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GATE 2015 Examination-31st After Noon

EC: Electronics & Communications Engineering

Duration: 180 minutes Maximum Marks: 100

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GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions.

Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject

specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark

each, while question numbers 26 to 55 are of 2-mark each.

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examination will stop automatically at the end of 180 minutes.

7. In each paper a candidate can answer a total of 65 questions carrying 100 marks.

8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type.

9. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the

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computer hardware allotted to me are in proper working condition.

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GATE-2015 SET-A(31st After Noon ) GENERAL ABILITY

Q.1 AWKWARD word is nearest to the word:

Sol: Word AWK word means Hard to deal with or person who causes inconvenience

Q.2. What is adverb of word misogyny?

Sol: Misogyny is a noun and its adjective is misogynous and adverb should be misogynously.

Q.3 One Q based upon Grammar correction on sentences:

Q.4 Consider the following statements:

(I) All film stars are singers

(II) All film directors are film stars.

Conclusions:

(I) All film directors are singers.

(II) Some film stars are film directors.

Which of the following is true?

(A) Conclusion (I) is possible

(B) Conclusion (II) is possible

(C) Conclusion (I) and (II) is possible

(D) Neither Conclusion (I) nor Conclusion (II) is possible

Sol: C

Q.5 If a2+b

2+c

2=1, then the value of ab+bc+ca will lie in the interval ?

Sol:

2 2 2 2a b c a b c 2 ab bc ac

2

a b c 1 2 ab bc ca

2

a b c 0

So ab bc ca 1/ 2

using AM GM in equality

2 2

2 2a b a b2

2 2a b 2ab

Similarly 2 2b c 2bc

2 2c a 2ac

2 2 22 a b c 2 ab bc ca

ab bc ca 1

Here it will lie in range 1/ 2, 1

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Q. 6 A tiger is 50 leaps of its own behind the deer as it starts chasing it. Tiger takes 5 leaps per min as

compared to 4 leaps per min of the deer. If the tiger covers a distance of 8 m in one leap while deer covers

5m in one leap, than how much distance tiger needs to run in order to catch the deer?

Sol: 2000 meter& Time will be 50 minute.

Q.7 Dhoni as well as his team member ___ present at occasion.

(A) was (B) were (C) has (D) have

Sol: (A)

In other words, when as well as is part of the subject, the verb must agree with the noun before as well as.

Q.8 A man travel along the steam in 5 hours and take 10 hours to travel same distance in

opposite direction to stream. The velocity of man in steady stream in meter/sec is___

Sol: 3.33

Q.9 Ram and Ramesh attends interview for two vacancies in same department, Ram has probability of

selection of 1/6 and Ramesh has 1/8, The probability of selection of either of them in interview is ___

Sol: 1/4

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GATE-2015 SET-A(31st After Noon) ELECTRONICS AND COMMUNICATION ENGINEERING-EC

Q. 1 A system is quantized with uniform quantization. If the SNR for quantization is 31.8 dB, then find the

number of levels of quantization.

Sol: L = 32 It is not mentioned what type of message signal so assume that it is sinusoidal signal

SNR in dB 1.76 6n 5n 5 L 2 32

Ref: Exact same concept Question on Page-196 class notes of Communication system.

Q. 2 If the transfer function of open loop second order system is G(s)=K/s(s+10), then what will be the

value of K for =0.25?

Sol:

kG s

s s 10

21 G s 0 s 10s k 0

n n2{ 10 200

2nk 400

Ref: Exact many same concept questions discussed. Very easy question

Q. 3 X and Y are two random variables. If P(X=0) = p and P(Y=0) = q, then what will be the probability of

P(X+Y>=1)?

A. (1-p)(1-q) B. 1-pq C. pq D. 1- (1-p)(1-q)

Sol: P X Y 1 1 P X Y 1

only one case is left

X 0 & Y 0

So P X Y 1 pq

P X Y 1 1 pq

Ref: Exact same concept Question has been asked in GATE exam and so discussed in class.

Q.4 In the network shown below, find the value of voltage across capacitor. (1)

Sol: 2 2 2

c100 80 V 40

cV 100 volt

Ref: Exact same concept Question on Page-58 class notes of Network Theory

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Q.5 For a source free medium in vacuum, if the value of electrostatic potential is = 2x2+y2+cz2, what will be the value of c?

Sol: 2 2 22x y cz

x y zE 4x a 2ya 2cza

E 0

4 2 2c 0 2c 6 c 3

Ref: Exact same concept Question on Page-17 of Electrometric Theory Class Notes

Q.6 In the figure shown, both the transistors shown are in active region with VBE=0.7V. Find the voltage

gain.

Sol: Base and collector are connected so that it work like on diode.

o ov 0 0.7 v 0.7

i iv 0 0.7 v 0.7

So o

i

v1

v

Ref: Bit New Question But question on similar concept was given in test series.

Q. 7 Find the solution of this differential equation. dy 1 cos 2y

dx 1 cos 2x

Sol:

2

2

dy 1 cos 2y cos y

dx 1 cos 2x sin x

2 2sec y dy cosec x dx

tan y cot x c

tan y cot x c

Ref: Basic Question

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Q. 8 Two capacitors of 1F and 3F are initially charged to 3V and 1V as shown in the figure. Find the total

energy dissipated in the circuit at t= 2sec if the switch is closed at t=0. (2)

Sol:

at t 0 , switch is closed

Then

1 2c R c

V V V 0

Taking Laplace transform;

1

2

1 31 1I s 10 I s I s 0SC S SSC

+

1 1 2I s 10 0

SS 3S

3 30.3S 1 2

I s3S S

4 90S 2

I s3S S

6

I s4 90S

6 / 90

I s4 / 90 S

t2/451

I t e15

4/451

i 2 e15

Power dissipated in 10 resistor at (t = 2) is 2

i 2 R

2

4/451 e 1015

0.0372 Watts

Ref: Same concept was discussed on Page-17 in Network theory Notes.

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Q. 9 What will be the voltage across the capacitor Vab in the steady state?

Sol:

When sinusoidal i/p is given then for steady state o/p take phasor representation.

3 3 36

15 0 10 2 10 j 5000 10 I

j 5000 10

+ 5

35 0 3 10 5j 200j I 5

abV 200jI

Ref: Same concept Qs were discussed on Page-40 in Network theory Notes

Q. 10 If X(z) is the z transform of x[n] and X(z)=2/z(z2-1)

2, then what will be the value of x[2]?

Sol:

22

2X z

z z 1

2 2

2X z

z z 1 z 1

2

4 2

2

z z 1 z

22

5

21 z

z

2 3 42 2 2 2

5

2 32 2x 3x 4 2x 3x 4x 51 2z z z z

z 2 3 4

As no coefficient of z2

exists so x 2 0 .

Ref: Same concept Qs were discussed on Page-264 in Signal&System class notes

Q. 11 Find the value of sin 4 t

I 12cos 2 t dt4 t

Sol: sin 4 t

I 12cos 2 t dt4 t

6

I sin 6 t sin 2 t dt4 t

sin 6 t sin 2 t6 dt 6 dt

4 t 4 t

sin 6 t sin 2 t

1.5 dt 1.5 dtt t

But sin x

dxx

dx

6 t x dt6

8

So sin x dx

6x 6

So I 3

Ref: Many Qs on same concept were discussed on Page-162 in Signal&System class notes

Q. 12 Find the value of

Sol: Z Z

2

Re z which is not analytic function hence this value should be zero

Q. 13 Find the Nortons Equivalent resistance in the circuit ?

Sol:

v 4I v v

1 02 2 4

2 v 4I 2v v 4 0

5v 8I 4 0 and I v/4

v5v 8 44 3v 4

v 4/3 Th4

R3

Ref: Many Qs on same concept were discussed on Page-87 in Network theory class notes

Q. 14 The two-sided power spectral density of white noise with mean zero is given as No/2. If it is passed

through the filter with impulse response h(t), then find the variance at the output.

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Sol:

0xx

N

2 & E[y] E[x]. h t dt 0

yy xxR R h t h t

Here 0xxN

R (t)2

z(t)= h t h t h h t d

Then yy xxR R h t h t

3

2

0

z 0 h d A d

2z 0 A 3

2 2yy 03

R 0 A N E Y2

2

2

2 2

YE Y Y E Y

= 2 0

3A N

2

Ref: Concept and formulas are discussed on Page No. 35 in Random variable class notes

Q. 15 When the switch is connected to input A, the output is VOA, while when the switch is connected to

input B, then the output is VOB, then what is the value of VOB/VOA ?

Sol:

For calculation of VOB :

OB1

V 1 5 6v1

Similarly OA1

V 1 5 4v1

So OB

OA

V1.5

V

Ref: Exactly same type of Qs were discussed on Page No. 217 in Analog class notes

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Q. 16 In the given figure, n-type silicon material is having doping concentration of 1016

/cm3 and mobility

n=1000cm2/Vs. It is connected to a battery of 10V as shown in the fig, find the time taken by the carriers (

in s) to move from one side to other of the material.

Sol: 3210

E 10 v / m10

So 2 31000cm 10 v

v Ev sec meter

4v 10 cm/sec

410 cm

d v 1cmsec

410 sec 100 sec

Ref: Exactly same type of Q was discussed on Page No. 34 in EDC class notes

Q. 17 A MOS Capacitance is having the width of the oxide layer as 10nm while the width of the

depletion layer is 100nm. If the ratio of the relative permittivity is si

ox

=3, then find the value of maximum

capacitance to the minimum capacitance.

Sol: si02ox

ox

C (max)t

si02 si

oxmin ox D

si02 si

ox

t dC C seriesC

t d

sio2 siminsi02 ox si

Cd t

max si02 ox si

min si ox

C d t

C t

si02

ox si

d1

t

10 1

1100 3

310 3.1

300 3 = (1.03)

Ref: Exactly same concept was discussed on Page No. 318 in EDC class notes

Q. 18 For a unit step input, y(t)= t2

1 e cos 3t63

then find the transfer function for the system.

Sol:

Compare with equation

n t

2

eC t 1 sin dt

1

t21 e sin 3t33

dw 3 60

cos 0.5 here n 2

11

Second order transfer function is 2

n

2 2

n ns 2 s

24

s 2s 4

Ref: Based upon very basic equation of control system

Q.19 An electric field is given as : j(wt z)x yE a j2 a e

then what type of polarization it has ?

Sol: Left Hand Elliptical polarization

Ref: Exactly same type of Question were discussed on Page No. 90&91 in EMT class notes

Q.20 If an electric field is given by 0x yE 2cos(wt z) a 5cos(wt z 90 ) a

then what type of

polarization it has ?

Sol: Right Hand Elliptical polarization

Ref: Exactly same type of Question were discussed on Page No. 90&91 in EMT class notes

Q.21 Two antenna are placed along X and Y axis carrying currents 900 out of phase with a

frequency 3 GHz. The distance between the two antennas to have a maximum field at 600 is ?

Sol: dcos Here 2

0 dcos60 d 5cm2 2

Ref: Exact formula and concept was discussed on Page No. 166 in EMT class notes

Q.22 An air filled rectangular wave guide have cut off frequency 6 GHz for TE10 and 15GHz for TM11.

The cut off frequency for TE01 is ____________GHz.

Sol: 13.75 GHz

Ref: Very easy question many discussed such type of Qs

Q.23 A fair coin is tossed until two consecutive head show up. If X denotes number of times

coin is tossed then the expectation of X is __________?

Sol: N

i i

i 1

E[X] x p(x ) 1 0.5 2 0.5 1.5

Ref: Exact formula and concept was discussed on Page No. 12 in Random variable class notes

Q.24 In case of Schmitt Trigger if 2 1R 20k R ? & HV 500mV and satV 5V

Sol: 2 satH1 2

2R VV

R R

1

2 200.5 5

20 R

1R 380k

Ref: Exact formula and same type of Q was discussed on Page No. 264 in Analog class notes

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Q.25 If f x, y,z xyz x zy xy z xyz write in POS form.

Sol: F x, y,z (x y z)(x z y)(x y z)(x y z)

Ref: Very basic Q

Q.26 In the Circuit (voltage regulator) If inv 20 20% and op-amp is ideal find the maximum power

dissipated in the transistor.

Sol: Power = CE CV I Here CEV 24 10 14V

I ' 0.4mA CI 200.4mA .

Ref: The same type of Q is asked in GATE exam.

Q.27 If F.B. diode then DV 0.7V otherwise diode is ideal then what is the value of I = ?

Sol: Since it is Wheat stone bridge

1 9

I9 6

90.6mA

15

Ref: Exactly same concept question in Network class notes at Page No.13-15

Q.28 21

G sMs Ns k

G j G j

Values of M, N & k ?

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Q.29 In a LC tank ckt, if element L has internal resistance R, then what is the resonant frequency ?

(A) 21 R L

1CLC

(B) 21 R C

1LLC

(C) 2

1 L1

R CLC (D)

2

1 C1

R LLC

Sol: (B)

Ref: Exactly same concept question in Network class notes at Page No.149

Q.30 y" y' 6y x If the system is neither causal nor stable then calculate value of h(t) = ?

Sol: 1 1 1

H s5 s 2 s 3

3t 2t1 1

e u t e u t5 5

Ref: Exactly same concept question in Signal&System class notes at Page No. 243

Q.31 0 1 1

x x u0 3 0

& y 0 1 x Find the transfer function

Sol: 1

H s c SI A B

s 3 1 10 1

0 s 0s s 3

= 0

Ref: Basic Q

Q.33 Which of following functions cannot be derived by cascading, adding or subtracting ?

(A) 1 2G s G s (B)

1

2

G s

G s

(C)

1 21

1G s G s

G s

(D)

1 2

1

1G s G s

G s

Sol: (B)

Ref: Basic Q

Q.34 1 2x n x n

1 2y k x k x k

3x 2 ?

Sol:

Q.35

10 5 j

A x 20

10

Find the value of x so that sum of all Eigen values is real.

Q36. Which of the commands can change the contents of the accumulator ?

(A) MOV B, C (B) MOVI B (C) PCHL (D) SBI 01 H

Sol: (D)

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Q.37 If the magnitude and phase of Fourier series coefficients L is as following;

Then the signal x(t) will be :

(A) Purely Imaginary (B) Real (C) Complex (D) None

Sol: (B) je 1 so x(t) will be real

Ref: : Exactly same concept question in Signal&System class notes at Page No. 121

Q.38 Find MOD of given counter:

Sol: It should be 0110 So it should be MOD-6

Ref: : Exactly same concept was discussed in Counter class notes

Q.39 Find mode of counter (Binary up counter)

Sol: it should be MOD-4 counter

Ref: : Exactly same concept was discussed in Counter class notes

Q.40 Design a 1 8 demultiplexer using 2 (1 4) decodes :

NOTE: The questions are based on memory and feedback of the students who given exam. We are not

responsible for any mistake in Questions. Because paper is purely based upon student feedback.