Indian Institute of Technology General GATE (ECE) 2009 University model question papers



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Posted Date: 21 Nov 2009      Posted By:: Suket    Member Level: Bronze  Points: 5 (₹ 1)

2009 Indian Institute of Technology General Other Bachelor's Degree GATE (ECE) 2009 University Question paper



Course: Other Bachelor's Degree   University/board: Indian Institute of Technology





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Q. No. 1 – 20 Carry One Mark Each
1. The order of the differential equation
2 3
4 t
2
d y dy
y e
dt dt
  -
+   + =
 
is
(A) 1 (B) 2 (C) 3 (D) 4
2. The Fourier series of a real periodic function has only
P. Cosine terms if it is even
Q. Sine terms if it is even
R. Cosine terms if it is odd
S. Sine terms if it is odd
Which of the above statements are correct?
(A) P and S (B) P and R (C) Q and S (D) Q and R
3. A function is given ( ) 2 f t = sin t + cos2t. Which of the following is true?
(A) f has frequency components at 0 and 1/2p Hz
(B) f has frequency components at 0 and 1/p Hz
(C) f has frequency components at 1/2p and 1/p Hz
(D) f has frequency components at 0, 1/2p and 1/p Hz
4. A fully charged mobile phone with a 12V battery is good for a 10minute talktime.
Assume that, during the talk-time, the battery delivers a constant current
of 2A and its voltage drops linearly from 12 V to 10V as shown in the figure. How
much energy does the battery deliver during this talk-time?
(A) 220J (B) 12kJ (C) 13.2kJ (D) 14.4kJ
5. In an n-type silicon crystal at room temperature, which of the following can have
a concentration of 19 3 4 ×10 cm- ?
(A) Silicon atoms (B) Holes
(C) Dopant atoms (D) Valence electrons
6. The full form of the abbreviations TTL and CMOS in reference to logic families are
(A) Triple Transistor Logic and Chip Metal Oxide Semiconductor
(B) Tristate Transistor Logic and Chip Metal Oxide Semiconductor
10min
t
0
10V
12V
v (t)
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(C) Transistor Transistor Logic and Complementary Metal Oxide Semiconductor
(D) Tristate Transistor Logic and Complementary Metal Oxide Silicon
7. The ROC of Z-transform of the discrete time sequence
( ) ( ) ( )
n n
1 1
x n u n u n 1 is
3 2
   
=   -   - -
   
(A)
1 1
z
3 2
< < (B)
1
z
2
> (C)
1
z
3
< (D) 2 < z < 3
8. The magnitude plot of a rational transfer function G(s) with real coefficients is
shown below. When of the following compensators has such a magnitude plot?
(A) Lead compensator (B) Lag compensator
(C) PID compensator (D) Lead-lag compensator
9. A white noise process X(t) with two-sided power spectral density 1×10-10 W/Hz is
input to a filter whose magnitude squared response is shown below
The power of the output process Y(t) is given by
(A) 7 5 ×10- W (B) 6 1×10- W (C) 6 2 ×10- W (D) 5 1×10- W
10. Which of the following statements is true regarding the fundamental mode of the
metallic waveguides shown?
(A) Only P has no cutoff-frequency (B) Only Q has no cutoff-frequency
(C) Only R has no cutoff-frequency (D) all three have cutoff-frequency
P. Coaxial Q. Cylindrical
R:Rectangular
-40dB
20dB
G(jw)
logw
-10kHz 10kHz
1
( )2
H f
X(t) Y (t)
f
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11. A fair coin is tossed 10times. What is the probability that ONLY the first two
tosses will yield heads?
(A)
2
1
2
 
 
 
(B)
2
10
2
1
C
2
 
 
 
(C)
10
1
2
 
 
 
(D)
10
10
2
1
C
2
 
 
 
12. If the power spectral density of stationary random process is a sine-squared
function of frequency, the shape of its autocorrelation is
(A) (B) (C) (D)
13. ( ) ( ) 1
0 1
unit
circle
1 f z
If f z c c z , then dz is given by
z
- +
= + 
(A) 2pc1 (B) ( ) 0 2p 1 + c (C) 1 2pjc (D) ( ) 0 2pj 1 + c
14. In the interconnection of ideal sources shown in the figure, it is known that the
60V source is absorbing power
Which of the following can be the value of the current source  ?
(A) 10A (B) 13A (C) 15A (D) 18A
15. The ratio of the mobility to the diffusion coefficient in a semiconductor has the
units
(A) 1 V- (B) 1 em× V- (C) 1 V × cm- (D) V . s
16. In a microprocessor, the service routine for a certain interrupt starts from a fixed
location of memory which cannot be externally set, but the interrupt can be
delayed or rejected. Such an interrupt is
(A) non-maskable and non-vectored (B) maskable and non-vectored
(C) non-maskable and vectored (D) maskable and vectored

+-
60V
12A
+ - 20V
R (t)
t
R (t)
t
R (t)
t
R (t)
t
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17. If the transfer function of the following network is
( )
( )
0
i
V s 1
V s 2 s CR
=
+
The value of the load resistance RL is
(A) R/4 (B) R/2 (C) R (D) 2R
18. Consider the system
dx Ax Bu with A 1 0 and B p
dt 0 1 q
= + =  = 




where p and q are
arbitrary real numbers. Which of the following statements about the
controllability of the system is true?
(A) The system is completely state controllable for any nonzero values of p and q
(B) Only p=0 and q=0 result in controllability
(C) The system is uncontrollable for all values of p and q
(D) We cannot conclude about controllability from the given data
19. For a message signal ( ) ( ) m m t = cos 2pf t and carrier of frequency fc, which of the
following represents a single side band (SSB) signal?
(A) ( ) ( ) m c cos 2pf t cos 2pf t (B) ( ) c cos 2pf t
(C) ( ) c m cos  2p f + f t
(D) ( ) ( ) m c  1 + cos 2pf t
cos 2pf t
20. Two infinitely long wires carrying current are as shown in the figure below. One
wire is in the y-z plane and parallel to the y-axis. The other wise is in the x-y
plane and parallel to the x-axis. Which components of the resulting magnetic field
are non-zero at the origin?
(A) x, y, z components (B) x, y components
(C) y, z components (D) x, z components
R
C
i V
+
-
0 V
+
-
L R
1A
1A
z
x
y
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Q. No. 21 – 56 Carry Two Marks Each
21. Consider two independent random variables X and Y with identical distributions.
The variables X and Y take values 0, 1 and 2 with probabilities
1 1 1
, and
2 4 4
respectively. What is the conditional probability P (X + Y = 2| X - Y = 0) ?
(A) 0 (B)
1
16
(C)
1
6
(D) 1
22. The Taylor series expansion of
sinx
at x is given by
x
= p
- p
(A)
( )2 x
1 ...
3!
- p
+ + (B)
( )2 x
1 ...
3!
- p
- - + (C)
( )2 x
1 ...
3!
- p
- + (D)
( )2 x
1 ...
3!
- p
- + +
23. If a vector field V

is related to another vector field A

through V = Ñ × A,
 
which
of the following is true? Note: C and SC refer to any closed contour and any
surface whose boundary is C.
(A)
C C S
 V × d =  A × dS
   
  (B)
C C S
 A × d =  V × dS
   
 
(C)
C C S
 Ñ × V × d =  Ñ × A × dS
   
  (D)
C C S
 Ñ × A × d =  V × dS
   
 
24. Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform
of ( )
t
0
 f t dt is
(A) sF (s) - f (0) (B) ( ) 1
F s
s
(C) ( )
s
0
 F t dt (D) ( ) ( ) 1
F s f 0
s
 -

25. Match each differential equation in Group I to its family of solution curves from
Group II.
Group – I Group – II
P.
dy y
dx x
= 1. Circles
Q.
dy y
dx x
= - 2. Straight lines
R.
dy x
dx y
= 3. Hyperbolas
S.
dy x
dx y
= -
(A) P-2,Q-3,R-3,S-1 (B) P-1,Q-3,R-2,S-1
(C) P-2,Q-1,R-3,S-3 (D) P-3,Q-2,R-1,S-2
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26. The eigen values of the following matrix are
-1 3 5
-3 -1 6
0 0 3








(A) 3,3 + 5j,6 - j (B) -6 + 5j,3 + j,3 - j
(C) 3 + j,3 - j,5 + j (D) 3, -1 + 3j, -1 - 3j
27. An AC source of RMS voltage 20V with internal impedance ( ) S Z = 1 + 2j W feeds a
load of impedance ( ) L Z = 7 + 4j W in the figure below. The reactive power
consumed by the load is
(A) 8VAR (B) 16VAR (C) 28VAR (D) 32VAR
28. The switch in the circuit shown was on position a for a long time, and is moved to
position b at time t=0. The current i(t) for t>0 is given by
(A) 125t ( ) 0.2e u t mA - (B) 1250t ( ) 20e u t mA -
(C) 1250t ( ) 0.2e u t mA - (D) 1000t ( ) 20e u t mA -
( ) L Z = 7 + 4j W
( ) S Z = 1 + 2j W
20Ð0ºV
+-
+-
5kW
i (t)
10kW a b
100V
0.5µF 0.3µF
0.2µF
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29. In the circuit shown, what value of RL maximizes the power delivered to RL?
(A) 2.4W (B)
8
3
W (C) 4W (D) 6W
30. The time domain behavior of an RL circuit is represented by
( Rt /L ) ( )
0
di
L Ri V 1 Be sint u t .
dt
+ = + -
For an initial current of ( ) 0 V
i 0 ,
R
= the steady state value of the current is given
by
(A) ( ) 0 V
i t
R
® (B) ( ) 0 2V
i t
R
®
(C) ( ) 0 ( ) V
i t 1 B
R
® + (D) ( ) 0 ( ) 2V
i t 1 B
R
® +
31. In the circuit below, the diode is ideal. The voltage V is given by
(A) ( ) i min V,1 (B) ( ) i max V,1 (C) ( ) i min -V,1 (D) ( ) i max -V,1
32. Consider the following two statements about the internal conditions in an
n-channel MOSFET operating in the active region
S1: The inversion charge decreases from source to drain
S2: The channel potential increases from source to drain
Which of the following is correct?
(A) Only S2 is true
+-
i V 100V
4W 4W
X -V +
- +
X 4W V
L R
+-
i V
1W 1W
+ V -
1A
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(B) Both S1 and S2 are false
(C) Both S1 and S2 are true, but S2 is not a reason for S1
(D) Both S1 and S2 are true, and S2 is a reason for S1
33. In the following astable multivibrator circuit, which properties of v0(t) depend on
R2?
(A) Only the frequency
(B) Only the amplitude
(C) Both the amplitude and the frequency
(D) Neither the amplitude nor the frequency
34. In the circuit shown below, the op-amp is ideal, the transistor has
VBE = 0.6V and b = 150. Decide whether the feedback in the circuit is positive or
negative and determine the voltage V at the output of the op-amp
(A) Positive feedback, V=10 V
(B) Positive feedback, V=0 V
(C) Negative feedback, V=5 V
(D) Negative feedback, V=2 V
35. A small signal source ( ) 6
i v t = A cos20t + B sin10 t is applied to a transistor
amplifier as shown below. The transistor has ie b = 150 and h = 3kW. Which
expression best approximates ( ) 0 V t
(A) ( ) ( 6 )
0 v t = -1500 A cos20t + Bsin10 t
(B) ( ) ( 6 )
0 v t = -150 A cos20t + B sin10 t
(C) ( ) 6
0 v t = -1500B sin10 t
(D) ( ) 6
0 v t = -150Bsin10 t
4 R
3 R
( ) 0 v t
C
2 R
1 R
-
+
V
1.4kW
+
-
5V
5kW
10V
20kW
12V
900W
100nF
( ) i v t
100kW 3kW
100nF
10µF
( ) 0 v t
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36. If X = 1 in the logic equation 
X + Z{Y + (Z + XY)} {X + Z(X + Y)} = 1, then

(A) Y=Z (B) Y = Z (C) Z=1 (D) Z=0
37. What are the minimum number of 2 to 1 multiplexers required to generate a 2
input AND gate and a 2 input Ex-OR gate?
(A) 1 and 2 (B) 1 and 3 (C) 1 and 1 (D) 2 and 2
38. Refer to the NAND and NOR latches shown in the figure. The inputs ( ) 1 2 P ,P for
both the latches are first made (0, 1) and then, after a few seconds, made (1, 1).
The corresponding stable outputs (Q1, Q2) are
(A) NAND: first (0, 1) then (0, 1) NOR: first (1, 0) then (0, 0)
(B) NAND: first (1, 0) then (1, 0) NOR: first (1, 0) then (1, 0)
(C) NAND: first (1, 0) then (1, 0) NOR: first (1, 0) then (0, 0)
(D) NAND: first (1, 0) then (1, 1) NOR: first (0, 1) then (0, 1)
39. What are the counting stages (Q1, Q2) for the counter shown in the figure below?
(A) 11,10,00,11,10,.... (B) 01,10,11,00,01,....
(C) 00,11,01,10,00,.... (D) 01,10,00,01,10,....
2 P
1 P
2 Q
1 Q
2 P
1 P
2 Q
1 Q
Clock JK Flip Flop JK Flip Flop
1 J
1 K
1 Q
1 Q
2 J
2 K
2 Q
2 Q
2 Q 1 Q
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40. A system with transfer function H(z) has impulse response h(.) defined as
h(2)=1, h(3)=-1 and h(k)=0 otherwise. Consider the following statements
( )
( )
S1:H z is a low pass filter
S2 :H z is a FIR filter
Which of the following is correct?
(A) Only S2 is true
(B) Both S1 and S2 are false
(C) Both S1 and S2 are true, and S2 is a reason for S1
(D) Both S1 and S2 are true, but S2 is not a reason for S1
41. Consider a system whose input x and output y are related by the equation
y (t) x (t )h(2 ) d
¥

=  - t t t
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system?
BIBO: Bounded input gives a bounded output
Causal: The system is causal
LP: The system is low pass
LTI: The system is linear and time invariant
(A) Causal, LP
(B) BIBO, LTI
(C) BIBO, Causal, LTI
(D) LP, LTI
42. The 4 point Discrete Fourier Transform (DFT) of a discrete time sequence
{1, 0, 2, 3} is
(A)  0, -2 + 2j,2, -2 - 2j
(B)  2,2 + 2j,6,2 - 2j

(C)  6,1 - 3j,2,1 + 3j
(D)  6, -1 + 3j,0, -1 - 3j

43. The feedback configuration and the pole-zero locations of ( ) 2
2
s 2s 2
G s
s 2s 2
- +
=
+ +
are
shown below. The root locus for negative values of k, i.e. for -¥ < k < 0, has
breakaway/break in points and angle of departure at pole P (with respect to the
positive real axis) equal to
(A) ± 2 and 0ºError! Not a valid link.
(B) ± 2 and 45º
(C) ± 3 and 0º
(D) ± 3 and 45º
0 t
h(t)
+
+
-
K G(s)
Im (s)
o ×
o ×P
Re(s)
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44. An LTI system having transfer function
2
2
s 1
s 2s 1
+
+ +
and input x(t)=sin(t+1) is in
steady state. The output is sampled at a rate wS rad/s to obtain the final output
{y(k)}. Which of the following is true?
(A) y(.) is zero for all sampling frequencies wS
(B) y(.) is nonzero for all sampling frequencies wS
(C) y(.) is nonzero for ws>2, but zero for ws>2
(D) y(.) is zero for ws>2 but nonzero for ws>2
45. The unit step response of an under-damped second order system has steady
state value of -2. Which one of the following transfer functions has these
properties?
(A) 2
2.24
s 2.59s 1.12
-
+ +
(B) 2
3.82
s 1.91s 1.91
-
+ +
(C) 2
2.24
s 2.59s 1.12
-
- +
(D) 2
3.82
s 1.91s 1.91
-
- +
46. A discrete random variable X takes values from 1 to 5 with probabilities as shown
in the table. A student calculates the mean of X and 3.5 and her teacher
calculates the variance of X as 1.5. Which of the following statements is true?
( )
k 1 2 3 4 5
P X = k 0.1 0.2 0.4 0.2 0.1
(A) Both the student and the teacher are right
(B) Both the student and the teacher are wrong
(C) Both the student is wrong but the teacher is right
(D) The student is right but the teacher is wrong
47. A message signal given by
( ) 1 2
1 1
m t cos t sin t
2 2
   
=   w -   w
   
Is amplitude modulated with a carrier of frequency wc to generate
( ) ( ) c s t =  1 + m t
cos w t
(A) 8.33% (B) 11.11% (C) 20% (D) 25%
48. A communication channel with AWGN operating at a signal to noise ratio SNR>>1
and bandwidth B has capacity C1. If the SNR is doubled keeping B constant, the
resulting capacity C2 is given by
(A) 2 1 C » 2C (B) 2 1 C » C + B (C) 2 1 C » C + 2B (D) 2 1 C » C + 0.3B
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49. A magnetic field in air is measured to be
0 2 2 2 2
x y
B B ˆy ˆx
x y x y
 
=  -   + + 

What current distribution leads to this field? [Hint: The algebra is trivial in
cylindrical coordinates.]
(A) 0
2 2
0
B ˆz 1
J ,r 0
x y
 
=   ¹ µ  + 

(B) 0
2 2
0
B ˆz 2
J ,r 0
x y
 
=   ¹ µ  + 

(C) J = 0,r ¹ 0

(D) 0
2 2
0
B ˆz 1
J ,r 0
x y
 
=   ¹ µ  + 

50. A transmission line terminates in two branches, each of length l/4, as shown.
The branches are terminated by 50W loads. The lines are lossless and have the
characteristic impedances shown. Determine the impedance Z1 as seen by the
source
(A) 200W (B) 100W (C) 50W (D) 25W
Common Data Questions: 51 & 52
Consider a silicon p-n junction at room temperature having the following
parameters:
Doping on the n-side = 1×1017cm-3
Depletion width on the n-side = 0.1µm
Depletion width on the p-side =1.0µm
Intrinsic carrier concentration = 1.4×1014F. cm-1
Thermal voltage = 26mV
Permittivity of free space = 8.85×10-14F. cm-1
Dielectric constant of silicon = 12
51. The built in potential of the junction
(A) is 0.70V
(B) is 0.76V
(C) is 0.82V
(D) cannot be estimated from the data given
l / 4
0 Z = 100W
0 Z = 100W
l / 4 L Z = 50W
L Z = 50W
l / 4
0 Z = 50W
i z
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52. The peak electric field in the device is
(A) 0.15 MV.cm-1, directed from p-region to n-region
(B) 0.15 MV.cm-1, directed from n-region to p-region
(C) 1.80 MV.cm-1, directed from p-region to n-region
(D) 1.80 MV.cm-1, directed from n-region to p-region
Common Data Questions: 53 & 54
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are
interested in the stability of the closed loop system in the feedback configuration
shown.
53. Which of the following statements is true?
(A) G(s) is an all-pass filter
(B) G(s) has a zero in the right-half plane
(C) G(s) is the impedance of a passive network
(D) G(s) is marginally stable
54. The gain and phase margins of G(s) for closed loop stability are
(A) 6dB and 180º (B) 3dB and 180º (C) 6dB and 90º (D) 3dB and 90º
Common Data Questions: 55 & 56
The amplitude of a random signal is uniformly distributed between -5V and 5V
55. If the signal to quantization noise ratio required in uniformly quantizing the signal
is 43.5dB, the step size of the quantization is approximately
(A) 0.0333V (B) 0.05V (C) 0.0667V (D) 0.10V
56. If the positive values of the signal are uniformly quantized with a step size of
0.05V, and the negative values are uniformly quantized with a step size of 0.1V,
the resulting signal to quantization noise ratio is approximately
(A) 46dB (B) 43.8dB (C) 42dB (D) 40dB
+
+
-
G(s)
Re
-j
-1 -0.5
Im
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Linked Answer Questions: Q.57 to Q.60 Carry Two Marks Each
Statement for Linked Answer Questions: 57 & 58
Consider the CMOS circuit shown, where the gate voltage VG of the n-MOSFET is
increased from zero, while the gate voltage of the p-MOSFET is kept constant at
3 V. Assume that, for both transistors, the magnitude of the threshold voltage is
1 V and the product of the transconductance parameter and the (W/L) ratio, i.e.
the quantity ( ) 2
µCox W/ L , is 1mA × V- .
57. For small increase in VG beyond 1V, which of the following gives the correct
description of the region of operation of each MOSFET?
(A) Both the MOSFETs are in saturation region
(B) Both the MOSFETs are in triode region
(C) n-MOSFET is in triode and p-MOSFET is in saturation region
(D) n-MOSFET is in saturation and p-MOSFET is in triode region
58. Estimate the output voltage V0 for VG=1.5V. [Hint: Use the appropriate current
voltage equation for each MOSFET, based on the answer to Q.57]
(A)
1
4 V
2
- (B)
1
4 V
2
+ (C)
3
4 V
2
- (D)
3
4 V
2
+
Statement for Linked Answer Questions: 59 & 60
Two products are sold from a vending machine, which has two push buttons P1
and P2. When a button is pressed, the price of the corresponding product is
displayed in a 7-segment display.
If no buttons are pressed, ‘0' is displayed, signifying ‘Rs. 0'.
If only P1 is pressed, ‘2' is displayed, signifying ‘Rs. 2'.
If only P2 is pressed, ‘5' is displayed, signifying ‘Rs. 5'.
If both P1 and P2 are pressed, ‘E' is displayed, signifying ‘Error'.
The names of the segments in the 7-segment display, and the glow of the display
for ‘0', ‘2', ‘5' and ‘E', are shown below
G V
3V
5V
0 V
EC½ GATE Paper 2009 www.gateforum.com
© All rights reserved by GATE Forum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission. Discuss this questions paper at www.gateforum.com. Page 15 of 15
Consider
(i) push button pressed/not pressed is equivalent to logic 1/0 respectively
(ii) a segment glowing / not glowing in the display is equivalent to logic 1/0
respectively
59. If segments a to g are considered as functions of P1 and P2, then which of the
following is correct?
(A) g = P1 + P2,d = c + e (B) 1 2 g = P + P ,d = c + e
(C) 1 2 g = P + P ,e = b + c (D) 1 2 g = P + P ,e = b + c
60. What are the minimum numbers of NOT gates and 2-input OR gates required to
design the logic of the driver for this 7-segment display?
(A) 3 NOT and 4 OR (B) 2 NOT and 4 OR
(C) 1 NOT and 3 OR (D) 2 NOT and 3 OR
a
g
f b
d
e c
0 2 5 E





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