ec20084q
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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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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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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
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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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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) 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)
+
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
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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
8132019 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
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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
8132019 EC20084Q
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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
8132019 EC20084Q
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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
8132019 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
8132019 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
8132019 EC20084Q
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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
8132019 EC20084Q
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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Prog
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
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
8132019 EC20084Q
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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Prog
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
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
8132019 EC20084Q
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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Prog
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
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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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Prog
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
8132019 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
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
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
8132019 EC20084Q
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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Prog
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
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
8132019 EC20084Q
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Correspondence Programme Classroom Programme All India Mock Test Series Postal Test Series Online Test Series Online Classroom Prog
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
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
8132019 EC20084Q
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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
8132019 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
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
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
8132019 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
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
8132019 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
8132019 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