ec20084q

22
8/13/2019 EC20084Q http://slidepdf.com/reader/full/ec20084q 1/22  Correspondence Programme  Classroom Programme  All India Mock Test Series  Postal Test Series  Online Test Series  Online Classroom Progr Head Office : A/114-115, Bhilai – 490 020 (C.G)  For Details Contact : 0788-4034176 +91-97131-13156, +91-93026-97686 Branch Office : Bangalore (Karnataka)  For Details Contact : +91-97138-85449, +91-99169-39408 Electronics & Communication 200 lectronics & Communication 200 lectronics & Communication 200 lectronics & Communication 2008 Q.1 to Q.25 carry one mark each Q.1. All the four entries of the 2 2 ×  matrix = 22 21 12 11  p  p  p  p P  are nonzero, and one of its eigenvalues is zero Which of the following statements is true? (A) 11 22 12 21 pp p p 1 =  (B) 11 22 12 21 pp p p 1 = −  (C) 11 22 12 21 pp p p 0 =  (D) 11 22 12 21 p p p p 0 + =  Q.2 The system of linear equations 7 2 4  = +  y  x  6 2  = + y  x  has (A) a unique solution (B) no solution (C) an infinite number of solutions (D) exactly two distinct solutions Q.3 The equation sin (z) = 10 has (A) no real or complex solution (B) exactly two distinct complex solutions (C) a unique solution (D) An infinite number of complex solutions Q.4 For real values of x, the minimum value of the function () exp( ) exp ( )  f x x x = +  is (A) 2 (B) 1 (C) 0.5 (D) 0 Q.5 Which of the following functions would have only odd powers of  x in its Taylor series expansion about the point  x = 0 ? (A) 3 sin ( )  x  (B) 2 sin ( )  x  (C) 3 cos ( )  x  (D) 2 cos ( )  x  Q.6 Which of the following is a solution to the differential equation () 3 () 0? dx t  x t dt + =  (A) 1 () 3  x t e =  (B) e  x 3 2 ) (  =  (C) 2 2 3 ) (   x  =  (D) 2 3 ) (   x  =  Q.7 In the following graph, the number of trees (P) and the number of cut-sets (Q) are (A) P = 2, Q = 2 (B) P = 2, Q = 6 (C) P = 4, Q = 6 (D) P = 4, Q = 10

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Page 1: EC20084Q

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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Progr

Head Office A114-115 Bhilai ndash 490 020 (CG) For Details Contact 0788-4034176 +91-97131-13156 +91-93026-97686Branch Office Bangalore (Karnataka) For Details Contact +91-97138-85449 +91-99169-39408

EEEElectronics amp Communication 200lectronics amp Communication 200lectronics amp Communication 200lectronics amp Communication 2008888

Q1 to Q25 carry one mark each

Q1 All the four entries of the 22times matrix

=

2221

1211

p p

p pP are nonzero and one of its eigenvalues is zero

Which of the following statements is true

(A)11 22 12 21

p p p p 1minus = (B)11 22 12 21

p p p p 1minus = minus

(C)11 22 12 21

p p p p 0minus = (D)11 22 12 21

p p p p 0+ =

Q2 The system of linear equations

724 =+ y x

62 =+ y x

has

(A) a unique solution (B) no solution

(C) an infinite number of solutions (D) exactly two distinct solutions

Q3 The equation sin (z) = 10 has

(A) no real or complex solution (B) exactly two distinct complex solutions

(C) a unique solution (D) An infinite number of complex solutions

Q4 For real values of x the minimum value of the function ( ) exp( ) exp( ) f x x x= + minus is

(A) 2 (B) 1 (C) 05 (D) 0

Q5 Which of the following functions would have only odd powers of x in its Taylor series expansion aboutthe point x = 0

(A) 3sin ( ) x (B) 2sin ( ) x (C) 3cos ( ) x (D) 2cos ( ) x

Q6 Which of the following is a solution to the differential equation( )

3 ( ) 0dx t

x t dt

+ =

(A) 1( ) 3 x t eminus= (B) t et x 32)( minus= (C) 2

2

3)( t t x minus= (D) 23)( t t x =

Q7 In the following graph the number of trees (P) and the number of cut-sets (Q) are

(A) P = 2 Q = 2 (B) P = 2 Q = 6 (C) P = 4 Q = 6 (D) P = 4 Q = 10

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Head Office A114-115 Bhilai ndash 490 020 (CG) For Details Contact 0788-4034176 +91-97131-13156 +91-93026-97686Branch Office Bangalore (Karnataka) For Details Contact +91-97138-85449 +91-99169-39408

Q8 In the following circuit the switch S is closed at t = 0 The rate of change of current (0 )di

dt + is given by

(A) 0 (B) L

I R ss (C) L

I R R ss )( + (D) infin

Q9 The input and output of a continuous time system are respectively denoted by )(t x and )(t y Which of

the following descriptions corresponds to a causal system

(A) )4()2()( ++minus= t xt xt y (B) ( ) ( 4) ( 1) y t t x t = minus +

(C) )1()4()( minus++= t xt t y (D) ( ) ( 5) ( 5) y t t x t = + +

Q10 The impulse response )(t h of a linear time-invariant continuous time system is described by

( ) exp( ) ( ) exp( ) ( )h t t u t t u t = α + β minus where )(t u denotes the unit step function and α and β are real

constants This system is stable if

(A) α is positive and β is positive (B) α is negative and β is negative

(C) α is positive and β is negative (D) α is negative and β is positive

Q11 The pole-zero plot given below corresponds to a

(A) Low pass filter (B) High pass filter

(C) Band pass filter (D) Notch filter

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Head Office A114-115 Bhilai ndash 490 020 (CG) For Details Contact 0788-4034176 +91-97131-13156 +91-93026-97686Branch Office Bangalore (Karnataka) For Details Contact +91-97138-85449 +91-99169-39408

Q12 Step responses of a set of three second-order underdamped systems all have the same percentage

overshoot Which of the following diagrams represents the poles of the three systems

Q13 Which of the following is NOT associated with a p-n junction

(A) Junction Capacitance (B) Charge Storage Capacitance

(C) Depletion Capacitance (D) Channel Length Modulation

Q14 Which of the following is true

(A) A silicon wafer heavily doped with boron is a + p substrate

(B) A silicon wafer lightly doped with boron is a + p substrate

(C) A silicon wafer heavily doped with arsenic is a + p substrate

(D) A silicon wafer lightly doped with arsenic is a + p substrate

Q15 For a Hertz dipole antenna the half power beam width (HPBW) in the E-plane is

(A) 0360 (B) 0180 (C) 090 (D) 045

Q16 For static electric and magnetic fields in an inhomogeneous source-free medium which of the followingrepresents the correct form of two of Maxwells equations

(A) 0 0 E Bnabla = nablatimes = (B) 0 0 E Bnabla sdot = nabla sdot =

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(C) 0 0 E Bnabla times = nablatimes = (D) 0 0 E Bnablatimes = nabla sdot =

Q17 In the following limiter circuit an input voltage t V π 100sin101 = is applied Assume that the diode drop

is 07 V when it is forward biased The Zener breakdown voltage is 68V

The maximum and minimum values of the output voltage respectively are

(A) 61 V - 07 V (B) 07 V - 75V (C) 75 V - 07 V (D) 75 V - 75 V

Q18 A silicon wafer has 100 nm of oxide on it and is inserted in a furnace at a temperature above C 0

1000 forfurther oxidation in dry oxygen The oxidation are

(A) is independent of current oxide thickness and temperature

(B) is independent of current oxide thickness but depends on temperature

(C) slows down as the oxide grows

(D) is zero as the existing oxide prevents further oxidation

Q19 The drain current of a MOSFET in saturation is given by 2)( T GS D V V K I minus= where K is a constant The

magnitude of the transconductance mg is

(A) DS

T GS

V

V V K 2)( minus (B) )(2 T GS V V K minus

(C) DS GS

d

V V I minus

(D)GS

T GS

V V V K

2

)( minus

Q20 Consider the amplitude modulated (AM) signal t t t A cmcc ω ω coscos2cos + For demodulating the

signal using envelope detector the minimum value of c A should be

(A) 2 (B) 1 (C) 05 (D) 0

Q21 to Q60 carry two marks each

Q21 The Thevenin equivalent impedance th Z between the nodes P and Q in the following circuit is

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(A) 1 (B)s

s1

1 ++ (C)s

s1

2 ++ (D)12

12

2

++

++

ss

ss

Q22 The driving point impedance of the following network

is given by210

20)(

2 ++=

ss

ss Z The component values are

(A) F C R H L 10505 =Ω== (B) F C R H L 55010 =Ω==

(C) F C R H L 1025 =Ω== (D) F C R H L 5210 =Ω==

Q23 The circuit shown in the figure is used to charge the capacitor C alternately from two current sources asindicated The switches S1 and S2 are mechanically coupled and connected as follows

For )12(2 T nt nT +ltle )210( =n S1 and P1 and S2 and P2

For (2 1) (2 2) n T t n T + le lt + )210( =n S1 and Q1 and S2 to Q2

Assume that the capacitor has zero initial charge Given that )(t u is a unit step function the voltage )(t V c

across the capacitor is given by

(A)0

( 1) ( )n

n

tu t nT α

=

minus minussum (B)1

( ) 2 ( 1) ( )n

n

u t u t nT α

=

+ minus minussum

(C)1

( ) 2 ( 1) ( ) ( )n

n

tu t t nT u t nT α

=

+ minus minus minussum (D) ( 2 ) ( 2 )

0

05 05t nT t nT T

n

e eα

minus minus minus minus minus

=

minus + sum

Q24 The probability density function (PDF) of a random variable X is as shown below

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213d=]

The corresponding cumulative distribution function (CDF) has the form

Q25 The recursion relation to solve xe x

minus= using Newton-Raphson method is

(A)nx

n+1X =eminus

(B) n+1 nX =X n x

e

minus

minus

(C)n

n

x

n+1 n x

eX =(1+X )

1+e

minus

minus (D)

n

n

x2

n nn+1 x

n

x (1 x ) 1x

x

e

e

minus

minus

minus + minus=

minus

Q26 The residue of the function22 )2()2(

1)(

minus+=

z z z f at 2= z is

(A)32

1minus (B)

16

1minus (C)

16

1 (D)

32

1

Q27 Consider the matrix minusminus= 32 10P The value of Pe is

(A)

minusminus

minusminusminusminusminusminus

minusminusminusminus

1212

2112

52232

eeeeeeee (B)

+minusminus+

minusminusminusminus

minusminusminusminus

2121

1221

23422

eeeeeeee

(C)

+minusminusminus

minusminusminusminus

minusminusminusminus

1212

2112

46235

eeeeeeee (D)

+minus+minusminusminus

minusminusminusminus

minusminusminusminus

2121

2111

2222

eeeeeeee

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Head Office A114-115 Bhilai ndash 490 020 (CG) For Details Contact 0788-4034176 +91-97131-13156 +91-93026-97686Branch Office Bangalore (Karnataka) For Details Contact +91-97138-85449 +91-99169-39408

Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 2: EC20084Q

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Q8 In the following circuit the switch S is closed at t = 0 The rate of change of current (0 )di

dt + is given by

(A) 0 (B) L

I R ss (C) L

I R R ss )( + (D) infin

Q9 The input and output of a continuous time system are respectively denoted by )(t x and )(t y Which of

the following descriptions corresponds to a causal system

(A) )4()2()( ++minus= t xt xt y (B) ( ) ( 4) ( 1) y t t x t = minus +

(C) )1()4()( minus++= t xt t y (D) ( ) ( 5) ( 5) y t t x t = + +

Q10 The impulse response )(t h of a linear time-invariant continuous time system is described by

( ) exp( ) ( ) exp( ) ( )h t t u t t u t = α + β minus where )(t u denotes the unit step function and α and β are real

constants This system is stable if

(A) α is positive and β is positive (B) α is negative and β is negative

(C) α is positive and β is negative (D) α is negative and β is positive

Q11 The pole-zero plot given below corresponds to a

(A) Low pass filter (B) High pass filter

(C) Band pass filter (D) Notch filter

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Q12 Step responses of a set of three second-order underdamped systems all have the same percentage

overshoot Which of the following diagrams represents the poles of the three systems

Q13 Which of the following is NOT associated with a p-n junction

(A) Junction Capacitance (B) Charge Storage Capacitance

(C) Depletion Capacitance (D) Channel Length Modulation

Q14 Which of the following is true

(A) A silicon wafer heavily doped with boron is a + p substrate

(B) A silicon wafer lightly doped with boron is a + p substrate

(C) A silicon wafer heavily doped with arsenic is a + p substrate

(D) A silicon wafer lightly doped with arsenic is a + p substrate

Q15 For a Hertz dipole antenna the half power beam width (HPBW) in the E-plane is

(A) 0360 (B) 0180 (C) 090 (D) 045

Q16 For static electric and magnetic fields in an inhomogeneous source-free medium which of the followingrepresents the correct form of two of Maxwells equations

(A) 0 0 E Bnabla = nablatimes = (B) 0 0 E Bnabla sdot = nabla sdot =

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(C) 0 0 E Bnabla times = nablatimes = (D) 0 0 E Bnablatimes = nabla sdot =

Q17 In the following limiter circuit an input voltage t V π 100sin101 = is applied Assume that the diode drop

is 07 V when it is forward biased The Zener breakdown voltage is 68V

The maximum and minimum values of the output voltage respectively are

(A) 61 V - 07 V (B) 07 V - 75V (C) 75 V - 07 V (D) 75 V - 75 V

Q18 A silicon wafer has 100 nm of oxide on it and is inserted in a furnace at a temperature above C 0

1000 forfurther oxidation in dry oxygen The oxidation are

(A) is independent of current oxide thickness and temperature

(B) is independent of current oxide thickness but depends on temperature

(C) slows down as the oxide grows

(D) is zero as the existing oxide prevents further oxidation

Q19 The drain current of a MOSFET in saturation is given by 2)( T GS D V V K I minus= where K is a constant The

magnitude of the transconductance mg is

(A) DS

T GS

V

V V K 2)( minus (B) )(2 T GS V V K minus

(C) DS GS

d

V V I minus

(D)GS

T GS

V V V K

2

)( minus

Q20 Consider the amplitude modulated (AM) signal t t t A cmcc ω ω coscos2cos + For demodulating the

signal using envelope detector the minimum value of c A should be

(A) 2 (B) 1 (C) 05 (D) 0

Q21 to Q60 carry two marks each

Q21 The Thevenin equivalent impedance th Z between the nodes P and Q in the following circuit is

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(A) 1 (B)s

s1

1 ++ (C)s

s1

2 ++ (D)12

12

2

++

++

ss

ss

Q22 The driving point impedance of the following network

is given by210

20)(

2 ++=

ss

ss Z The component values are

(A) F C R H L 10505 =Ω== (B) F C R H L 55010 =Ω==

(C) F C R H L 1025 =Ω== (D) F C R H L 5210 =Ω==

Q23 The circuit shown in the figure is used to charge the capacitor C alternately from two current sources asindicated The switches S1 and S2 are mechanically coupled and connected as follows

For )12(2 T nt nT +ltle )210( =n S1 and P1 and S2 and P2

For (2 1) (2 2) n T t n T + le lt + )210( =n S1 and Q1 and S2 to Q2

Assume that the capacitor has zero initial charge Given that )(t u is a unit step function the voltage )(t V c

across the capacitor is given by

(A)0

( 1) ( )n

n

tu t nT α

=

minus minussum (B)1

( ) 2 ( 1) ( )n

n

u t u t nT α

=

+ minus minussum

(C)1

( ) 2 ( 1) ( ) ( )n

n

tu t t nT u t nT α

=

+ minus minus minussum (D) ( 2 ) ( 2 )

0

05 05t nT t nT T

n

e eα

minus minus minus minus minus

=

minus + sum

Q24 The probability density function (PDF) of a random variable X is as shown below

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213d=]

The corresponding cumulative distribution function (CDF) has the form

Q25 The recursion relation to solve xe x

minus= using Newton-Raphson method is

(A)nx

n+1X =eminus

(B) n+1 nX =X n x

e

minus

minus

(C)n

n

x

n+1 n x

eX =(1+X )

1+e

minus

minus (D)

n

n

x2

n nn+1 x

n

x (1 x ) 1x

x

e

e

minus

minus

minus + minus=

minus

Q26 The residue of the function22 )2()2(

1)(

minus+=

z z z f at 2= z is

(A)32

1minus (B)

16

1minus (C)

16

1 (D)

32

1

Q27 Consider the matrix minusminus= 32 10P The value of Pe is

(A)

minusminus

minusminusminusminusminusminus

minusminusminusminus

1212

2112

52232

eeeeeeee (B)

+minusminus+

minusminusminusminus

minusminusminusminus

2121

1221

23422

eeeeeeee

(C)

+minusminusminus

minusminusminusminus

minusminusminusminus

1212

2112

46235

eeeeeeee (D)

+minus+minusminusminus

minusminusminusminus

minusminusminusminus

2121

2111

2222

eeeeeeee

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Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q12 Step responses of a set of three second-order underdamped systems all have the same percentage

overshoot Which of the following diagrams represents the poles of the three systems

Q13 Which of the following is NOT associated with a p-n junction

(A) Junction Capacitance (B) Charge Storage Capacitance

(C) Depletion Capacitance (D) Channel Length Modulation

Q14 Which of the following is true

(A) A silicon wafer heavily doped with boron is a + p substrate

(B) A silicon wafer lightly doped with boron is a + p substrate

(C) A silicon wafer heavily doped with arsenic is a + p substrate

(D) A silicon wafer lightly doped with arsenic is a + p substrate

Q15 For a Hertz dipole antenna the half power beam width (HPBW) in the E-plane is

(A) 0360 (B) 0180 (C) 090 (D) 045

Q16 For static electric and magnetic fields in an inhomogeneous source-free medium which of the followingrepresents the correct form of two of Maxwells equations

(A) 0 0 E Bnabla = nablatimes = (B) 0 0 E Bnabla sdot = nabla sdot =

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(C) 0 0 E Bnabla times = nablatimes = (D) 0 0 E Bnablatimes = nabla sdot =

Q17 In the following limiter circuit an input voltage t V π 100sin101 = is applied Assume that the diode drop

is 07 V when it is forward biased The Zener breakdown voltage is 68V

The maximum and minimum values of the output voltage respectively are

(A) 61 V - 07 V (B) 07 V - 75V (C) 75 V - 07 V (D) 75 V - 75 V

Q18 A silicon wafer has 100 nm of oxide on it and is inserted in a furnace at a temperature above C 0

1000 forfurther oxidation in dry oxygen The oxidation are

(A) is independent of current oxide thickness and temperature

(B) is independent of current oxide thickness but depends on temperature

(C) slows down as the oxide grows

(D) is zero as the existing oxide prevents further oxidation

Q19 The drain current of a MOSFET in saturation is given by 2)( T GS D V V K I minus= where K is a constant The

magnitude of the transconductance mg is

(A) DS

T GS

V

V V K 2)( minus (B) )(2 T GS V V K minus

(C) DS GS

d

V V I minus

(D)GS

T GS

V V V K

2

)( minus

Q20 Consider the amplitude modulated (AM) signal t t t A cmcc ω ω coscos2cos + For demodulating the

signal using envelope detector the minimum value of c A should be

(A) 2 (B) 1 (C) 05 (D) 0

Q21 to Q60 carry two marks each

Q21 The Thevenin equivalent impedance th Z between the nodes P and Q in the following circuit is

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(A) 1 (B)s

s1

1 ++ (C)s

s1

2 ++ (D)12

12

2

++

++

ss

ss

Q22 The driving point impedance of the following network

is given by210

20)(

2 ++=

ss

ss Z The component values are

(A) F C R H L 10505 =Ω== (B) F C R H L 55010 =Ω==

(C) F C R H L 1025 =Ω== (D) F C R H L 5210 =Ω==

Q23 The circuit shown in the figure is used to charge the capacitor C alternately from two current sources asindicated The switches S1 and S2 are mechanically coupled and connected as follows

For )12(2 T nt nT +ltle )210( =n S1 and P1 and S2 and P2

For (2 1) (2 2) n T t n T + le lt + )210( =n S1 and Q1 and S2 to Q2

Assume that the capacitor has zero initial charge Given that )(t u is a unit step function the voltage )(t V c

across the capacitor is given by

(A)0

( 1) ( )n

n

tu t nT α

=

minus minussum (B)1

( ) 2 ( 1) ( )n

n

u t u t nT α

=

+ minus minussum

(C)1

( ) 2 ( 1) ( ) ( )n

n

tu t t nT u t nT α

=

+ minus minus minussum (D) ( 2 ) ( 2 )

0

05 05t nT t nT T

n

e eα

minus minus minus minus minus

=

minus + sum

Q24 The probability density function (PDF) of a random variable X is as shown below

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213d=]

The corresponding cumulative distribution function (CDF) has the form

Q25 The recursion relation to solve xe x

minus= using Newton-Raphson method is

(A)nx

n+1X =eminus

(B) n+1 nX =X n x

e

minus

minus

(C)n

n

x

n+1 n x

eX =(1+X )

1+e

minus

minus (D)

n

n

x2

n nn+1 x

n

x (1 x ) 1x

x

e

e

minus

minus

minus + minus=

minus

Q26 The residue of the function22 )2()2(

1)(

minus+=

z z z f at 2= z is

(A)32

1minus (B)

16

1minus (C)

16

1 (D)

32

1

Q27 Consider the matrix minusminus= 32 10P The value of Pe is

(A)

minusminus

minusminusminusminusminusminus

minusminusminusminus

1212

2112

52232

eeeeeeee (B)

+minusminus+

minusminusminusminus

minusminusminusminus

2121

1221

23422

eeeeeeee

(C)

+minusminusminus

minusminusminusminus

minusminusminusminus

1212

2112

46235

eeeeeeee (D)

+minus+minusminusminus

minusminusminusminus

minusminusminusminus

2121

2111

2222

eeeeeeee

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Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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(C) 0 0 E Bnabla times = nablatimes = (D) 0 0 E Bnablatimes = nabla sdot =

Q17 In the following limiter circuit an input voltage t V π 100sin101 = is applied Assume that the diode drop

is 07 V when it is forward biased The Zener breakdown voltage is 68V

The maximum and minimum values of the output voltage respectively are

(A) 61 V - 07 V (B) 07 V - 75V (C) 75 V - 07 V (D) 75 V - 75 V

Q18 A silicon wafer has 100 nm of oxide on it and is inserted in a furnace at a temperature above C 0

1000 forfurther oxidation in dry oxygen The oxidation are

(A) is independent of current oxide thickness and temperature

(B) is independent of current oxide thickness but depends on temperature

(C) slows down as the oxide grows

(D) is zero as the existing oxide prevents further oxidation

Q19 The drain current of a MOSFET in saturation is given by 2)( T GS D V V K I minus= where K is a constant The

magnitude of the transconductance mg is

(A) DS

T GS

V

V V K 2)( minus (B) )(2 T GS V V K minus

(C) DS GS

d

V V I minus

(D)GS

T GS

V V V K

2

)( minus

Q20 Consider the amplitude modulated (AM) signal t t t A cmcc ω ω coscos2cos + For demodulating the

signal using envelope detector the minimum value of c A should be

(A) 2 (B) 1 (C) 05 (D) 0

Q21 to Q60 carry two marks each

Q21 The Thevenin equivalent impedance th Z between the nodes P and Q in the following circuit is

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(A) 1 (B)s

s1

1 ++ (C)s

s1

2 ++ (D)12

12

2

++

++

ss

ss

Q22 The driving point impedance of the following network

is given by210

20)(

2 ++=

ss

ss Z The component values are

(A) F C R H L 10505 =Ω== (B) F C R H L 55010 =Ω==

(C) F C R H L 1025 =Ω== (D) F C R H L 5210 =Ω==

Q23 The circuit shown in the figure is used to charge the capacitor C alternately from two current sources asindicated The switches S1 and S2 are mechanically coupled and connected as follows

For )12(2 T nt nT +ltle )210( =n S1 and P1 and S2 and P2

For (2 1) (2 2) n T t n T + le lt + )210( =n S1 and Q1 and S2 to Q2

Assume that the capacitor has zero initial charge Given that )(t u is a unit step function the voltage )(t V c

across the capacitor is given by

(A)0

( 1) ( )n

n

tu t nT α

=

minus minussum (B)1

( ) 2 ( 1) ( )n

n

u t u t nT α

=

+ minus minussum

(C)1

( ) 2 ( 1) ( ) ( )n

n

tu t t nT u t nT α

=

+ minus minus minussum (D) ( 2 ) ( 2 )

0

05 05t nT t nT T

n

e eα

minus minus minus minus minus

=

minus + sum

Q24 The probability density function (PDF) of a random variable X is as shown below

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213d=]

The corresponding cumulative distribution function (CDF) has the form

Q25 The recursion relation to solve xe x

minus= using Newton-Raphson method is

(A)nx

n+1X =eminus

(B) n+1 nX =X n x

e

minus

minus

(C)n

n

x

n+1 n x

eX =(1+X )

1+e

minus

minus (D)

n

n

x2

n nn+1 x

n

x (1 x ) 1x

x

e

e

minus

minus

minus + minus=

minus

Q26 The residue of the function22 )2()2(

1)(

minus+=

z z z f at 2= z is

(A)32

1minus (B)

16

1minus (C)

16

1 (D)

32

1

Q27 Consider the matrix minusminus= 32 10P The value of Pe is

(A)

minusminus

minusminusminusminusminusminus

minusminusminusminus

1212

2112

52232

eeeeeeee (B)

+minusminus+

minusminusminusminus

minusminusminusminus

2121

1221

23422

eeeeeeee

(C)

+minusminusminus

minusminusminusminus

minusminusminusminus

1212

2112

46235

eeeeeeee (D)

+minus+minusminusminus

minusminusminusminus

minusminusminusminus

2121

2111

2222

eeeeeeee

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Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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(A) 1 (B)s

s1

1 ++ (C)s

s1

2 ++ (D)12

12

2

++

++

ss

ss

Q22 The driving point impedance of the following network

is given by210

20)(

2 ++=

ss

ss Z The component values are

(A) F C R H L 10505 =Ω== (B) F C R H L 55010 =Ω==

(C) F C R H L 1025 =Ω== (D) F C R H L 5210 =Ω==

Q23 The circuit shown in the figure is used to charge the capacitor C alternately from two current sources asindicated The switches S1 and S2 are mechanically coupled and connected as follows

For )12(2 T nt nT +ltle )210( =n S1 and P1 and S2 and P2

For (2 1) (2 2) n T t n T + le lt + )210( =n S1 and Q1 and S2 to Q2

Assume that the capacitor has zero initial charge Given that )(t u is a unit step function the voltage )(t V c

across the capacitor is given by

(A)0

( 1) ( )n

n

tu t nT α

=

minus minussum (B)1

( ) 2 ( 1) ( )n

n

u t u t nT α

=

+ minus minussum

(C)1

( ) 2 ( 1) ( ) ( )n

n

tu t t nT u t nT α

=

+ minus minus minussum (D) ( 2 ) ( 2 )

0

05 05t nT t nT T

n

e eα

minus minus minus minus minus

=

minus + sum

Q24 The probability density function (PDF) of a random variable X is as shown below

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213d=]

The corresponding cumulative distribution function (CDF) has the form

Q25 The recursion relation to solve xe x

minus= using Newton-Raphson method is

(A)nx

n+1X =eminus

(B) n+1 nX =X n x

e

minus

minus

(C)n

n

x

n+1 n x

eX =(1+X )

1+e

minus

minus (D)

n

n

x2

n nn+1 x

n

x (1 x ) 1x

x

e

e

minus

minus

minus + minus=

minus

Q26 The residue of the function22 )2()2(

1)(

minus+=

z z z f at 2= z is

(A)32

1minus (B)

16

1minus (C)

16

1 (D)

32

1

Q27 Consider the matrix minusminus= 32 10P The value of Pe is

(A)

minusminus

minusminusminusminusminusminus

minusminusminusminus

1212

2112

52232

eeeeeeee (B)

+minusminus+

minusminusminusminus

minusminusminusminus

2121

1221

23422

eeeeeeee

(C)

+minusminusminus

minusminusminusminus

minusminusminusminus

1212

2112

46235

eeeeeeee (D)

+minus+minusminusminus

minusminusminusminus

minusminusminusminus

2121

2111

2222

eeeeeeee

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Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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213d=]

The corresponding cumulative distribution function (CDF) has the form

Q25 The recursion relation to solve xe x

minus= using Newton-Raphson method is

(A)nx

n+1X =eminus

(B) n+1 nX =X n x

e

minus

minus

(C)n

n

x

n+1 n x

eX =(1+X )

1+e

minus

minus (D)

n

n

x2

n nn+1 x

n

x (1 x ) 1x

x

e

e

minus

minus

minus + minus=

minus

Q26 The residue of the function22 )2()2(

1)(

minus+=

z z z f at 2= z is

(A)32

1minus (B)

16

1minus (C)

16

1 (D)

32

1

Q27 Consider the matrix minusminus= 32 10P The value of Pe is

(A)

minusminus

minusminusminusminusminusminus

minusminusminusminus

1212

2112

52232

eeeeeeee (B)

+minusminus+

minusminusminusminus

minusminusminusminus

2121

1221

23422

eeeeeeee

(C)

+minusminusminus

minusminusminusminus

minusminusminusminus

1212

2112

46235

eeeeeeee (D)

+minus+minusminusminus

minusminusminusminus

minusminusminusminus

2121

2111

2222

eeeeeeee

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Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 7: EC20084Q

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Q28 In the Taylor series expansion of )sin()exp( x x + about the point π = x the coefficient of 2)( π minus x is

(A) )exp(π (B) )exp(50 π (C) 1)exp( +π (D) 1)exp( minusπ

Q29 |)|3exp(|)|2exp()( x N x M xP x minus+minus= is the probability density function for the real random variable X

over the entire axis M and N are both positive real numbers The equation relating M and N is

(A)2

13

M N minus = (B) 13

12 =+ N M

(C) 1=+ N M (D) 3=+ N M

Q30 The value of the integral of the function 43 104)( y x y xg += along the straight line segment from the

point (0 0) to the point (1 2) in the x ndash y plane is

(A) 33 (B) 35 (C) 40 (D) 56

Q31 A linear time-invariant causal continuous time system has a rational transfer function with simple poles

at 2minus=s and 4minus=s and one simple zero at 1minus=s A unit step )(t u is applied at the input of the system

At steady state the output has constant value of 1 The impulse response of this system is

(A) )()]4exp()2[exp( t ut t minus+minus (B) [ 4exp( 2 ) 12exp( 4 ) exp( )] ( )t t t u t minus minus minus minus minus minus

(C) )()]4exp(12)2exp(4[ t ut t minus+minusminus (D) )()]4exp(51)2exp(50[ t ut t minus+minusminus

Q32 The signal )(t x is described by

otherwise

11for01

)( +leleminus

=

t t x

Two of the angular frequencies at which its Foureir transform becomes zero are

(A) π π 2 (B) π π 5150 (C) π 0 (D) π π 522

Q33 A discrete time linear shift-invariant system has an impulse response [ ]h n with [ ]0 1h = [ ]1 1h = minus 2]2[ =h

and zero otherwise The system is given an input sequence ][n x with 1]2[]0[ == x x and zero otherwise

The number of nonzero samples in the output sequence ][n y and the value of y[2] are respectively

(A) 5 2 (B) 6 2 (C) 6 1 (D) 5 3

Q34 Consider points P and Q in the x plane with )01(=P The line integral int +Q

P

ydy xdx )(2 along the

semicircle with the line segment PQ as its diameter

(A) is -1 (B) is 0 (C) is 1

(D) depends on the direction (Clockwise or anti-clockwise) of the semicircle

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 8: EC20084Q

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Q35 Let )(t x be the input and )(t y be the output of a continous time system Match the system properties P1

P2 and P3 with system relations R1 R2 R3 R4

Properties Relations

P1 Linear but NOT time-invariant R1 )()( 2t xt t y =

P2 Time-invariant but NOT linear R2 |)(|)( t xt t y =

P3 Linear and time-invariant R3 |)(|)( t xt y =

R4 )5()( minus= t xt y

(A) R4)(P3R3)(P2R1)(P1 (B) R4)(P3R3)(P2R2)(P1

(C) R2)(P3R1)(P2R3)(P1 (D) R3)(P3R2)(P2R1)(P1

Q36 A memoryless source emits n symboly each with a probability p The entropy of the source as a functionof n

(A) increase as log n (B) decreases as log (1 n)

(C) increases as n (D) increases as n log n

Q37 )(n x is a real-valued periodic sequence with a period N )(n x and )(k X form N-point Discrete Fourier

Transform (DFT) pairs The DFT Y(k) of the sequence

sum

minus

=+=

1

0)()(

1

)(

N

r r n xr x N n y is

(A) 2|)(| k X (B)1

0

1( ) ( )

N

r

X r X k r N

minus

=

+sum

(C) )()(1 1

0

r k X r X N

N

r

+summinus

=

(D) 0

Q38 Group 1 lists a set of four transfer functions Group II gives a list of possible step responses y(t) Match

the step responses with the corresponding transfer functions

Group I

25

252 +

=s

P 3620

362 ++

=ss

Q 3612

362 ++

=ss

R 497

492 ++

=ss

S

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 9: EC20084Q

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

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

Q39 A certain system has transfer function 4

8)(2 minus+

+=ss

ssGα

where α is a parameter Consider the standard

negative unity feedback configuration as shown below

Which of the following statements is true

(A) The closed loop system is never stable for any value of α

(B) For some positive values of α the closed loop system is stable but not for all positive valuss

(C) For all positive values of α the closed loop system is stable

(D) The closed loop system is stable for all values of α both positive and negative

Q40 A signal flow graph of a system is given below

The set of equations that correspond to this signal flow graph is

(A)1 1

1

2 2

2

3 3

0 0 0

0 0 0

0 1 1

x xud

x xudt

x x

β minusγ = γ α + minusα minusβ

(B)1 1

1

2 2

2

3 3

0 0 0

0 0 1

0 1 0

x xud

x xudt

x x

α γ = minusα minusγ + β β

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 10: EC20084Q

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(C)

+

minusminus

minus=

2

1

3

2

1

3

2

1

010

001

000

u

u

x

x

x

x

x

x

dt

d

γ α γ β

β α (D)

+

minusminus

minus=

2

1

3

2

1

3

2

1

001

100

000

u

u

x

x

x

x

x

x

dt

d

α β α γ β γ

Q41 The number of open right half plane poles of35632

10)(

2345 +++++=

ssssssG is

(A) 0 (B) 1 (C) 2 (D) 3

Q42 The magnitude of frequency response of underdamped second order system is 5 at 0 radsec and peaks to

3

10 at 25 radsec The transfer function of the system is

(A)10010

5002 ++ ss

(B)755

3752 ++ ss

(C)14412

7202 ++ ss

(D)22525

11252 ++ ss

Q43 Group I gives two possible choices for the impedance Z in the diagram The circuit elements in Z satisfy

the condition 1122 C RC R gt The transfer functioniV

V 0 represents a kind of controller Match the

impedances in Group I with the types of controllers in Group II

Group I Group II

Q 1 PID controller

R 2 Lead Compensator

3 Lag compensator

(A) Q -1 R -2 (B) Q-1 R-3 (C) Q-2 R-3 (D) Q-3 R-2

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q44 For the circuit shown in the following figure transistors M1 and M2 are identical NMOS transistors

Assume that M2 is in saturation and the output is unloaded

The current X I is related to

bias I as

(A) S bias X I I I += (B) bias X I I =

(C) S bias X I I I minus= (D)

minusminus=

E

out DDbias X R

V V I I

Q45 The measured transconductance mg of an NMOS transistor operating in the linear region is plotted against

the gate voltage GV at a constant drain voltage DV Which of the following figures represents the expected

dependence of mg on GV

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q46 Consider the following circuit using an ideal OPAMP The I-V characteristics of the diode is described by

the relation

minus= 10

T V

V

e I I where mV V T 25= A I micro 10 = and V is the voltage across the diode (taken as

positive for forward bias)

For an input voltage 1 T

V V = minus the output voltage 0V is

(A) 0 V (B) 01 V (C) 07 V (D) 11 V

Q47

The OPAMP circuit shown above represents a

(A) High pass filter (B) Low pass filter

(C) band pass filter (D) band reject filter

Q48 Two identical NMOS transistor M1 and M2 are connected as shown below biasV is chosen so that both

transistor are in saturation The equivalent mg of the pair is defined to bei

out

V

I

partpart at constant out V

The equivalent mg of the pair is

(A) the sum of individual

mg s of the transistors

(B) the product of individual mg s of the transistors

(C) nearly equal to the mg of M1

(D) nearly equal to 0ggm of M2

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 13: EC20084Q

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Q49 An 8085 exectutres the following instructions

2710 LXI H 30A0H

2713 DAD H

2714 PCHL

All addresses and constants are in Hex Let PC be he contents of the program counter and HL be thecontents of the HL register pair just after executing PCHL

Which of the following statements is correct

(A) H A HL H PC 030

2715== (B)

H HL H APC

2715030

== (C)

H HL H PC

61406140

== (D)

H HL H PC

27156140

==

Q50 An stable multivibrator circuit using IC 555 timer is shown below Assume that the circuit is oscillatingsteadily

The voltage C V across the capacitor varies between

(A) 3 V to 5V (B) 3V to 6V (C) 36 V to 6V (D) 36 V to 5V

Q51 Silicon is doped with boron to a concentration of 17 34 10 atomcmtimes Assume the intrinsic carrier

concentration of silicon to be

310

1051 cmtimes and the value of q

kT

to be 25 mV at 300K

Compared to undoped silicon the Fermi level of doped silicon

(A) goes down by 013 eV (B) goes up by 013 eV

(C) goes down by 0427 eV (D) goes up by 0427 eV

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q52 The cross section of a JFET is shown in the following figure Let GV be -2V and let pV be the initia

pinch-off voltage If the width W is doubled (with other geometrical parameters and doping levelsremaining the same) then the ratio between the mutual transconductances of the intial and the modidfied

JFET is

(A) 4 (B)1 2

1 1 (2 )

p

p

V

V

minus minus

(C))2 (11

21

p

p

V

V

minus

minus (D)

))2 1(1

2(1

p

p

V

V

minus

minus

Q53 Consider the schmitdt trigger circuit shown below

A triangular wave which goes from -12 V to 12V is applied to the inverting input of the OP AMP Assume

that the output of the OPAMP swings from +15 V to -15V The voltage at the non-inverting inputswitches between

(A) -12 V and +12 V (B) -75 V and +75 V

(C) -5V and +5 V (D) 0V and 5V

Q54 The logic function implemented by the following circuit at the terminal OUT is

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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(A) P NOR Q (B) P NAND Q (C) P OR Q (D) P AND Q

Q55 Consider the following assertions

S1 For Zener effect to occur a very abrupt junction is required

S2 For quantum tunneling to occur a very narrow energy barrier is required

Which of the following is correct

(A) Only S2 is true

(B) S1 and S2 are both true but S2 is not a reason for S1

(C) S1 and S2 are both true and S2 is a reason for S1

(D) Both S1 and S2 are false

Q56 The two numbers represented in signed 2s complement form are

P = 11101101 and Q = 11100110 If Q is subtracyted from P the value obtained in signed 2s complementform is

(A) 100000111 (B) 00000111 (C) 11111001 (D) 111111001

Q57 Which of the following Boolean Expressions correctly represents the relation between P Q R and 1 M

(A) ( ) M P OR Q XOR R= (B) R XORQ ANDP M )(1 =

(C) ( ) M P NOR Q XOR R= (D) R XORQ XORP M )(1 =

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q58 For the circuit shown in the following figure 30 I I minus are inputs to the 4 1 multiplexer R (MSB) and S are

control bits

The output Z can be represented by

(A) PQ + PQS + QR S (B) PQ + PQR + PQS

(C) PQ R+PQR+PQ RS+QR S (D) PQ R+PQR S - PQ RS+QR S

Q59 For each of the positive edge-triggered J-K flip flop used in the following figure the propagation delay is

T ∆

Which of the following waveforms correctly represents the output at 1Q

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q60 For the circuit shown in the figure D has a transition from 0 to 1 after CLK changes from 1 to 0 Assume

gate delays to be negligible

Which of the following statements is true

(A) Q goes to 1 at the CLK transition and stays at 1

(B) Q goes to 0 at the CLK transition and stays at 0

(C) Q goes to 1 at the CLK transition and goes to 0 when D goes to 1

(D) Q goes to 0 at the CLK transition and goes to 1 when D goes to 1

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q61 A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm) is to be operated in 11TE mode

The minimum operating frequency is

(A) 625 GHz (B) 60 GHz (C) 50 GHz (D) 375 GHz

Q62 One end of a loss-less transmission line having the characteristic impedance of Ω75 and length of 1cm is

short-circuited At 3GHz the input impedance at the other end of the transmission line is

(A) 0 (B) Resistive (C) Capacitive (D) Inductive

Q63 A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric

constant 9=r ε ) The magnitude of the reflection coefficient is

(A) 0 (B) 03 (C) 05 (D) 08

Q64 In the design of a single mode step index optical fiber close to upper cut-off the single-mode operation is

NOT preserved if

(A) radius as well as operating wavelength are halved

(B) radius as well as operating wavelength are doubled

(C) radius is halved and operating wavelength is doubled

(D) radius is doubled and operating wavelength is halved

Q65 At 20 GHz the gain of a parabolic dish antenna of 1 meter diameter and 70 efficiency is

(A) 15 dB (B) 25 dB (C) 35 dB (D) 45 dB

Q66 Noise with double-sided spectral density of K over all frequencies is passed through a RC low pass filter

with 3 dB cut-off frequency of f The noise power at the filter output is

(A) K (B) cKf (C) c f K π (D) infin

Q67 Consider a Binary symmetric channel (BSC) with probability of error being p To transmit a bit say 1 wetransmit a sequence of three 1s The receiver will interpret the received sequence to represent 1 if at least

two bits are 1 The probability that the transmitted bit will be received in error is

(A) )1(3 23 p p p minus+ (B) 3 p

(C) 3)1( pminus (D) )1(23 p p p minus+

Q68 Four messages band limited to W W 2W and 3W respectively are to be multiplexed using Time DivisionMultiplexing (TDM) The minimum bandwidth required for transmission of this TDM signal is

(A) W (B) 3W (C) 6W (D) 7W

Q69 Consider the frequency modulated signal )]10002sin(57)15002sin(5102cos[10 5t t times+times+times π π π with

carrier frequency of5

10 Hz The modulation index is

(A) 125 (B) 10 (C) 75 (D) 5

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

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Q70 The signal t t t cmc ω sincos50cos + is

(A) FM only (B) AM only

(C) Both AM and FM (D) Neither AM nor FM

Common Data Question 71 72 amp 73

A speech signal band limited to 4 KHz and Peak voltage varying between +5V and -5V is sampled at the

Nyquiest rate Each sampled is quantized and represented by 8 bits

Q71 If the bits 0 and 1 are transmitted using bipolar pulses the minimum bandwidth required for distortion free

transmission is

(A) 64 KHz (B) 32 KHz (C) 8 KHz (D) 4 KHz

Q72 Assuming the signal to be uniformly distributed between its peak to peak value the signal to noise rationat the quantizer output is

(A) 16 dB (B) 32 dB (C) 48 dB (D) 64 dB

Q73 The number of quantization levels required to reduce the quantization noise by a factor of 4 would be

(A) 1024 (B) 512 (C) 256 (D) 64

Common Data Question 74 amp75

The following series RLC circuit with zero initial conditions is excited by a unit impulse function )(t δ

Q74 For 0gtt the output voltage )(t V c is

(A)1 3

2 22

3

t t

e eminus

minus

(B)t

te 2

1

3

2 minus

(C)

minust e

t

2

3cos

3

22

1

(D)

minust e

t

2

3sin

3

22

1

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

8132019 EC20084Q

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Head Office A114-115 Bhilai ndash 490 020 (CG) For Details Contact 0788-4034176 +91-97131-13156 +91-93026-97686Branch Office Bangalore (Karnataka) For Details Contact +91-97138-85449 +91-99169-39408

Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 20: EC20084Q

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Q75 For 0gtt voltage across the resistor is

(A)3 1

2 21

3

t t

e eminus minus

minus

(B)1

23 1 3

cos sin2 23

t

e t t minus

minus

(C)

minust e

t

2

3sin

3

22

1

(D)

minust e

t

2

3cos

3

22

1

Statement For Linked Answer Questions 76 amp 77

A two-port network shown below is excited by external dc sources The voltages and the currents are measured

with voltmeters 21 V V and ammeters 21 A A (all assumed to be ideal) as indicated Under following switch

conditions the readings obtained are

(i) minus1S open minus2S closed A AV V V V A A 151540 2211 ====

(ii) minus1S closed minus2S open A AV V V V A A 0664 2211 ====

Q76 The z-parameter matrix for this network is

(A)

51545151

(B)

54515451

(C)

51515451

(D)

54515154

Q77 The h-parameter matrix for this network is

(A)

minusminus

670133

(B)

minusminus

670313

(C)

670133

(D)

minusminus 670313

Statement For Linked Answer Questions 78 amp 79

In the following network the switch is closed at t = 0- and the sampling starts from t = 0 The sampling

frequency is 10 Hz

8132019 EC20084Q

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 21: EC20084Q

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Q78 The samples )(n x )210( =n are given by

(A) ( )ne05015 minusminus (B)

ne

0505

minus (C) )1(5 5ne

minusminus (D)n

e5

5 minus

Q79 The expression and the region of convergence of the z-tranform of the sampled signal are

(A)

5

5

5 | |

z z e

z e

minusltminus (B)

050

050 ||

5 minus

minus ltminus

minus

e ze z

z

(C) 050

050||

5 minus

minus gt

minuse z

e z

z (D) 5

5||

5 minus

minus gt

minuse z

e z

z

Statement For Linked Answer Questions 80 amp 81

In the following transistor circuit 07 25 BE e E V V r mV I asymp = and β and all the capacitances are very large

Q80 The value of DC current E I is

(A) 1 mA (B) 2 mA (C) 5 mA (D) 10 mA

Q81 The mid-band voltage gain of the amplifier is approximately

(A) -180 (B) -120 (C) -90 (D) -60

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER

Page 22: EC20084Q

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Statement For Linked Answer Questions 82 amp 83

In the following circuit the camparator output is logic 1 if 21 V V gt and is logic 0 otherwise The DA

conversion is done as per the relation

31

0

2n

DAC n

r

V b+

=

= sum Volts where 3b (MSB) 12 bb and 0b (LSB) are the counter outputs

The counter starts from the clear state

Q82 The stable reading of the LED displays is

(A) 06 (B) 07 (C) 12 (D) 13

Q83 The magnitude of the error between DAC V and inV at steady state in volts is

(A) 02 (B) 03 (C) 05 (D) 10

Statement For Linked Answer Questions 84 amp 85

The impulse response )(t h of a linear time-invariant continuous time system is given by

)()2exp()( t ut t h minus= where )(t u denotes the nit step function

Q84 The frequency response )(ω H of this system in terms of angular frequency ω is given by =)(ω H

(A)ω 21

1

j+ (B)

ω

)sin( (C)

ω j+2

1 (D)

ω

ω

j

j

+2

Q85 The output of this system to the sinusoidal input )2cos(2)( t t x = for all time t is

(A) 0 (B) )12502cos(2 250 π minusminust

(C) )12502cos(2 50 π minusminus t (D) )2502cos(2 50 π minusminus t

END OF THE QUESTION PAPER