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GATE 2015 Examination-31st Morning

EC: Electronics & Communications Engineering

Duration: 180 minutes Maximum Marks: 100

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symbols used in the test and understand their meaning before you start the examination.

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3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific

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

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

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

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

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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

correct answer. The candidate has to choose the correct answer by clicking on the bubble (⃝) placed before

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11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice

type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in

deduction of 1/3 marks for a 1-mark question and 2/3 marks for a 2-mark question.

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on the admit card and shall follow the same. I also understand that in case I am found to violate any of these

instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the

computer hardware allotted to me are in proper working condition”.

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GATE-2015 SET-A(31st Morning ) GENERAL ABILITY

Q. 1 - Q. 5 carry one mark each

Q.1 If xlog 5/7 1/3 then what is the value of x __________

Sol: 1/3 1/35x 7/5 x

7

3

x 7/5 2.744

Q.2 Principle presented chief guest with ________ as a token of gratitude

(A) Momentum (B) Moment (C) Momento (D) Memento

Sol: (D) Memento is an object kept as a reminder of a person or a event.

Q.3 What is meaning of word “Educe”

(A) Extract (B) Educate (C) Exert (D) Training

Sol: (A)

Q. 4 Question on Frog

Sol: Croak

Q.5 If □ ◇ and are defined as

a b

a ba b

□

a b

a ba b

◇

a b ab

Then calculate the value of 66 6 66 6□ ◇

Sol: 66 6 66 6

166 6 66 6

Q. 6 – Q. 10 carry two marks each.

Q.6 Cube of 3 side unit is constructed using cube of side 1 unit then ratio of no of visible faces 0 to non

visible faces is:

(A) 1: 2 (B) 2: 3 (C) 1: 3 (D) 3: 4

Sol: (A)

Q.7 Question on missing number:

6 5 4

7 4 7 2 1

1 9 2 8 1 2 1

4 1 5 2 3

3 3

3

Sol: (3)

6 4

52

7 4 2 1

72

1 9 2 1 2 1

82

4 1 2 3

52

3 3

32

Q.8 Passage Question:

Tabacusisism as considered rank one of the cause of death:

Ans: B Rank one of the cause

Q.9. Passage Question:

(A) Human program is controlled by environment

(B) Human program is contradicted by environment

(C) Human program and society are linked with environment

(D) None

Q.10. Humpy Dumpty Question:

Humpy Dumpty Sit on wall daily to have lunch. Wall some time fall when one a person sit on it.

Which of the following statement is correct:

Statement-I : The wall will fall when Humpty Dumpty will have lunch on it

Statement-II : The wall will not fall when Humpty Dumpty will have lunch on it

Statements-III: The wall will some time fall when Humpty Dumpty will have lunch on it

Statement-IV: …………..

Statement-IV will be correct.

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

Q.1 - Q.25 carry one mark each:

Q.1 ˆs t m t cos 2 ft m t sin 2 ft is what type of signal where m̂ t is Hilbert Transform

(A) Low pass (B) High pass (C) Band pass (D) DSB-SC

Sol: (C) It is Band pass signal because it is SSB-SC (LSB) and frequency component present is from

c mf f to cf .

Ref: Page-95 class notes of Communication system . Discussed same concept in filter method

Q.2 What is the result of convolution of signal 0x t t t

Sol: 0x t t t

0x t t t

0x t t

Ref: Basic property of Impulse Page-30 Class Notes of Signal&System

Q.3 The polar plot of transfer function

10 s 1G s

s 10

for 0 will lie in which quadrant:

Sol: at 0 G s H s 1

G s H s 10

Answer is 1st quadrant

Ref : Basic Question of Polar Plot discussed same Question in class notes in polar plot

Q.4 Which of the following statement is not true where it is given that z x jy

(A) 2

cz dz value is zero (B) Residue of

2

z

z 1 at z = 1 is 1/2

(C) Conjugate of z i.e. z is analytic (D) None

Sol: (C)

z x jy

du

u x 1dx

dv

v y 1dy

du dv

dx dy here it is not analytic function.

Ref : Discussed many such type of Qs in Maths class as it is basic Question.

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Q.5 If 8 zE 2cos 10 t

2

is in a perfect dielectric medium then calculate value of wavelength in

meter.

Sol: 1 2

2

2 2 meter 8.88 meter

Ref : Exactly same type of many questions in class notes of EMT at page No.72

Q.6 If capacitor is initially uncharged and capacitor is moved from position B to position A then what is

energy taken from the source to change capacitor.

Sol: Energy taken to charge capacitor will be CV2 out of which 1/2 CV

2 will be stored.

0.1 9 0.9 J is energy supplied by battery but energy dissipated by source in capacitor is 0.45 J

Ref : Exactly same Question in Network Assignment Chapter No.2 Question No.16

Q.7 What is the output voltage across Zener diode if it is given that zV 6 volt

Sol: Maximum voltage which can appear across zener is 10

1 5V2 which is not sufficient to make

zener ON, so zener will not be ON & 0v 5 volt So Ans=5 Volt

Ref : Exactly same concept question in EDC class notes at Page No.127

Q.8 Calculate value of resistivity in (–cm) if 16 3

DN 10 / cm 2

n 1800cm /vsec

Sol: D nN e

16 2

19

3

10 1800cm1.6 10 c

cm vsec

1.6 1.8 / ohm.cm

0.3472 cm

Ref : Exactly same concept questions in EDC class notes at Page No.29-30

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Q.9 For the given series RLC Network calculate value of

For the given series RLC Network calculate value of

Sol: R C

2 L

Ref : Exactly same question in Network class Notes at Page No.142

Q.10 In the circuit shown in figure what is the amplitude of sinusoidal voltage (in volt) across capacitor if

it is given that circuit shown is at resonance.

Sol: 4

c 6

1 10V Q.V 10 25V

4 10

Ref : Exactly same concept question in Network class Notes at Page No. 139

Q.11 Negative Feedback in a closed loop control system does not

(A) Reduces overall gain (B) Reduces B.W

(C) Improves distance rejection (D) Reduce sensitivity to

Sol: (B) Negative Feedback reduces gain but Bandwidth is ()

Ref : Exactly same concept question in Analog class Notes at Page No. 151

Q.12 Negative differential resistance is observed in PN junction diode if

(A) Both P & N are heavily doped (B) Only P is heavily doped

(C) Only N is heavily doped (D) An intrinsic Si is inserted b/w junction of P & N.

Sol: (A)

Ref: Basic property of Tunnel Diode which Refer Tunneling in EDC class notes at Page No.125

Q.13 If 2 3f x 1 x x is defined in closed interval [–1, 1]. The value of x in open interval for which

mean value theorem is satisfied is :

(A) –1/2 (B) +1/2 (C) –1/3 (D) +1/3

Sol: (C)

Q.14 If zH cos 25 x cos 303 y cos z

if a 0.08cm, b 0.033cm

Then calculate the mode in waveguide :

(A) TE12 (B) TE21 (C) TM12 (D) TM21

Sol: (B) Since wave is propagating in z direction & Hz is also present so it can be TEmn mode only and no

chance of TMmn.

7

m x

25 xa

m 25 0.08 2

n y

30.3 yb

n 0.033 30.3 1

So Possible mode is TE21 only.

Ref: : Exactly same concept question in EMT class Notes at Page No. 136

Q.15 If x 2y z 1 & 2x 4y 2z k has solutions then what is the value of k ??

Sol 2k 2 0 k 2

Ref : Discussed many such type of Qs in Maths class

Q.16 If 16 K bits are arranged in square matrix of equal rows and columns then for rows address how

many address lines are required for a decoder.

Sol: 1416K 2

So No. of rows = 27

No. of columns = 27

Address lines required for decoder = 7

Ref: Based upon basic concept discussed at Page No. 206 in Digital Class notes

Q.17 The result of addition is stored in which resistor in case of overflow ??

(A) B & H (B) A & F (C) H & F (D) A & C

Sol: (B)

Ref: Based upon definition of Registers in Microprocessors

Q.18 H represents the magn. of field intensity if conductor carries uniform current then magn. of H at

distance of r is .If a current element is on z-axis then what is the relation between H & r.

Sol: I

H2 r

Ref: Discussed same concept in EMT class notes at page No. 48

Q. 19 If A & B are independent events then which statement is NOT correct :

(A) P A B P A P B (B) P A B P A P B

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

Sol: (A)

Ref: General Mathematics

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Q.20 Consider a 4-bit DAC converter. If output voltage (analog) for 0000 and 0001 are 0 volt & 0.0625

volt respectively. What is the value for analog voltage for 1111 ??

Sol. 4

0V 2 1 0.0625

15 0.0625

0.9375 volt

Ref: Exactly same concept question in Digital class Notes at Page No. 183

Q.21 Calculate power of signal

t 2

g t x2

if x(t) is shown in figure.

Sol:

2

22 33 1 0 1 1

3 3 23

Ref: Exactly same concept question in Network class Notes at Page No. 68

Q.22 Calculate value of Am for Delta modulation

Sol: If Sf 20,000Hz, S 0.01Volt

mm t Amcos t mWhere 2000

To avoid slope overload problem

m m s m

0.01 20,000A Sf A

2000

= 0.1/

Ref: Exactly same concept question in Communication class notes at Page No. 208

Q.23 If a given vector P is 3 2 2 2

x y zP x ya x y a x yza check whether vector is sinusoidal or

irrotational??

Sol: 3 2 2 2

x y zP x ya x y a x yza

2 2 2P 3x y 2x y x y 0

P 0 it is solenoidal but not rotational.

Ref: Same Concept question on Page No. 16 in EMT Notes

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Q.24 If s 2

H ss 4

is a phase lead compensator, if R and C are connected in parallel in a series fed

feedback network then what are the values of R & C in sec.

Sol: 1 1

2 & 4RC RC

RC 0.5sec

Ref: Same Q asked in IES paper and discussed in class.

Q.25 If matrix

1

2

3

is Eigen vector of matrix

4 1 2

P 2 1

14 4 10

Then what is the value of P

Sol: P = 17

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

Q.26 Which of the followings represent graph of x 2f x e x x 1

Sol: (B)

Just check by values

f 0 1

f 1 3/e 1.1

Ref: General Mathematics

Q.27 If DI 1mA, Vgs 0.5V &

10.05V

Calculate value of dsr if MOS is in saturation

Sol: 2

D GS T DSI k V V 1 V

2D

GS T

DS

Ik V V

V

ds 2

GS T

1r 20.5k

k V V

10

Ref: Exactly same concept question in EDC class notes at Page No. 305 ( Here is due to channel length

modulation)

Q.28 Differential equation is given as

2

2

d y dy2 y 0

dt dt

y 0 y' 0 1

Then o/p y(t) is

(A) t2 t e (B) t1 2t e (C) t2 t e (D) t1 2t e

Sol: (D)

Ref: Basic Laplace Q discussed many type of Questions.

Q.29 For the circuit shown in figure calculate values of V1 & V2.

Sol: 1 2V 5V V 25V

2 1 1V V V5 & I

4 4

2 1V VI 2I I

4

By solving V1 = 5 volt & V2 = 25 Volt

Ref: Basic KVL dependent questions Many such type of Questions in Network Notes Page 15-20

Q.30 what is the value of Req:

Sol: (R/3)

11

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

Q.31 If built in potential (V0) of an abrupt (P-N) junction is 0.75 volt. If value of junction capacitance at a

Rev. bias (VR) of 1.25 volt is 5 pF. What is the value of Cj in pF when RV 7.25 volt

Sol: 2.5 pF

2

1

R 01

2 R 0

V VC

C V V

2

5 7.25 0.75 2

C 1.25 0.75 1

2C 2.5pF

Ref: Exactly same concept question in EDC class notes at Page No.100

Q.32 What is the value of output voltage V0 :

If input is

Sol: Circuit will be :

Ref: Basic concepts of diode

Q.33 what is the value of Vo if =0.05

12

Sol: 0.25 V& (250 mV)

xV 1 100 0.02

xV 3V

1 xV V 250 1 0.01

2 xV V 250 1 0.01

1 2V V 2.5 1 1

5 5 0.05

0.25V .

Ref: Same Type of Question was given in GATE-2015 test series .

Q.34 If each gate has propagation delay of 20 n sec for how much time output X will remain high if ACB

is changed from 001 to 110 at t = 0

Sol: 40 n sec

For t < 0

13

A B C O / P

0 (1) 0 X 0

1 0 (1)

Ref: Exactly same concept question asked in IES Exam.

Q.35 O.L.T.F is

kG s

s s 1 s 3

for unity negative feedback system. What is the value of k(>0) at

which root locus crosses the imaginary axis

Sol: k = 12

1 G s H s 0

k1 0

s s 1 s 3

3 2s 4s 3s k 0

3

2

1

0

s 1 3

s 4 k

12 ks 0

4

s k 0

To cut imaginary axis 12 k

0 k 124

Ref: Very easy questions /exactly same concept many questions

Q.36 For a –ve f/b system if root locus satisfies the condition that it has s 1 2j roots then calculate

value of k.

Sol: If

2

k s 2G s , H s 1

s 8 s 9

Make G s H s 1

k 25.54

Or can be solved by use of characteristic equation also.

Ref: Easy basic Question

Q.37 For the given circuit calculate value of cV t at t = 1 sec.

Sol: By Thevenin-theorem

14

Here cap. Is charging

So t /

cV t 4 1 e

Here RC 1sec

1

cV 1 4 1 e

Ref: Exactly same concept question in Network class notes at Page No. 210

Q.38 For the discrete system shown in figure .Poles of system are located at :

Sol: 2 11 5X z z Y z z Y z Y z

6 6

1 2

Y z 1

5 1X z1 z z

6 6

2 2

2

z z

5 1 1 1z zz z 2 36 6

Poles are located at 1 1,2 3

Ref: Exactly same concept question in Signal class notes at Page No. 271

Q.39 For the given circuit calculate value of 0 and relation between R1 & R2.

Sol: 0

1

2RC & 1 2R 4R

15

Frequency of wein bridge is 0

1

RC but here Time constant is doubled so frequency becomes

halved 0

1

2RC

1

1z 2R 2 R jR

j C

2

1 R 1R 2 R

2j C 2 jz

1 R jRR

2j C

2

1 2

z 1

z z 5

Now A = 5 1

2

R1 5

R

1 2R 4R

Ref: Exactly same question in Analog class notes at Page No. 187

Q.40 For the circuit shown in figure plot ID V’s Vss :

16

Sol: Now DS GS TV V V hence MOS will be in saturation.

2

D GS TI k V V

2

DS Tk V V 2

DD SS Tk V V V

2

D DD T SSI k V V V

Ref: Question is bit new But by using concept of Page No. 291in EDC class notes it can be done easily.

Q.41 If zE 24 cos t X a V/m then calculate the total average power across a square plane of

10cm 10cm which lies on X + Y = 1 is __________

Sol:

22

2mav x

24EP a W/m

2 240

x y2a a

ds 100cm2

2 4 2

total

24 100 10 mP

240 2

324 10

Watt2

Ref: Exactly same question in GATE -2015 test series

Q.42 What is the magnitude of value of E2

Sol: P jw ( jw ) =0

0 o

0 0

0 0

P jw (0 jw ) jw (1 2j)

2w

w

17

0

0

1 2

t 2

i 1 2

E 21

E

Here

0 0

0 0

PZ Z

t t t t

t i

E E e But E E e

whereE E 10V / m

Here z=0.1 meter and α can be calculated from above equation

Q.43 1 2

2 4

A 1 1 1 a

B 1 W W b

C 1 W W c

2 1

2 4 2

P 1 1 1 1 0 0 A / 3

Q 1 W W 0 W 0 B / 3

R 1 W W 0 0 W C / 3

(A) b a c (B) b c a (C) c a b (D) c b a

Sol: C

Ref: Basic Question based upon DFT property discussed in Signal class notes Page 196

Q.44 A system has zeros origin in multiple of 4 and following pole pattern is shown in figure, which of the

option is correct according to system pole-zero location. (2 Mark)

This pole-zero location is in z-plane of system the impulse response of system is h[n] if h[0] = 1 then

(A) h[n] is real for all ‘n’ (B) h[n] is imaginary for all n

(C) h[n] is real for even n (D) h[n] is imaginary for odd n

Sol: C

Calculate transfer function 4

2 2

zH(z)

(z 0.25)((z 0.25)

Then divide it then only even values will exit.

Ref: Similar type of Q was asked in IES paper and is available in assignment and was discussed in class.

Q.45 If f a,b,c ab bc ca then f f a,b,c , f a,b, c ,c can be implemented by

(A) NAND gate (B) NOR gate (C) 3 i/p XOR gate (D) 3 i/p NOR gate

Sol: C

18

Let W f a,b,c where W f a,b,c

X f a,b, c

Z c

W ab bc ca 3,5,6,7

W 0,1,2,4 c 1,3,5,7

X 2,4,6,7

So 0,1,2,4 , 2,4,6,7 , 1,3,5,7

2,4 7 1

1,2,4,7 a b c

Q.46 For the circuit shown in figure if TV 26mV at T 27ºC calculate the value of V1 – V2 at 50ºC.

(2 Mark)

Sol: Since base and collector are connected so it will work like a diode.

Value of TV at 50ºC T

313V 27mV

11600

2 1

T T

V V

V V

0 080 I e &16 I e

1 2

T

V V

V 1 2

T

V V1e & n 1/5

5 V

Ref: Based upon basic concept of diode

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Q.47 If P X 0 0.2 and P X 1 0.8 what is the probability that X = 1 is transmitted and Y = 0 is

received.

Sol: 0.8 1/ 7

P Y 0/X 10.2 6 / 7 0.8 1/ 7

0.8

0.42

Ref: Same Concept question on Page No.250 In communication class notes

Q.48 One question was based upon TDM

In GSM-8 users share the B.W of 200 KHz by TDMA if no. of Simultaneous as calls the base station

receiving are 12, what is minimum possible B.W

Sol: 200KHz

Ref: Based upon FDMA and TDMA concept of GSM

Q.49 Given the Ellipse 2 2x 4y 1 .

Calculate the maximum area of rectangle lies inside the Ellipse such that rectangle vertices lie on the

Ellipse.

Sol: (1)

area of Rectangle A 4xy

21 1A 4 x 1 x x

2 2

For Maxima or Minima dA

0dx

A 1

Q.50 What is the value of maximum power delivered to Load in Watt ??

20

Sol: 1st calculate VTh & ZTh :

OC

4 0º j2 8 90ºV

2 j2 2 2 45º

ThV 2 2 45º

Th

2 j2 j2Z 2 || j2

2 j2 1 j

2

Th

j2 1 jZ j j 1 j

2

2

2 2I

1 2 1

2

LP I R

2

2 2 8 22

4 2 2 4 2 2

Ref: Same Q with little change in values was asked in GATE 2015 Test series.

Q.51 If

IP

Kk

sG s H s

s s 1 s 2

Then what is the condition for stability

Sol: IP

Kk 0

2

Ref: Basic Question on RH criterion .

Q.52 Probability of zero transmission is 1/3 .Probability Density function when zero is transmitted is

uniform from -3 to +1 and Pdf when one is transmitted is uniform from -1 to +5 .what is the

minimum probability error of received signal:

(A) 1/4 (B) 1/6 (C)1/9 (D)1/12

Sol: (B)

Ref: Same type of Q has been asked in GATE exam in previous year so discussed in class.

Q.53 For the given system

cx t m t cos t

where c 2400 rad / sec

21

Here m(t) has maximum frequency ‘W’ Hz.

If 2y t 10x t 2x t and y(t) is passed through a band pass filter whose frequency response is

shown and output is z(t). If output z(t) has value 10 x(t) only then W shd be strictly less than _____

Sol: 350

Since m(t) has maximum frequency (W)

O/P y(t) will have following +ve frequency

O/P requires only y t 10x t

So 2W 700 W 350

Q.54 Calculate value of Diffusion Current Density of holes if V F.bias 308mv

19q 1.6 10 C

2 2

p nD 35cm /sec D 40cm /sec

2 2

n p3800cm /vsec 1000cm /vsec

p n 1 sec

16 3 14 3

D AN 10 /cm & N 10 /cm

Sol. T

V2

p i V

p

D p

q D nJ e 1

N L

where 2

P p pL D

Ref: Concept and formula is derived at Page No. 89 in EDC class notes

END OF THE QUESTION PAPER