = 0

9

Vx Vx

Vout

4 V2

Key: Exp:

(A) 1.8V1 7.2V2 V3

(B) 2V1 8V2 9V3

(C) 7.2V1 1.8V2 V3

(D) 8V1 2V2 9V3

(D) Vx V1 Vx V2 4V V2 0; Vx 1 1 4 5

Vx V3

Vx Vout 0 1 9 4V1 V2 V out 4V1 V2 V 5 0 3 5 9 4V V 5V 4V1 V2 5V3 1 92 out 0 36V1 9V2 45V3 4V1 V2 5Vout 0 40V1 10V2 45V3 5 8V1 2V2 9V3

Vout

Vout

13

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Let x1 t X1 and x 2 t X 2 be two signals whose Fourier Transforms are as shown

28.

in the figure below. In the figure h(t) = e

2 t

denotes the impulse response.

X1

B1

B1 2

X 2

B1 2

B2

B1

B2

x1 t h t e

2 t

yt

x2 t

For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is (A) 2B1

(B) 2 B1 B2

Key:

(B)

Exp:

y t x1 t x 2 t * h t

(C) 4 B1 B2

(D)

In frequency duration y X1 *X2 H

Max. Frequency of X1 B1 Max, frequency of X 2 B2 Max frequency of X1 *X 2 B1 B2 Max frequency of H Thus max, freq of y B1 B2 Max frequency

Nyquist frequency = 2 B1 B2 sin 2t The value of the integral 2 dt is equal to t (A) 0 (B) 0.5 (C) 1

29.

Key:

(D) 2

(D)

14

|EE|

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Exp:

sin 2 t sin 2 t 2 dt dt 2 2 t t 0

4 e0.t 0

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sin 2 t t is an even function

sin 2 t .dt t

By the defining of L.T; we have

sin 2t 4L ; where S 0 t

4 4 sin 2t 1 2 L ; wheres 0 tan ; where s 0 t s

sin at 1 a L t tan s

Putting s = 0; than

4 4 tan 1 2 2

2

30.

sin 2t dt 2 t

Let y(x) be the solution of the differential equation

y 0 0 and Key: Exp:

dy dx

d2 y dy 4 4y 0 with initial conditions 2 dx dx

1. Then the value of y (1) is _________. x 0

7.398 The operate form of given D.E is

D2 4D 4 y 0 The A.E is D2 4D 4 0 D 2 0 D 2,2 2

D 2 0 D 2,2 2

The solution is y e 2x C1 C2 x 1 Given that

from 1 y e

y 0 0

&

y '0 1

i.e x 0 y 0

i.e at x 0, y' 1

from (1); 0 1 C1 0

from 1 y1 e2x C2 C1 C2 x 2c 2x

C1 0

1 C2 0 C2 1

2x

0 1.x y xe

y 1 1e 21 e 2 y 1 e 2

2x

or y 1 7.389

15

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The line integral of the vector field F = 5xziˆ 3x 2 2y ˆj x 2 zkˆ along a path from (0,0,0) to

31.

(1,1,1) parametrized by t, t 2 , t is _________. Key: Exp:

4.4167

F 5xzi 3x 2 2y j x 2 z k x t; y t 2 ; z t

dx dt d 2t dt; dz dt The line integral of the vector field is

F.dr 5xzdx 3x

2

2y dy x 2 z dz

C

1

5t

2

dt 10t 3dt t 3dt

2

dt 11t 3dt

t 0 1

5t

t 0

1

1

t3 t4 5 11 3 0 4 0

20 23 53 5 11 4.4167 3 4 `12 12

32.

Key: Exp:

a x 3 1 x Let P = . Consider the set S of all vector such than a 2 b 2 1 where p . b y 1 3 y Then S is 1 (A) A circle of radius 10 (B) a circle of radius = 10 1 1 (C) an ellipse with major axis along (D) an ellipse with minor axis along 1 1 (D) 3 1 P 1 3 a x a 3 1 x b P y b 1 3 y 3x y a x 3y b

a 2 b2 1 3x y x 3y 1 2

2

10x 2 10y2 12xy 1

a 10; b 10; h 6 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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It represents ellipse

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The length of semi-axes is ab h 2 r 4 a b r 2 1 0

1 1 or r 2 4 16 2 Both r values are positive, so it represents ellipse 1 1 r or r 2 4 Length of major axis = 2r 1 64r 4 20r 2 1 0 r 2

1 Length of minor axis = 2r 2 1 2 4 1 Equation of the major axis is a 2 x hy 0 r1

10 4 x 6y 0 x y 0 1 Equation of the minor axis is a 2 x hy 0 r2

10 16 x 6y 0 y x 0

Major axis exists along y = -x and minor axis exists along y = x. 1 The vector Lies on the line y = x 1 33.

Let the probability density function of random variable, X, be given as: 3 f x x e 3x u x ae 4x u x 2 where u(x) is the unit step function. Then the value of ‘a’ and Prob X 0 , respectively, are (A) 2,

Key:

1 2

(B) 4,

1 2

(C) 2,

1 4

(D) 4,

1 4

(A)

Exp:

we have

f x dx 1 x

f x dx f x dx 1 x

x

4x a e dx

3

2 e

3x

dx 1

u x 1 for x 0 0, other wise

17

|EE|

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u x 1 for x 0 0,otherwise

ae

4x

e4x 3 3 e3x dx e 3x dx 1 a 1 2 4 2 3 0 0

a 1 a 1 1 1 a 0 0 1 1 1 a 2 4 2 4 2 4 2 Prob x 0

f x x dx

4x a.e dx a

e

4x

dx

e4x 2 1 2 1 0 2 y 4 The driving point input impedance seen from the source V S of the circuit shown below, in , is __________.

34.

IS VS

Key: Exp:

V1

2

2 3

4V1

4

20 The Driving point impedance is nothing but the ratio of voltage to current from the defined port. V In this case it is S Vx 2 V1 IS Writing KCL at node x V V IS x 4V1 x 0 3 6 Substituting these in Eq(1) V 2Is V 2Is IS S 8Is S 0 3 6

2 2 1 1 VS IS 1 8 3 6 3 6

IS VS

2 3

4

4V1 Vx 3

V1 6

I1

VS 2 1 IS 6 4 48 2

VS 60 20 IS 3

18

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The z-parameters of the two port network shown in the figure are Z11 40, Z12 60 ,

35.

Z21 80, Z22 100 . The average power delivered to R L 20, in watts, is ____. I2

10 I1 20V

Key: Exp:

V1

Z

V2

RL

35.55 In the given terminated 2 port network the Z matrix is known and for load of 20 we want to find power on the load. → The get it assuming R L as load let first obtain the thevenin equivalent of 2 port → Thevenin equivalent means Vth & R th Vth V2 I

2 0

i.e., O.C voltage of port 2

ISC I2 V2 0 i.e., s.c current of port 2, R in

Vth Isc.

→ Evaluation of Vth . The Z matrix equation is V1 40I1 60I2

V2 80I1 100I2 In the above two equations if I2 0 then

V1 40I1

(1)

V2 80I1

(2)

From the input side we can say V1 20 10I1

20 10I1 40I1 2 I1 2 A Then equation 2 becomes 5 3 2 V2 80 I1 80 32 V 5 so Vth V2 32 Evaluation of ISC In the Z matrix equation if we put V2 0 then

V1 40I1 60I2

…(5)

0 80I1 100I2

…(4)

19

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10 100 I 2 & V1 20 10I1 20 I2 8 8 Using these V1 & I1 in equation 3 I1

100 400 I2 I 2 60I 2 8 8 160 100I2 400I2 480I2 20

160 20I2 I2 8A ISC I2 8A R in

R th 4

Vin 32 4 Isc 8

Now the ckt is from port 2is

R L 20

Vth 32

P20 I20 20 2

32 20 35.55watt 4 20 36.

In the balanced 3-phase, 50Hz, circuit shown below, the value of inductance (L) is 10mH. The value of the capacitance (C) for which all the line current are zero, in millifarads, is _____.

C

L

C

L

C

L

Key: Exp:

IL

3.04 IL 0 2ph jL j X L .XC 3 c Zph jL j X L XC 3 c L 1 b c 3 314 10 103 C C 3.04 mF

L 3

C

L3

L3

C

C

20

|EE| 37.

GATE-2016-PAPER-02

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S1

In the circuit shown below, the initial capacitor voltage is 4V. Switch S1 is closed at t = 0. The charge in C lost by the capacitor from t 25s to t 100s is _______. 4V

5

5F

Key:

6.99

Exp:

It is given VC 0 4

1 40000 RC Since it is a source free network we can say VC t VC 0 e t ; t 0 4e40000 t

R 5, C 54f so →

→

We are asked to find the charge last by capacitor From t 25s to 100 s We know in a capacitor Q CV or Q C V

Q C VC 25 sec VC 100 sec → VC 4e40000t 6

VC

4e40000 2510 1.47

VC

4e 40000 10010 0.073

t 25 sec 6

t 100 sec

Q 5 1.47 0.073 6.99s

38.

The single line diagram of a balanced power system is shown in the figure. The voltage magnitude at the generator internal bus is constant and 1.0 p.u. the p.u. reactances of different components in the system are also shown in the figure. The infinite bus voltage magnitude is 1.0p.u. A three phase fault occurs at the middle of line 2. The ratio of the maximum real power that can be transferred during the pre-fault condition to the maximum real power that can be transferred under the faulted condition is ______ Generator int ernal bus

inf inite bus

j0.1 j0.5 Line 1

j0.2 ~

j0.5 Line 2 j0.1 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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|EE| Key: Exp:

GATE-2016-PAPER-02

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2.286 During fault

Before fault

0.6

0.5

0.1

0.2

0.2

~

~

0.5

0.1

Xeq 0.2

0.1 0.25

0.1 0.5 0.5 P.U 2

0.6 0.2 ~

EV Pe max 2EV Xeq

0.35

Converting Y c

0.175

xe

0.35

0.125

C

b

xc

C

0.25

b

0.6 b

xb

0.25

a

0.375

0.125

a C

Xac

C

0.0729

0.25

0.0729

0.375 0.125 0.125 0.0729 0.0729 0.375 1.143 0.0729 Pe Prefault EV 1.143 Pe max 2.286 Pe during fault 1.143 20.5

X ac

39.

The open loop transfer function of a unity feedback control system is given by K s 1 G s , K 0, T 0. s 1 Ts 1 2s The closed loop system will be stable if (A) 0 T (C) 0 K

Key: Exp:

4 K 1 K 1 T2 T 1

(B) 0 K (D) 0 T

4 T 2 T2 8 K 1

K 1 (C) To comment closed 100b system stability we need the characteristic equation. Here it is given that it is a unity feedback system. Unity feedback system So the characteristic equation is S 1 TS 1 2S K S 1 0

22

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S TS2 1 2S KS K 0 S 2S2 TS2 2TS3 KS K 0

S3 2T S2 2 T S 1 k k 0

k 2 T 2 k 1 s3 0 s s 2T 2T 2T for stability using R t criterion

2 T K 1 K 2T 2T 2T K 1 1 T 2 K 1 K K T2 1 1 1 T 1 T 2 `1 K K T2 K T2 T 1

40.

Key:

At no load condition a 3-phase, 50Hz, lossless power transmission line has sending –end and receiving-end voltage of 400 kV and 420kV respectively. Assuming the velocity of traveling wave to be the velocity of light, the length of the line, in km, is __________. 294.84

2 2 1010 Exp: VS Vr 1 18 3142 2 1010 400 420 1 294.84km 18 41. The power consumption of industry is 500kVA, at 0.8 p.f. lagging. A synchronous motor is added to raise the power factor of the industry to unity. If the power intake of the motor is 100kW. The p.f. of the motor is _________. Key: 0.3162 2 400 Exp: cos 2 1 100

2 0 1 36.86

36.86

P S P1 400; P2 100

cos 1

Qmotor P1 tan 1 P1 P2 tan 2 400 tan36.86 500 tan 300 kW

Smotor 100 j300 cos m 0.3162

23

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The flux linkage and current (i) relation for an electromagnetic system is

42.

i

g . When i

= 2A and g air gap length 10cm, the magnitude of mechanical force on the moving part, in N, is ________. Key:

186 to 190

43.

Key:

The starting line current of a 415V. 3-phase, delta connected induction motor is 120A, when the rated voltage is applied to its stator winding. The starting line current at a reduced voltage of 110V, in ampere is _________. 31 to 33

44.

A single-phase, 2kVA, 100 200V transformer is reconnected as an auto-transformer such that its

kVA rating is maximum. The new rating in kVA, is _______. Key: 6 20A Exp: ` max 30A

100V

10A 200V

45.

300V

KVA rating 300 200 6kVA

A full-bridge converter supplying in RLE load is shown in figure. The firing angle of the bridge converter is 120O. The supply voltage m t 200 sin 100 t V, R 20, E 800V. The inductor L is large enough to make the output current IL a smooth dc current. Switches are lossless. The real power fed back to the source. In kW is ________. Load

IL

T1 ~ Vin

L

T3 R 20

Bridge

` T4

T2

E 800V

Key: 6 Exp: V0

2Vm 200 cos 2 cos120 200V

24

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E V0 800 200 30A R 20 Pfedback V0 I0 200 30 6kW . I0

A three – phase Voltage Source Inverter (VSI) as shown in the figure is feeding a delta connected resistive load of 30 phase . If it is fed from a 600V battery, with 180O conduction of solid-state

46.

devices, the power consumed by the load, in kW, is _________.

30

30 600V

Key:

24

Exp: Vph

R ph 47.

30

2 2 Vdc 600 200 2 V 3 3

200 2 R 30 3Vph 2 10 PLoad 3 3 3 R ph 10

2

24kW

A DC-DC boost converter, as shown in the figure below, is used to boost 360V to 400V, at a power of kW. All devices are ideal. Considering continuous inductor current, the rms current in the solid state switch (S), in ampere, is ______. 10mH

Load

S

360V

1mF

400 V

Key:

3 to 4

48.

A single-phase bi-directional voltage source converter (VSC) is shown in the figure below. All devices are ideal. It is used to charge a battery at 400V with power of 5kW from a source Vs 220V(rms),50Hz sinusoidal AC mains at unity p.f. If its ac side interfacing inductor is 5mH and the switches are operated at 20kHz, then the phase shift between AC mains voltage VS and fundamental AC rms VSC voltage VC1 , in degree, is________.

25

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5mH

IS

220VAC ~

1mH

XS

400V

IS

VS

VC1

I1X1

Key:

9.1 to 9.3

49.

Consider a linear time invariant system x Ax, with initial condition x(0) at t = 0. Suppose

2 2 matrix A corresponding to distinct eigenvalues 1 and 2 respectively. Then the response x t of the system due to initial condition x (0) = is and are eigenvectors of (A) e1t Key: Exp:

(B) e1t

(C) e2 t

(D) e2 t e2 t

(A) Eigen values are nothing but pole location Here with respect to the pole is 1

wrt Pole is 2 The section should be of form e1t e

2t

but we are asking w.r.t

Initial condition x 0 only so the response should be e1t 50.

A second-order real system has the following properties: (a) the damping ratio 0.5 and undamped natural frequency n 10 rad s,

Key: Exp:

(b) the steady state value of the output, to a unit step input, is 1.02. The transfer function of the system is 1.02 102 100 (A) 2 (B) 2 (C) 2 s 5s 100 s 10s 100 s 10s 100 (B) n 2 The standard 2nd order T/F is K 2 2 s 2n s n

(D)

102 s 5s 100 2

it is given that 0.5 & n 10 G s K

100 s 10s 100 2

Now to satisfy the steady state O/P 1.02 y t

s 0

G s

1 100 2 K 1.02 K 1.02 s s 10s 100

1.02 100 102 2 s 10s 100 s 10s 100 2

26

|EE| 51.

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Three single-phase transformers are connected to form a delta-star three-phase transformer of 110kV 11kV. The transformer supplies at 11kV a load of 8MW at 0.8 p.f. lagging to a nearby plant. Neglect the transformer losses. The ratio of phase current in delta side to star side is (A) 1: 10 3

Key:

(A)

Exp:

N1 : N2 110 :

(B) 10 3 :1

(C) 1:10

(D)

3 :10

11 10 3 :1 3

I1N1 I2 N2

Ii 10 3 I 2 .1

I1 1 I2 10 3

52.

The gain at the breakaway point of the root locus of a unity feedback system with open loop Ks transfer function G s is s 1 s 4

Key:

(A) 1 (A)

Exp:

G s

(B) 2

(C) 5

(D) 9

Ks s 1 s 4

To find Break away point

dk 0 where We need to find the root of ds s 1 s 4 s 2 5s 4 K s s

1

4

d d 2 s s 5s 4 s 2 5s 4 s dk ds ds ds s2

S 2S 5 S2 5S 4 0 2S2 5S S2 5S 4 0

S2 4 0 S 2

From the pole zero plot it is clean that Break away point must be S 2 as it is in between 2 poles Now to find gain at this point use magnitude condition

KS KS 1 1 K 1 s 1 s 4 s2 1 2

27

|EE| 53.

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Two identical unloaded generators are connected in parallel as shown in the figure. Both the generators are having positive, negative and zero sequence impedance of j0.4p.u, j0.3p.u and terminals of the generators, the fault current, in p.u., is ________. ~

~

Key:

6

0.4 0.3 Z2 0.15P.U 0.2 P.U ; 2 2 3Vprefault 3 If 6p.u ZO Z1 Z2 0.15 0.2 0.15

Exp: Z0 0.15 P.U ; Z1

An energy meter, having meter constant of 1200 revolutions kWh, makes 20 revolutions in 30 seconds for a constant load. The load, in kW is ______ Key: 2 20revolutions Exp: K 1200re v kwh 30 P kW hr 3600 P 2kW 54.

z

55.

Key: Exp:

A rotating conductor of 1m length is placed in a radially outward (about the z-axis) magnetic flux density (B) of 1 Tesla as shown in figure below. Conductor is parallel to and at 1m distance from the z-axis. The speed of the conductor in r.p,m. required to induce a voltage of 1V across it, should be ______. 9.55 Voltage = B Velocity

B

1m 1m

Voltage 1 1m s B 11

i.e, 1m takes 2 21 2 m Takes 2r

2r for 1 rotation in 1 minute =

Velocity =

60 2

60 9.55 rpm 2

28

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Electrical Engineering Q. No. 1 – 25 Carry One Mark Each

1.

t t , t 0 Consider g t , where t t t , otherwise

Here, t represents the largest integer less than or equal to t and t denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________. Key: 0 to 0

t t 0 Exp: Given g t t t otherwise If we plot the above signal, we get gt

1

2

3

1

Since this wave form contain hidden half wave symmetry, even harmonics does not exist. Thus coefficient of second harmonic component of Fourier series will be zero. 2.

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are Van=220sin 100t V and

i a 10sin 100t A, respectively. Similarly for phase-b the instantaneous voltage and current are Vbn 220cos 100t V and i b 10cos 100t A, respectively.

ia

a'

Van i b

b'

a

b

Load

Source

n

Vbn

n'

The total instantaneous power flowing form the source to the load is (A) 2200 W

(B) 2200sin2 100t W

(C) 440 W

(D) 2200sin 100t cos 100t W

Key: (A)

1

|EE|

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Exp: Pins tan eous Van ia Vbn ib

220sin 100t 10sin 100t t 220cos 100t 10cos 100 t 2200sin 2 100t 2200cos 2 100t 2200W 3.

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

Key:

835 to 842

Exp:

Vt 6.6kV

30

V I a Xs E b

Ia

V 6600 3 cos cos30o E b 4400 volts Eb

Ia

E b 30o

E b cos V

E b cos

~ cos 1

P 3.

E b .V 4400 3810.51 sin 3. sin 30o Xs 30

P 838.31 kW

4.

For a complex number z, lim z i

(A) -2i Key: (D) Exp: lim z i

z2 1 is z3 2z i z 2 2

(B) -i

(C) i

(D) 2i

z2 1 zi 2i lim 2 2i 3 2 z i z 2 1 2 z 2z i z 2

5.

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first? (A) The particles will never collide (B) All will collide together (C) Proton and Neutron (D) Electron and Neutron Key: (D) mp mn me Exp: e n p q e q e q0

2

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

e 2 F , accelleration q ;q e q p 2 4o r M

Due to this force, the electron as well as the proton will move towards each other, since me m p , the speed and acceleration of the electron will be much greater than that of proton. This causes electron to collide with the neutron faster when compared to proton. 6.

Let z t x t y t , where “ ” denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct). (A) c.x ct y ct

(B) x ct y ct

(C) c.x t y ct

(D) c.x ct y t

Key: (A) Exp: z t x t * y t z s x s .y s Converting into Laplace transform and applying time sealing property. 1 z ct z s / c c 1 s / c y s / c c 1 1 c s / c y s / c c c z ct c.x ct * y ct

7.

A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are Y11 j12pu, Y22 j15pu and Y33 j7pu Bus 1

Bus 2

jq

jr

jp

Bus 3

The per unit values of the line reactances p, q and r shown in the figure are (A) p 0.2, q 0.1, r 0.5 (B) p 0.2, q 0.1, r 0.5 (C) p 5, q 10, r 2

(D) p 5, q 10, r 2

Key: (B)

Exp: Y11 y10 y12 y13 j12 jq1 jr1

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q1 r1 12 Y22 j15 y 20 y 21 y 23 jq1 jp1 p1 q1 15

Y33 j7 y30 y31 y32 jp1 jr1 p1 r1 7 solving P1 5,q1 10, r1 2 admit tan ces P 0.2,q 0.1, r 0.5 reac tan ces

The equivalent resistance between the terminals A and B is ______ .

8.

2

1

1

A 6 3

1

6

0.8

3

B

Key: 2.9 to 3.1 Exp: The Ckt will become 2 1

1

1 A

3

1

3

6

6

1.2

B 0.8

0.8

R AB 1 1.2 0.8 3 The Boolean expression AB AC BC simplifies to

9.

(A) BC AC Key: (A)

(B) AB AC B

Exp: AB AC BC A 0 1

BC AC

10.

BC 00

01

11

(C) AB AC

(D) AB BC

10

1 1

1

BC

1

AC

The following measurements are obtained on a single phase load: V 220V 1%, I 5.0A 1% and W 555W 2%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ________.

4

|EE| Key:

4 to 4

Exp:

P VIcos cos

11.

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P 555 2% 555 2% 0.504 4% V.I 220 1% 5 1% 1100 2%

The transfer function of a system is given by,

Vo s Vi s

1 s Let the output of the system be 1 s

vo t Vm sin t for the input vi t Vm sin t . Then the minimum and maximum values of (in radians) are respectively (A)

and 2 2

(B)

and 0 2

(C) 0 and

2

(D) and 0

Key: (D) Exp:

Vo s Vi s

1 s H s 1 s

H 1 2Tan 1, If 0, 0 If , Vo t Vm sin t 2Tan 1

12.

3 2 The matrix A 0 1 2

1 2 1 0 has three distinct eigenvalues and one of its eigenvectors is 3 0 2 Which one of the following can be another eigenvector of A? 0 (A) 0 1

1 (B) 0 0

1 (C) 0 1

1 0 1

1 (D) 1 1

Key: (C) 1 Exp: By the properties of Eigen values and Eigen vectors, another eigen vector of A is 0 1 The eigen vectors corresponding to distinct eigen values of a real symmetric matrix are orthogonal i.e., pair wise dot product is zero.

13.

For the power semiconductor devices IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE? (A) All of the four are majority carrier devices. (B) All the four are minority carrier devices (C) IGBT and MOSFET are majority carrier devices, whereas Diode and Thyristor are minority carrier devices. (D) MOSFET is majority carrier device, whereas IGBT, Diode, Thyristor are minority carrier devices. ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India

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Key: (D) Exp: MOSFET → Majority carrier device (NMOS, PMOS) Diode → both majority & minority carrier device Transister → Npn, pnp IGBT → input is MOSFET, Output is BJT 14.

Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30o is _______. Key: 1.01 to 1.06 Exp: PM 180 G gc

G s

U s

Ke s s

Y s

Ke s s

For gc | G s |

K 1

gc K G s

180 90o

180o 90o 180o K 60 K 1.047 3

30o 180o K

15.

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will (A) bend closer to the cylinder axis (B) bend farther away from the axis (C) remain uniform as before (D) cease to exist inside the cylinder Key: (A) Exp: Flux always chooses less reluctance path. So flux tried to flow inside the conductor and closer to the axis of the cylinder. 16.

Let I c R xy2dxdy, where R is the region shown in the figure and c 6 104. The value of I equals________. y 10

R

2

1

5

x

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Key: 0.99 to 1.01 Exp:

xy dxdy xy dxdy xy dxdy 2

2

R

2

R1

R2

5

2

x 1 y 0

5

2

2x

x 2 y3 5 y3 2 xy dx x dx 2 1 3 0 1 3 2 y 2

5

xy 2 dxdy

2x

x 1

5 5 5 x2 1 x5 8 1 3 12 x 8x 8 dx 32 8 8 3 5 1 3 3 1 2 1

1 24992 24992 32 32 3 5 15 2 C xy 2 dxdy 24992 104 0.99968 1 5 R OR 2x 2 R xy dxdy x1 y0 xy dy dx 5

2

2x

5 5 y3 8 x dx x x 3 dx 3 31 1 5

8 x5 8 24992 3124 3 5 1 15 15 24992 2 C xy 2 dxdy 104 6 2.4992 0.9968 1 15 5 R

17.

Consider the system with following input-output relation y n 1 1 x n n

where, x[n] is the input and y[n] is the output. The system is (A) invertible and time invariant (B) invertible and time varying (C) non-invertible and time invariant (D) non-invertible and time varying Key: (D)

Exp: Given y n 1 1 x n n

For time invariance

y' n 1 1 x n n o (1) n

y n n o 1 1

n no

x n n (2) o

Since (1) is not equal to (2) System is time variant For inverse system For each unique x n , there should be unique y n If x n n 1 n y n 1 1 n 1

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y 1 0 if x n 2 n 1 y n 1 1 2 n 1 y(1)=0 For two different inputs we have same output. Thus one to one mapping is not possible. Hence the systems is non invertible n

18.

The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of (A) 150 ns has to be inserted into the y-channel (B) 150 ns has to be inserted into the x-channel (C) 150 ns has to be inserted into both x and y channels (D) 100 ns has to be inserted into both x and y channels

Key: (A) Exp: The delay line should be inverted in VDP (Y-channel) only. 19.

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

20

600V

20

20

Key: 8.5 to 9.5 Exp: Vdc 600V R L 20 / Ph 120o mod e

RMS value of phase voltage VP 0.4082Vdc 244.92V Load power

20.

3Vph 2 3 244.922 8.99kW 9kW R 20

3 2 A closed loop system has the characteristic equation given by s Ks K 2 s 3 0. For

this system to be stable, which one of the following conditions should be satisfied? (A) 0 < K < 0.5 (B) 0.5 < K < 1 (C) 0 < K < 1 (D) K > 1 Key: (D) 3 2 Exp: Given CE s ks k 2 s 3 0

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For stable

k k 2 3 k 2 2k 3 0

k 1 k 3 0 k 1 k 3 k 1 (OR) By R-H criteria s3

1

k2

2

k

3

s

k k 2 3

s

k

s0

3

k 0 k 3 k 1 0 K 0 k 1 k 3 k 1

21.

A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is (A) 1350 (B) 1650 (C) 1950 (D) 2250

Key: (C) Exp:

Ns

120 60 1800 rpm 4

Rotor speed should be greater than syn.speeed, to ge inductance generator mode. N NS S r NS fr 5 1 f r sf s f 60 12

N r NS 1 S 1 N r 1800 1 1950 rpm 12

22.

For the circuit shown in the figure below, assume that diodes D1, D2 and D3 are ideal. D1 R

v1 v t sin 100t V

D2

D3

R

v2

The DC components of voltages v1 and v2, respectively are (A) 0 V and 1 V (B) -0.5 V and 0.5 V (C) 1 V and 0.5 V

(D) 1 V and 1 V

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Key: (B) Exp: For half wave Rectifier Vdc

Vm

V1 Vdc for ve pulse Vdc for ve pulse V2

1 1 0.5V 2 2

0 0.5V 2

23.

A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______. Key: 14 to 14 Exp: Total no of buses=10 Given G1=slack bus, G2=generator/PQ bus G 3 ,G 4 are PV buses PQ buses L1 , L 2 , L5 , L 6 (4) Voltagecontrolled PV buses L3 , L 4 (2) Minimum no of nonlinear equations to be solved 2 10 2 4 14 R1

I

24.

The power supplied by the 25 V source in the figure shown below is ________W. Key: 248 to 252 Exp: KCL 25V I 0.4I 14

17V

R2

14A

0.4I

1.4I 14 I 10A The power supplied by 25 V = 25 10 250W 25.

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

S3

S1 220V

LOAD

S4

v t 0

S2

The RMS value of the fundamental component of vo(t) in volts is _______. Key : 196 to 200

10

|EE| Exp: Vo t

4Vs

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4VS 1 1 sin t sin 3 t sin 5 t sin nt 3 5 n 1,3,5 n

4 VS 2 n 4 VS Vol 0.9VS 2 0.9 220 198.069V

Vo t

Von

Vs 220V

2

t

Vs 220V Q. No. 26 – 55 Carry Two Marks Each

26.

The output expression for the Karnaugh map shown below is CD AB

(A) BD BCD Key: (D) CD Exp: 00 AB

00

01

11

10

00

01

1

1

11

1

1

1

10

(B) BD AB 01

11

10

00

01

1

1

11

1

1

1

10

(C) BD ABC

(D) BD ABC

BD ABC

27.

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

Key: 9.5 to 12 Exp:

E b1 220 30 0.5 205 volts E b2 220 I a 2 0.5 R X

Given T N2 and IR We know that, in series motor T Ia2 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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T Ia2 N 2

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Ia2

30A

Ia 2

N2 Ia 2 0.5. Ia1 15 Amp N1 Ia1 Eb N 2 E b2 1 N1 E b1 2

N

0.1

0.1

0.4

220V

Rx 220V 0.4

E b1

0.5N1 220 15 0.5 R x 30 N1 205 15

E b2

R x 10.75

28.

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: x 1 t 1 2 x1 t 1 ut x 2 t 2 0 x 2 t 2 x t y t 10 1 x 2 t

(A)

s

s 2 2

2s 2

(B)

s

s 2 2

s 4

(C)

s

s 4 2

s 4

(D)

s

s 4 2

s 4

Key: (D) Exp: Given x 1 t 1 2 x1 t 1 u(t) x 2 t 2 0 x 2 t 2 x t Ax Bu

Transfer function = CSI A B D 1

Here D = 0 C 1 0 1 2 1 A B 2 0 2 1

s 1 2 1 T / F 1 0 s 2 2 2 1 s 2 s 1 2 1 0 2 s s4 s4 2 2s 2 1 0 2 s s4 s4 T/F 2 s s4

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The load shown in the figure is supplied by a 400 V (line to line) 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three watt-meters W1, W2 and W3 read 577.35 W each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

(A) W1 1732and W2 W3 0

(B) W1 0, W2 1732and W3 0

(C) W1 866, W2 0, W3 866

(D) W1 W2 0and W3 1732

Key: (D) Exp: R 3 Y Supply

B

W1 3 load

W2

W3 Y S

N

N

If the switch is connected to Neutral, then each wattmeter will read 1 power. W1 W2 W3 3.Vph .I ph cos 1732.05

VR

cos 0.51agg. 60

V4

Given that, load drawing Apparent power of 3464 VA.

3VL I L 3464

60

IR

30

VB4

3464 IL 5A 3 400 If the switch connected to “Y”, then W2=0

V4

VB I4

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W1 Vpc Icc cos Vpc & Icc VRy I R cos VRy & I R 400 5cos 90 0W

W3 VBy IB cos VBy & IB 400 5 cos30 1732watts 30.

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

Given V1 A1V2 B1I 2 I1 C1V2 D1I 2 V2 A 2 V3 B2 I3 I 2 C 2 V3 D 2 I3 A1 ,B1 ,C1 ,D1 ,A2 ,B2 ,C2 and D2 are the generalized circuit constants. If the Thevenin equivalent

circuit at port 3 consists of a voltage source VT and impedance ZT connected in series, then V A B B1D2 V1 A B B1D2 (A) VT 1 , ZT 1 2 (B) VT , ZT 1 2 A1A2 A1A2 B1C2 A1A2 B1C2 A1A2 (C) VT

V1 A B B1D2 , ZT 1 2 A1 A2 A1 A2

(D) VT

V1 A B B1D2 , ZT 1 2 A1A2 B1C2 A1A2 B1C2

Key: (D) Exp: We can write V1 ,I1 in terms of V3 I3

V1 A1 B1 A 2 B2 V3 I C D C D I 1 2 2 3 1 1 V1 A1A 2 B1C2 V3 A1B2 B1D 2 I3 I1 C1A 2 D1C 2 V3 C1B2 D1D 2 I3

To find Vth or Voc I3 0

V1 A1A 2 B1C2 Vth Vth Voc

V1 A1A 2 B1C 2

To find ISC V3 0

V1 A1B2 B1D2 ISC ISC To find R th R th

V1 A1B2 B1D2

VOC A1B2 B1D2 ISC A1A2 B1C2

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The circuit shown in the figure uses matched transistors with a thermal voltage VT 25mV. The base currents of the transistors are negligible. The value of the resistance R in k that is required to provide 1 A bias current for the differential amplifier block shown is ______.

Key: 170 to 174 Exp: R

VT IC1 ln ; IC2 IC2

IC1 1mA;IC2 1A R 32.

25 103 1 103 ln 172.7k 6 1 106 1 10

The figure below shows an uncontrolled diode bridge rectifier supplied form a 220 V, 50 Hz 1-phase ac source. The load draws a constant current Io 14A. The conduction angle of the diode D1 in degrees is___________.

Key: 220 to 230 Exp: Average reduction in output voltage due to Ls

Vo 4f s Ls Io 4 50 10 103 14 28V

Vm cos cos for a diode, 0 V Vo m 1 cos 220 2 28 1 cos 44.17o conduction angle of diode 180 224.17 o Vo

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t

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81

dy 5ty sin t with y 1 2 . There exists a dt unique solution for this differential equation when t belongs to the interval (A) (-2,2) (B) (-10,10) (C) (-10,2) (D) (0,10) Key: (A)

33.

Consider the differential equation

sin t dy 5t 2 y 2 is a first order linear eq. dt t 81 t 81

Exp: D.E is

5t

I.F = e

2

t 2 81dt

5

e2

ln t 2 81

t 2 81

5/2

Solution is y t 2 81

t y

2

5/ 2

81 .sin tdt

5/ 2 3/ 2 sin t 2 t 81 t 2 81 sin tdt c t 81 2

3/2

t

2

81

5/2

C

t

2

81

5/2

If t 9,9 then the solution exists. Options (b), (c), (d) contain either -9 or 9 or both. So answer is option A 34.

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

Key:

548 to 552

Exp:

145V

150A

Grid

Ra

0.1

E g1

0.1

E g2

800 rpm

1000 rpm E g2 Ia 2 0.1 145

E g1 150 0.1 145 E g1 160V N E g constant N 2 E g2 N1 E g1 E g2

150A Grid

Ra

145V

200 145 Ia 2 0.1

55 Ia 2 0.1

Ia 2 550 amps

1000 160 200 volts 800

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

3

Key: 3 to 3.1 Exp: To find Vth

5

5 6 10 21 2.1A 10 10 Vth 5 5 2.1 5.5V

5 6V

5V

Vth

To find R th

I

10V

55 2.5 55 The maximum power transferred to R th

R

I

36.

www.gateforum.com

Vth2 5.52 3.025W 4R th 4 2.5

5

5

R th

Let a causal LTI system be characterized by the following differential equation, with initial rest condition dx t d2 y dy 7 10y t 4x t 5 2 dt dt dt Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

(A) 2e 2t u(t) 7e 5t u t

(B) 2e2t u t 7e 5t u t

(C) 7e2t u t 2e 5t u t

(D) 7e2t u t 2e5t u t

Key: (B) Exp: Given causal LTI system d2 y t

7dy t

5dx(t) dt dt dt 2 s y s 7sy s 10y s u x s 5sx(s) 2

Y s X s

10y t ux t

4 5s 5s 4 H s s 7s 10 s 2 s 5 2

Inverse Laplace transform will give h t (impulse response).

2 7 s2 s5 h t 2e2t u t 7e 5t u t H s

17

|EE| 37.

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

Key: (A) 38.

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

(A) 2.5e4t Key: (A)

(B) 5e4t

Exp: at t 0

(D) 5e0.25t

8

I 6 50V

(C) 2.5e0.25t

8

IL O

50 5A 64 5 IL 0 2.5A 2 I

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For t 0

8 32

T

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32

2H

2.5A

L 2 1 Req 8 4

IL 0 bc3 it is a sourcefreeckt i L t I L I L 0 I L e t /T 2.5e 4t

39.

j20 j20 j39.9 j39.9 j20 pu The bus admittance matrix for a power system network is j20 j20 j20 j39.9 There is a transmission line, connected between buses 1 and 3, which is represented by the circuit shown in figure.

If this transmission line is removed from service, What is the modified bus admittance matrix? j20 0 j19.9 j39.9 j20 pu (A) j20 0 j20 j19.9

j20 0 j39.95 j39.9 j20 pu (B) j20 0 j20 j39.95

j20 0 j19.95 j39.9 j20 pu (C) j20 0 j20 j19.95

j20 j20 j19.95 j39.9 j20 pu (D) j20 j20 j20 j19.95

Key: (C) Exp: When the line 1-3 is removed z13 0.05 z31 y13

1 j20, 0.05

y13 y31 0

' y13 Half line shunt susceptance = j0.05 2 y' y11 new = y11 old y13 13 j39.9 j20 j0.05 j19.95 2 y' y33 new = y33 old y13 13 j39.9 j20 j0.05 j19.95 2 j20 0 j19.95 Modified Bus admittance matrix: yBus new j20 j39.9 j20 0 j20 j19.95 pu

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|EE| 40.

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In the system whose signal flow graph is shown in the figure, U1(s) and U2 (s) are inputs. The Y(s) transfer function is U1 (s)

(A) (C)

k1 JLs JRs k1k 2

(B)

2

k1 U 2 R sL

JLs JR U 2 L s k1k 2 U 2 R 2

(D)

k1 JLs JRs k1k 2 2

k1 U 2 sL R

JLs JR U 2 L s k1k 2 U 2 R 2

Key: (A) Exp:

Y s

U1 s U

2

s 0

By Masons gain formula Y s

U1 s

P11 1 L1 L 2

Here P1

1 k1 . k 2 LJ

1 1 R1 Ls 1 1 L 2 . 2 k 2 k1 LJ s 1 k1 . 2 Y s s LJ R 1 1 U1 s 1 . . 1 k k 2 1 L s LJ s 2 k1 T/F 2 s LJ sRJ k1k 2 L1

s 1 , a unit step input is applied at time t=0. s 1 The value of the response of the system at t=1.5 sec is __________. Key: 0.550 to 0.556

For a system having transfer function G s

41.

Exp:

Y s R s

s 1 s 1

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1 s 1 . s 1 s 1 2 Y s s s 1 Apply Inverse L.T Y s

y t u t 2e t u t y 1.5 1 2e1.5 1 0.44626 y 1.5 0.5537

42.

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

Key: 0.65 to 0.75 Exp: For a finite length conductor B at a point P I B o cos 1 cos 2 1 4r

2

P

2

For a given hexagon 4 for a side 3 2 1 2 60o r

60o o

60

3 2 60o

I o I cos 1 cos 2 4r 4 107 1 6 cos 60o cos 60o 4 3 / 2 6.9 107

Total flux density B 6

0.69 107 Tesla

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

Key: 1.21 to 1.23 Exp: Given m 1.22rad 69.958

PC

P 1 sin 1 m 1.5 1 sin 1 41.81 0.729 rad 1.5 Using equal area criterion A1=A2 2

m

Pm0 Pm1 sin d

1

P

max1

2

sin Pm0 d

1.5sin

1.5

Pm sin

Pm =1 Pm0 =1

1 2 m

By solving above integration Pmax1

44.

Pm0 m 1 cos 1 cos m

11.221 0.7297 1.22pu cos 41.81 cos 69.95

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

Za 24.50 j12.75 (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in F ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______. Key: 95 to 100 Exp:

x xe X tan 1 m tan 1 a 90 Rm Ra 15.75 1 12.75 X c tan 1 tan 90 12.5 24.5 12.75 X c 12.75 X c 51.562 tan 1 90 tan 1 38.43 24.5 24.5 12.75 X c 0.793 X c 32.194 24.5 1 Xc 98.87F 2 50 32.194

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x x 1 e , A function f(x) is defined as f (x) where x . Which one of the 2 1nx ax bx, x 1 following statements is TRUE? (A) f(x) is NOT differentiable at x=1 for any values of a and b. (B) f(x) is differentiable at x = 1 for the unique values of a and b (C) f(x) is differentiable at x = 1 for all values of a and b such that a + b = e (D) f(x) is differentiable at x = 1 for all values of a and b. Key: (A) Not matching with IIT key

45.

Exp: Lf 1 1 Lt

f x f 1

x 1 x 1

x 1

Lt

x 1

ex a b x 1

does not exists, for any values of a and b

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

46.

Consider a causal and stable LTI system with rational transfer function H(z). Whose 5 corresponding impulse response begins at n = 0. Furthermore, H 1 . The poles of H(z) are 4

Pk

2k 1 1 n exp j for k = 1,2,3,4. The zeros of H(z) are all at z = 0. Let g[n] = j h[n]. 4 2

The value of g[8] equals ___________. Key: 0.06 to 0.065 Only one of the real roots of f x x 6 x 1 lies in the interval 1 x 2 and bisection method

47.

is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is ________. Key: 10 to 10 ba Exp: a 1, b 2and n 0.001 using bisection method 2

2n 1000 n 10 is the minimum number of iterations 48.

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

Key: 2.05 to 2.13 Exp:

syn. Condencors current‟s supplied both the machines

50 MVAR

1

are same 2624.31 1312.159 Amps 2 As the two motors, supplying reactive power only, the phasor diagaram will be

3

I1 I 2

I1

I2

~

~

A

B

IL

50 106 2624.31 3 11103

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E jIa Xs Vt

I a Xs

E V jIa Xs

Consider magnitudes E2 V Ia Xs E

V Ia XS

E

Vt 2

2

90o

EA

6350.85 1312.159 1

EB

6350.85 1312.159 3

2

2

5038.7 volts

Ia

2414.14Volts

IfA E A 5038.7 2.086 IfB E B 2414.14 49.

The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero). Key: 0.1 to 0.1 3Ef Exp: If Z0 Z1 Z2 3Zn 3 1 0.1 0.2 0.2 3Zn Zn 0.1P.U

3.75

50.

Let the signal x t

1

k

k

k t be passed through an LTI system with frequency 2000

response H , as given in the figure below

The Fourier series representation of the output is given as (A) 4000+4000cos 2000t 4000cos 4000t (B) 2000 2000cos 2000t 2000cos 4000t (C) 4000cos 2000t (D) 2000cos 2000t Key: (C) Exp: Given x t is a periodic signal for which Fourier transform x is to be calculated

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x 2 Dn n n

D n is exponential Fourier series coefficient for x(t) xt

3 2000

1 2000

3 2000

1 2000

2 2000

t

2 2000 1

1 x t t t 2000

Define x t over one period

1 sec; o 2000 rad/sec 1000 1 1 D n 1 e jno t o ; t o To 2000 n D n 1000 1 e jn D n 1 1 1000

Where as To

At n 0,2,4,...........Dn =0

for even values of n 0 i.e., Dn 2000 for odd values of n x 2 D0 D1 2000 D 1 2000 D 2 4000 D 2 4000 ..................] x D3

D1

D1

t

6000 4000 2000

Given x is

D3

2000 4000 6000

x

500

500

Thus the filtered output is

y 2 D1 2000 D1 2000 D1 D1 2000 y 4000 2000 2000 y t 4000cos 2000t ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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The logical gate implemented using the circuit shown below where. V 1 and V2 are inputs (with 0 V as digital 0 and 5 V as digital 1) and VOUT is the output is

(A) NOT Key: (B) Exp: V1 V2 0 0 0 1 1 0 1 1

(B) NOR

Q1 OFF OFF ON ON

Q2 OFF ON OFF ON

Vout 5V 0V 0V 0V

(C) NAND

(D) XOR

Logic Level 1 0 0 0

So, this logic level o/p is showing the functionality of NOR-gate. 52.

A load is supplied by a 230 V, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that 1 kW P 2kW and 1kVAR Q kVAR . A capacitor connected across the load for power factor correction generates 1 kVAR reactive power. The worst case power factor after power factor correction is (A) 0.447 lag (B) 0.707 lag (C) 0.894 lag (D) 1 Key: (B) P Exp: Under worst case, 2 Pmax 2kW 1 Q max 2kVAR Q 1 tan 1 45o P cos 45 0.707lag 53.

The input voltage VDC of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio D of the converter for which the magnitude of the steady state output voltage remains constant at 48 V is 2 3 2 3 (A) D (B) D (C) 0 D 1 5 5 3 4 Key: (A)

(D)

1 2 D 3 3

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Exp: Vdc 32V

Vdc 72V

Vo 48V

Vo 48V

Vo D Vdc 1 D

Vo D Vdc 1 D

48 D 32 1 D 3 D 2 1 D 3 3D 2D

2 D 3 1 D 3D 2 2D

3 5D D

5D 2 2 D 5

3 5

2 3 D 5 5

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

54.

Key:

623 to 627

Exp:

3 , 3 winding T F

//Y per phase representation

6.6 kV

I1

1.1 kV

3

~

I2

3

900 103 78.73 Amps 3 6.6 103 I Iph 2 45.45 36.87o 3

I3

I2

I2 KI 2

900 kVA 0.8

300 kVA 0.6

400 3

6.6 103 45.45 I2 272.7 36 .87 o 1.1 103

300 103 433.01 Amp 3 400 I ph I L I3 433.01 53.13 I3

I3

400 3 433.01 I3 90.91 53.13o 3 1.1 10

I1 I2 I3 I1 360.87 40.91 I1 3 I1 625.05 40.91

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Consider the line integral I C x 2 iy2 dz where z = x + iy. The line C is shown in the figure below.

The value of I is 1 2 (A) i (B) i 2 3 Key: (B) Exp: curve „C‟ is y x dy dx

I x2 i x 1

2

dx idx 1 i

(C)

3 i 4

(D)

4 i 5

1

2

x3 2 2 x dx 2i i 0 3 0 3 1

General Aptitude Q. No. 1 – 5 Carry One Mark Each 1.

Research in the workplace reveals that people work for many reasons_________. (A) money beside (B) beside money (C) money besides (D) besides money Key: (D) 2.

The probability that a k-digit number does NOT contain the digits 0.5, or 9 is (A) 0.3k (B) 0.6k (C) 0.7k (D) 0.9k Key: (C)

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

7 So required probability is or 0.7 k. 10

Find the smallest number y such that y 162 is a perfect cube. (A) 24 (B) 27 (C) 32 Key: (D) 3.

(D) 36

Exp: Factorization of 162 is 2 3 3 3 3

y 162 is a perfect cube y 2 3 3 3 3 Perfect cube For perfect cube 2's & 3's are two more required each.

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4.

After Rajendra Chola returned from his voyage to Indoneisa, he _______ to visit the temple in Thanjavur. (A) was wishing (B) is wishing (C) wished (D) had wished Key: (C) 5.

Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other? (A) Rahul and Murali (B) Srinivas and Anil (C) Srinivas and Murali (D) Srinivas and Rahul Key: (C) Exp:

Srinivas Rahul

Arul Murali

Q. No. 6 – 10 Carry Two Marks Each 6.

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is (A) 2 (B) 3 (C) 4 (D) Cannot be determined Key: (A) Exp: Out of six people, 3 place definitely occupied by right handed people as atleast 2 women are there so these two will sit adjacently. Now as only one seat is left it will be occupied by a left handed man because on right side of this seat is sitting an right handed man.

R m R m

Lw

Lw

R m

?

Therefore, answer should be 2 women.

7.

The expression

x y | x y |

2 (A) the maximum of x and y (C) 1 Key: (B)

is equal to (B) the minimum of x and y (D) none of the above

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Exp: If x y Exp

x y x y 2

y min

If x y Exp

x y y x 2

The expression

8.

x min

x y x y 2

is equal to min imum of x & y

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

(A) P, Q (C) R,S,T Key: (C)

(B) P,Q,T (D) Q,R,S

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

9.

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white, Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes? (A) 21 (B) 18 (C) 16 (D) 14 Key: (D) Exp: As there are 4 people A,G,N,S and 4 colours so without any restriction total ways have to be

4 4 16

Now, Arun dislikes Red and Shweta dislikes white So 16-2=14 ways “The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history.” Which of the following statements best reflects the author‟s opinion? (A) Nationalists are highly imaginative. (B) History is viewed through the filter of nationalism. (C) Our colonial past never happened (D) Nationalism has to be both adequately and properly imagined. Key: (B) 10.

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Electrical Engineering Q. No. 1 – 25 Carry One Mark Each In the circuit shown, the diodes are ideal, the inductance is small, and Io 0. Which one of the

1.

following statements is true?

(A) D1 conducts for greater than 180o and D 2 conducts for greater than 180o (B) D 2 conducts for more than 180o and D1 conducts for 180o (C) D1 conducts for 180o and D 2 conducts for 180o . (D) D1 conducts for more than 180o and D 2 conducts for 180o Key: (A) 2.

For a 3-input logic circuit shown below, the output Z can be expressed as P Z

Q R

(A) Q R

(B) PQ R

(C) Q R

(D) P Q R

Key: (C) Exp:

PQ.Q.QR PQ Q QR Q QR QR

3.

P

PQ

Z

Q QP Q A AB A B

Q

PQ.Q.QR

R

QR

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is 1 4 5 6 (A) (B) (C) (D) 2 9 9 9 49

Key: (A) Exp:

1 2

4R, 5B 59

R

B

5R 5B 1 2

R

5R, 5B B

59

R

49 B

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Here R is red ball, B is black ball

The probability to get a red ball in the second draw is

4.

1 4 1 5 1 2 9 2 9 2

When a unit ramp input is applied to the unity feedback system having closed loop transfer function

C s

R s

Ks b a 0, b 0, K 0 , the steady state error will be s as b 2

(A) 0

(B)

a b

(C)

aK b

(D)

aK b

Key: (D) Exp: Given T s

C s

R s

Ct r t t

Apply L.T to above equations

E s R s 1 T s ess C lt S.E s lt .s. s 0

ess

5.

s 0

Ks b lt 1 s2 s a K lt s a K 1 1 s 0 s 2 as b s 2 s 2 as b s 0 s s 2 as b

aK b

A three-phase voltage source inverter with ideal devices operating in 180o conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is Vdc . The peak of the

fundamental component of the phase voltage is V 2Vdc 3Vdc (A) dc (B) (C) Key: (B) Exp: Fourier series expansion of line to neutral voltage Vao is given by

(D)

4Vdc

2Vs sin nt n 6k 1 n 2V for n 1, Vao s max value Vao

6.

The figures show diagrammatic representations of vector fields X, Y and Z respectively. Which one of the following choices is true?

(A) .X 0, Y 0, Z 0 (C) .X 0, Y 0, Z 0

(B) .X 0, Y 0, Z 0 (D) .X 0, Y 0, Z 0

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Key: (C) Exp: for x Divergence not equal to zero x 0

for y

Divergence 0 t 0 Curl 0

for z

Divergence 0 z 0 Curl 0

7.

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________. Key: 0.9 to 0.9 8.

Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed. (A) uniformly over the entire volume of the sphere (B) uniformly over the outer surface of the sphere (C) concentrated around the centre of the sphere (D) along a straight line passing through the centre of the sphere

Key: Exp:

(B) For a perfect conductor the charge is present only on the surface.

i.e,

Pu 0 inside the conductor E0

The transfer function C s of a compensator is given below.

9.

s s 1 1 0.1 100 C s s 1 s 1 10 The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is (A) 0.1 1 (B) 1 10 (C) 10 100 (D) 100 Key: (A)

10.

The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where is a complex number with non-zero real and imaginary parts.

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For the given circuit, Ybus and Zbus are bus admittance matrix and bus impedance matrix, respectively, each of size 2 2. Which one of the following statements is true? (A) Both Ybus and Zbus are symmetric (B) Ybus is symmetric and Zbus is unsymmetric (C) Ybus is unsymmetric and Zbus is symmetric (D) Both Ybus and Zbus are unsymmetric Key: (D) yt 2 a Exp: YBUS yt a z BUS y bus 1

yt a* yt

11.

A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is (A) 25 (B) 50 (C) 100 (D) 300 Key: (C) Exp: Vo Vm

o

2

2

Q

For one input pulse, Vo has 2 pulses frequency of Vo ripple = 2f supply 2 50 100Hz 12.

Let x and y be integers satisfying the following equations

2x 2 y 2 34 x 2y 11 The value of x y is ________. Key: 7 to 7 Exp:

Clearly x = 3 and y = 4 satisfies the given two equation

x y 7 13.

Consider a function f x, y, z given by

f x, y,z x 2 y2 2z 2 y2 z 2 The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is ________ Key: 40 to 40 f Exp: y 2 z 2 2x at x 2, y 1, z 3 1 9 4 40 x

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For the given 2-port network, the value of transfer impedance Z21 in ohms is_______

Key: 3 to 3 Exp:

V Z21 2 I1

I1

I1

I2 0

I1 2I1 3I1 2 V Z21 2 3 I1 V2 2

15.

I1

2

2

2x

2

I1

4

V1

2

I1

2

2

V2

2I1

The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)

Key: 99 to 101 Exp:

Before initial charge on the capacitor 0 Vc 0 0V Final voltage Vc 10V To find time constant

10 10 5 10 10 R eq ; C 5 R eq

5

5 5

Vc t VC VC 0 VC e t 10 10e t d i C t C C 2e t 5 dt We know that i r i C 2e

5

5

t 5

Instantaneous power p i r 10 2e t 5 20e t 5

Energy transferred pdt 20e

t 5

e t 5 dt 20 100 0 1 100J 1 5 0

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The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T1 and T2 are 90o and 270o , respectively.

The RMS value of the current through diode D 3 in amperes is ________ Key: 0 to 0 Exp: 0A since D2 is OFF and it will not turn ON for R load. 17.

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 100. If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________. Key: 61 to 61 Exp: Given the size of bus is 100*100. so [J]= 100 we have formula for [J] = [2n-m-2] 100= [2n-20-2] total no.of buses ,n = 61 18.

A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to (A) 1500 (B) 1470 (C) 157 (D) 154

Key:

(C)

Exp:

3 4P 400V

S.C.I.M s 0.02 r N r

Rotor flux speed is same as stator flux speed. 120 50 1500 4 2N 2 1500 Ws 157.08 rad sec 60 60 Ns

19.

Two resistors with nominal resistance values R1 and R 2 have additive uncertainties R1 and R 2 , respectively. When these resistances are connected in parallel, the standard

deviation of the error in the equivalent resistance R is 2

R R R1 R 2 (A) R1 R 2

2

2

R R R1 R 2 (B) R 2 R1

2

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2

R R (C) R 2 R 1 R1 R 2

Key:

(A)

Exp:

R eq

www.gateforum.com 2

2

R R (D) R1 R 2 R1 R 2

R1R 2 R1 R 2 2

2

R 2 R 2 R1 R 2 R1 R 2 OR 2

R R R1 R 2 R1 R 2

2

The nominal- circuit of a transmission line is shown in the figure.

20.

Impedance Z 100 80o and reactance X 3300 . The magnitude of the characteristic impedance of the transmission line, in , is _______________. (Give the answer up to one decimal place.) Key: 404 to 408 y 1 Exp: 2 x 2 2 y 6.06 10 4 x 3300 z 100 z0 406.2 y 6.06 104 21.

The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Which one of the following is TRUE about the frequency selectivity of these systems? (A) All three are high-pass filters. (B) All three are band-pass filters. (C) All three are low-pass filters. (D) P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter. Key:

(B)

Exp:

0 rad / samples reprsent lowfrequencies

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rad / samples reprsent highfrequencies Since zeros are located at 0 rad / samples and rad / samples they cannot be high pass and low pass filters. Thus they all replresent band pass filters. The mean square value of the given periodic waveform f t is_________

22.

Key:

6 to 6

Exp: Mean square value

f 2 t

Area under the squarred function Period of the function

16

Area 16 0.7 0.3 4 2.7 0.7 16 8 24 volt second Period 2.7 1.3 4 Mean square value

23.

4

24 6 4

1.3

0.3

0.7

2.7

A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHZ. The frequency of the vertical input is (A) 1.5 kHz (B) 2 kHz (C) 3 kHz (D) 4.5 kHz

Key:

(D)

Exp:

3 9 f r 3 4.5 kHz 2 2

n 3

fy fx

nx ny

ny 2

24.

Let y 2 2y 1 x and x y 5. The value of x y equals _________. (Give the answer up

to three decimal places) Key: 5.7 to 5.8 Exp: y 2 2y 1 x x y 1

x y 5 gives 2y 1 5 y 3 x 4 x y 4 1.732 5.732 ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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If a synchronous motor is running at a leading power factor, its excitation induced voltage E f is

25.

Key: Exp:

(A) equal to terminal voltage Vt

(B) higher than the terminal voltage Vt

(C) less than terminal voltage Vt

(D) dependent upon supply voltage Vt

(B) Higher than the terminal voltage.

Ef

iIa X s V

Ei Ia

Q

Q. No. 26 – 55 Carry Two Marks Each 26.

Which of the following systems has maximum peak overshoot due to a unit step input? 100 100 (A) 2 (B) 2 s 10s 100 s 15s 100 100 100 (C) 2 (D) 2 s 20s 100 s 5s 100 Key: (C)

Exp: Peak over shoot e

12

If 0,peak over shoot 100% Maximum In General If 1 peak over shoot 0% Minimum Here which of the following has ' ' value less, the system will have maximum over shoot. Option „A‟, n 10, 2n 10 0.5 Option „B‟ n 10, 2n 15 0.75 Option „C‟ n 10, 2n 5 0.25 Option „D‟ n 10, 2n 20 1 So, option „C‟ is correct (OR) By Inspection, see all options n cons tan t, 2n varies, so, 2n less means, that system have maximum over shoot. 27.

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab Dbc Dca 1m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in / km (rounded off to three decimal places) is ________ ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India

© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Key: 0.271 to 0.301 Exp: Deq 3 Dab Dbc Dca 1m GMD

DS GMR 0.01m Inductance/phase/m 2 107 ln

Dm 1 7 2 107 ln 9.21 10 H DS 0.01

Inductance/phase/km 9.21104 H Reactance L 2 50 9.21104 0.2892 / km 28.

Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger unit is _______ MW.

Key: Exp:

395 to 405 Assume No – load speed regulations are equal % Speed Reg A x 4% B G

6% F

E

300MW

C D

400MW

H

Power

Power

From similar triangles method A

F

6%

E

x

B D

300

x

G

C

400

B

4%

H

BG AB CH AC

FB AB ED AD

P1 300

A

x 6

P2 400

x 4

P2 100x

P1 50x

Given that P1 P2 600MW 150x 600 x4

The load supplied by largest machine is P2=100×4=400MW

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For the network given in figure below, the Thevenin‟s voltage Vab is

29.

(A) -1.5 V Key: Exp:

(B) -0.5 V

(C) 0.5 V

(A) The equivalent CKT is

10

5

(D) 1.5 V Vth

Apply nodal Vth 30 Vth Vth 16 0 15 10 10 2Vth 60 3Vth 3Vth 48 0

30V

a

16V

10 b

8Vth 12 Vth 1.5V

30.

The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

(A) 1000 samples/s Key: Exp:

(B) 1500 sample/s

(C) 2000 samples/s

(D) 3000samples/s

(B)

500

f cos 1000t

Convolution

x f

500

f

500

500

f

Consider 1 F cos 1000t f 500 f 500 2 Input signal to the LTI system is

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1 x f f 500 f 500 2 1 1 W f f 500 f 500 2 2

If the input signal is defined as w(t) then its Fourier transform can be drawn as follows: f

1000

1000

f

H f

sin 150t 1500 sinc 1500t t f H f rect 1500

Given h f

Y f W f H f has a max frequency 750 HZ

∴ Minimum sampling rate = 1500 HZ

750

f

750

A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance R a 0.02.

31.

When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is (A) 34.2 A (B) 30 A (C) 22 A (D) 4.84 A Key: Exp:

(B) Separately excited d.c. motor 2NT 60 2 900 70 E b Ia 6597 60 6597 Ia ...(1) Eb

Ia

P

V Ia R a E b 220

k

0.02 V 220V

Eb

6597 0.02 E b Eb

220E b 6597 0.02 E 2b By solving above equation

We get E b1 219.39, E b2 0.61 Ia

V E b 220 E b 220 219.39 Ia Ia 30.5 Amps Ra 0.02 0.02

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A cascade system having the impulse responses h1 n 1, 1 and h 2 n 1,1 is shown in the

32.

figure below, where symbol ↑ denotes the time origin.

The input sequence x n for which the cascade system produces an output sequence

y n 1,2,1, 1, 2, 1 is

x n 1,1,1,1

(D) x n 1,2,2,1

(A) x n 1,2,1,1

(B) x n 1,1,2,2

(C)

Key: (D) Exp:

Y1

h(n) h1[n]*h2[n] {1, 0, 1}

Y[n]=h(n)*x(n) Given

y[n] {1, 2, 1, 1, 2, 1} By observation x[n] should be{1,2,2,1}

2000

1000

For the circuit shown in the figure below, it is given that VCE

33.

1000 2000

VCC . The transistor has 2

29and VBE 0.7V when the B-E junction is forward biased.

RB is R (B) 92

For this circuit, the value of (A) 43 Key:

(C) 121

(D) 129

(D)

Exp: Given VCE

Vec 10 5V 2 2

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10 1 I B 4R I B R B 0.7 1 I B .R 10 30I B 4R I B R B 0.7 30I B R 9.3 I B 120R 30R R B 9.3 I B 150R R B

...(1)

10 4 R 1 I B VCE 1 I B R 10 120RI B 5 30I B .R 5 1 ...(2) 150R 30R Substituting equation (2) in equation (1) 1 9.3 150 R B 30R R RB 279 150 B ; 279 150 129 R R IB

34.

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ________ electrical degrees. Key: 12.5 to 12.9 Pa Pm Pe Exp:

60 0 60mw GH 1000 1 180f 180 50 9 10 t 10cycles 0.25sec 50 5 t 5cycles 0.1sec 50

m

2 Pa t 2 60 0.1 . 2.7 1 m 2 2 9 New ratio, 10 2.7 12.7

35.

For the circuit shown below, assume that the OPAMP is ideal.

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Which one of the following is TRUE? (A) vO vS (B) vO 1.5vS Key: Exp:

(C) vO 2.5vS

(D) vO 5vS

(C) At node (1)

Vx

Vs 2R Vs 4R 2

At node (2)

R

Vx Vx Vy 0 R R 2Vx Vy ;

R

Vy

2Vs Vs 2

R

Vy R

V

y

Vx

V

y

Vo

R R V Vs Vs s Vs Vo 0; 2 Vs 3Vs Vo 2 5V Vo s ; Vo 2.5Vs 2

R

3

Vy

2

At node (3)

36.

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Vx

Vo

0

2R 1

Vx

Vs 2R

The root locus of the feedback control system having the characteristic equation

s 6Ks 2s 5 0 where K 0, enters into the real axis at (A) s 1

(C) s 5

(B) s 5

(D) s 5

Key: (B) Exp: C.E s2 6ks 2s 5 0 6ks 1 2 0 s 2s 5 6ks G s 1 2 s 2s 5 s 2 2s 5 1 5 K s 2 6s 6 s dk 5 0 1 2 0 ds s

j 2j

5

1

2j

s2 5 0 s 5

S= 5 it enters

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For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions QA QBQC Q'A Q'BQ'C 100.

The minimum number of clock cycles after which the output Z would again become zero is ________ Key: 6 to 6 Exp: Upper part of the circuit is ring counter and lower part of the circuit is Johnson counter as per the connection established. Outputs of the Ring counter and Johnson counter is given to Ex-OR. Gates, whose output is given to the three inputs OR-gate. Ring counter output Ring counter output

Jonson counter

output

QA

QB

QC

Q1A

Q1B

Q1C

Z

1

1

0 Inital valume

1

1

1

1

1 CP

1

1

1

1

1

2 CP

1

1

1

1

3CP

1

1

1

4CP

1

1

5CP

1

1

6CP

So, output Z will become again 1 after 6 clock pulses.

38.

In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

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(B) 1 F

(A) 1 nF Key: Exp:

(C) 1 mF

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(D) 10 mF

(D) To get the maximum power the load Ckt must be at resonance i.e. imaginary part of load impedance is zero.

1 R 1 jRC R jC ZL jL jL jL 1 1 jRC 1 2 R 2 C2 R jC j term 0 R

R 2 C R 2C C L 5 103 2 2 2 2 2 2 1 R C 1 R C 1 104 C 2 From options C 10mF will satisfy the about equation L

39.

In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is ________. (Give the answer up to one decimal place.)

Key: 39 to 41 Exp: Given is Buckboost converter DVS V0 1 D Given Vs 50V, D 0.6, Vo 75V

Vo Is D 0.6 1.5 Vs Io 1 D 1 0.6 Vo 75 15A R 5 D 3 Is . Io 15 22.5A 1 D 2 Since capacitor is very large, ic 0 Io

i L avg is avg i o avg I L Is Io 22.5 15 37.5A IL

DVS 0.6 50 5A fL 10,000 0.6 103

IL 5 37.5 40A 2 2 Peak current drawn from source is 40A i L peak IL

17

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In the circuit shown in the figure, the diode used is ideal. The input power factor is _______. (Give the answer up to two decimal places.)

Key: 0.70 to 0.71 V Exp: Vor m 2

Vo

Vm 2VS

Vm Vor Vm Ior R 2R 0 2 VS Vm 2 VS 2 2 2 Vor Ior Vor PLoad VS 1 IPF 0.707 InputVA VS Ior VS 2 VS 2

41.

3

Consider the system described by the following state space representation x1 t 0 1 x1 t 0 u t 0 2 x t 1 2 x 2 t x1 t y t 1 0 x 2 t x1 0 1 If u t is a unit step input and , the value of output y t at t = 1 sec (rounded x 2 0 0

off to three decimal places) is_________ Key: 1.280 to 1.287

0 1 Exp: Given A 0 2 0 B 1 C 1 0 s 2 1 s 2 1 0 0 s 1 0 s 1 1 X s SI A x 0 Bu s 2 1 / S s 2s 0 1 s s 2 s

1 s 2 s 1 ; x s s s 2

y s

s s 2 1 s2 s 2

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1 1 1 1 1 1 y s 2 2 s s s 2 s 4s 2s 4 s 2 3 1 1 3 1 1 y l 4 t t4 t e 2t 4 t e 2 4 2 4 4 2 4 y 1 1.2838 42.

A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R1 0.3,R 2 0.3,X1 0.41,X2 0.41. Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3phase AC source is __________.

Key: Exp:

69 to 71 Reactance offered by stator and Rotor will be changes, because of change in frequency. R1

20 0.41 0.13666 60 20 x 2 0.41 0.1366 60 Vph Ist I ph Isc Zeq x1

0.3

R2 0.3

80 v, 20Hz 3

X1

X2

0.4

0.4

Ist Isc

80 3 46.18 0.3 0.3 j 0.1366 0.1366 0.65

71.4 24.46o Amps

A 25 kVA, 400 V, - connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.

43.

Key:

-15 to -14

Exp:

25kVA, 400V, connection Voc 360V

25 103 36.084 Amps 3 400 I ph 20.833 Amps IL

ISC I rated , If 5A Xs Zs E

Voc phase 360 17.28 Isc phase 20.833

V cos Ia R a

2

Vsin Ia Xs 2

400 0.8 0

2

400 0.6 20.833 17.28

2

E ph 341.758 volts 341.758 400 14.6% 400 Hint: Obtained regulation should be negative. % Reg

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If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA. Y transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is_____.

44. Key:

37 to 39

Exp:

25KVA, Y D, 3.3kV N1 : N 2 5 :1

25 103 3 3.3 103 IL Iph 4.374 Amps Ist

Transformer is a constant-Power device

E 2 I2 E1I1 N 2 I2 N1I1 I2

N1 5 .I1 4.374 N2 1

Iph I2 21.869 Amps side IL 3 I2 3 21.869 37.879 Amps

45.

For the balanced Y-Y connected 3-Phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is (A) 33 53.1o

(B) 6053.1o

(C) 60 53.1o

(D) 180 53.1o

Key:

(C)

Exp:

VL 208V, P 432W

cos 0.6 leading P 3 Vph I ph cos 2

208 3 2 0.6 Vph 3 P 3. .cos z ph 60.08 z ph 432 cos 1 0.6 53.1o z ph 60 53.1o z ph

Vph o

I ph 53.1

Vph Iph

53.1o

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A thin soap bubble of radius R = 1 cm, and thickness a 3.3m a R , is at a potential of 1

46.

V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap 4 in the thin bubble is 4R 2a and that of the drop is r 3 . The potential in volts, of the resulting 3 single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.)

Key: Exp:

9.50 to 10.50 Charge must be same 4R 2a P 43 r3 P

r

3

3R 2 a

0.996 103 The potential of thin bubble is 1 V Q 1 4E 0 1 102 Q 40 102 C

Potential of Soap drop Q V 40 r

40 102 40 0.9966 103

10.03V 47.

The value of the contour integral in the complex-plane

z 3 2z 3 z 2 dz Along the contour |Z| = 3, taken counter-clockwise is (A) 18i (B) 0 (C) 14i Key: (C)

Exp:

(D) 48i

z = 2 is the singularity lies inside C : z 3 C

z3 2z 3 dz 2i z3 2z 3 14i z2 z2

(Using Cauchy‟s Integral formula) ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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1 x x 0 x x 1 andf x 2 Let g x x 1, x 1 x , x 0

48.

Consider the composition of f and g, i.e., f g x f g x . The number of discontinuities in f g x present in the interval ,0 is: (A) 0

(B) 1

(C) 2

(D) 4

Key:

(A)

Exp:

1 x, x 1 Clearly fog x 2 is discontinuous at x 1 ,0 x , x 1

The number of discontinuities in (fog) (x) present in the interval , 0 is 0 Alternative Method:

f x 1 x for x 0 and g x x for x < 0

Both f(x) and g(x) are continuous when x < 0 fog x is also continuous for x < 0 (Since the composite function of two continuous functions is continuous)

The number of discontinuities in the interval ,0 i.e., x < 0 is „0‟ 49.

A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 , and the shunt field resistance is 240 . The no load speed, in rpm, is _______________.

Key: 1235 to 1250 Exp:

2A

0.5

0.8

240

0.8

120

240

120

1.5A

6.5

E b1

N Eb

2A

0.5

No load, N1 ?

Eb2 Full load, N2 1200rpm

120 1.5 0.8 N1 E b1 N1 1200 1241.82 rpm N 2 E b2 120 6.5 0.8

50.

A 10 ½ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is _______. Key: 10000 to 10000 51.

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var Y , where var . denotes the variance, equals ICP–Intensive Classroom Program eGATE-Live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparation 65+ Centers across India

© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission.

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7 8

(B)

49 64

(C)

7 64

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(D)

105 64

Key: (C) 52.

The figure below shows a half-bridge voltage source inverter supplying an RL-load with 0.3 R 40 and L H. The desired fundamental frequency of the load voltage is 50 Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. M = 0.6. At 50 Hz, the RL-load draws an active power of 1.44 kW. The value of DC source voltage VDC in volts is

(B) 500

(A) 300 2 Key: (C)

(C) 500 2

(D) 1000 2

0.3 30 z R L jx L 40 j30 50 36.86

Exp: x L L 100 M 0.6 I Load

PL 1440 6A RL 40

VA o1 VA o1 6 z1 50 VA o1 300V rms I Load

VAo1 300 2 V max VAo1 m.vdc 300 2 0.6 vdc Vdc 500 2 The range of K for which all the roots of the equation s3 3s2 2s K 0 are in the left half of the complex s-plane is (A) 0 < K < 6 (B) 0 < K < 16 (C) 6< K < 36 (D) 6< K < 16 Key: (A) 53.

Exp: C.E s3 3s2 2s k 0 If system to be stable K 06 K 0K6

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|EE| 54.

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The eigen values of the matrix given below are 0 0 0 (A)

1 0 0 1 3 4 (0,-1,-3)

(B) (0,-2,-3)

(C) (0,2,3)

(D) (0,1,3)

Key: (A) Exp:

1 0 1 0 Characteristic equation is 0 0 3 4

4 2 3 0 1 3 0 0, 1, 3 are the eigen values 55.

A 3-phase 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25 and 3.925 respectively. If the voltage at the generator terminal is 17.87 kV, the power

factor of the load is ________. Key: 0.75 to 0.85 Exp: PS 3MW Z 3.9329 86.35 ph 17.87 E f 17.32 KV Vt 10317.249 V ph 3 Z 0.25 j3.925 ph E f 10.000 V ph V 17.87 KV t

2 90 86.35 3.65 2

V EV Pog f t sin 2 t ra Zs Zs 10000 10317.249 10317.249 sin 3.65 0.25 3.9329 3.9329 2.3024 2

106

I a Zs

2

E f 2 Vt 2 2E f Vt cos

Ia 131.43 A / ph PS 3MW 3 17.87 103 131.43 cos cos 0.737

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General Aptitude Q. No. 1 – 5 Carry One Mark Each 1.

There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W, Z is to the East of X and the West of V, W is to the West of Y. Which is the building in the middle? (A) V (B) W (C) X (D) Y Key: (A) Exp:

From the given data, the following is formed

X

Z

V

W

Y

N W

East

West

E S

The building „V‟ is in the middle 2.

Saturn is _________ to be seen on a clear night with the naked eye. (A) enough bright (B) bright enough (C) as enough bright (D) bright as enough Key: (B) 3.

Choose the option with words that are not synonyms. (A) aversion, dislike (B) luminous, radiant (C) plunder, loot (D) yielding, resistant Key: (D) 4.

There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is (A) 1/5 (B) 7/30 (C) 1/4 (D) 4/15 Key: (D) 3

Exp:

C2 4 C2 3 C2 12 4 10 C2 45 15

5.

A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have? (A) 12 (B) 15 (C) 18 (D) 19 Key: (B) Exp: x y 20 x MCQ

3x 11y 100 x 15, y 5

y essay type

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Q. No. 6 – 10 Carry Two Marks Each 6.

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm? (A) P (B) Q (C) R (D) S Key: (C) Exp: Region

Air pressure difference

P

0.95 – 0.90 = 0.05

Q

0.80 – 0.75 = 0.05

R

0.85 – 0.65 = 0.20

S

0.95 – 0.90 = 0.05

In general thunder storms are occurred in a region where suddenly air pressure changes (i.e.,) should rise (or) sudden fall of air pressure. From the given contour map in „R‟ region only more changes in air pressure. So, the possibility of a thunder storms in this region. So option (C) is correct. 7.

There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes? (A) The box labelled „Apples‟ (B) The box labelled „Apples and Oranges‟ (C) The box labelled „Oranges‟ (D) Cannot be determined Key: (B) Exp:

The person who is opening the boxes, he knew that all 3 are marked wrong. Suppose if 3 boxes are labelled as below.

(1) Apples

(2) Oranges

(3) Apples & Oranges

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If he inspected from Box(1), picked one fruit, found orange, then he don‟t know whether box contains oranges (or) both apples and oranges. Similarly, if he picked one fruit from box(2), found apple then he don‟t know whether box contain apples (or) both apples and oranges. But if he picked one fruit from box(3), i.e., labelled is “apples and oranges‟, if he found apple then he can decide compulsorily that box(3) contains apples and as he knew all boxes are labelled as incorrect, he can tell box(2) contains both apples and oranges, box(1) contain remaining oranges. So, he should open box labelled „Apples and Oranges‟ to determine contents of all the three boxes. “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”

8.

The author‟s belief that ideology is not as important as literature is revealed by the word: (A) „culture‟ (B) „seemingly‟ (C) „urgent‟ (D) „political‟ Key: (B) X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have (A) 90 digits (B) 91 digits (C) 92 digits (D) 93 digits Key: (A) 9.

Exp:

X 47........... 30 digits Suppose 47 2 2 2 digits in (47)3 3

Similarly 47 contains 30 + 30 + 30 digits = 90 digits. 3

The number of roots of ex 0.5x 2 2 0 in the range 5,5 is

10.

(A) 0 Key: (C) Exp:

(B) 1

(C) 2

(D) 3

f x e x 0.5x 2 2

f 5 10.50; f 4 6.01, f 2 0.135; f 1 1.13; f 0 1, f 1 1.21, f 2 7.38, f 3 , f 4 , f 5 also ve.

As there are 2 sign changes from +ve to –ve and –ve to +ve, two roots will be there in the range [-5, 5].

27