EC-GATE-2015 PAPER-01| General Aptitude Q. No. 1 – 5 Carry One

Transcription

EC-GATE-2015 PAPER-01|
www.gateforum.com
General Aptitude
Q. No. 1 – 5 Carry One Mark Each
1.
Choose the word most similar in meaning to the given word:
Educe
(A) Exert
Answer:
2.
(B) Educate
(C) Extract
(D) Extend
(C) -25/49
(D) -49/25
(C)
If logx (5/7) = -1/3, then the value of x is
(A) 343/125
Answer:
(B) 125/343
(A)
3
Exp:
5
7
7
 x 1 3   x1 3     x  2.74
7
5
5
3.
Operators ,  and  aredefined by : a  b 
 66  6   66 6 .
(A) -2
Answer: (C)
Exp:
666 
(B) -1
ab
ab
;a  b 
;a  b  ab. Find the value
ab
a b
(C) 1
(D) 2
66  6 60 5


66  6 72 6
66 6 
66  6 72 6


66  6 60 5
5 6
(666)(66 6)    1
6 5
4.
Choose the most appropriate word from the options given below to complete the following
sentence.
The principal presented the chief guest with a ____________, as token of appreciation.
(A) momento
Answer:
5.
(B) memento
(C) momentum
(D) moment
(B)
Choose the appropriate word/phrase, out of the four options given below, to complete the
following sentence:
Frogs ____________________.
(A) Croak
Answer:
Exp:
(B) Roar
(C) Hiss
(D) Patter
(A)
Frogs make ‘croak’ sound.
© All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the
written permission.
1
www.gateforum.com
Q. No. 6 – 10 Carry Two Marks Each
6.
A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the
proportion of the number of faces of the smaller cubes visible to those which are NOT
visible.
(A) 1 : 4
(B) 1 : 3
(C) 1 : 2
(D) 2 : 3
Answer:
(C)
Exp:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Number of faces per cube = 6
Total number of cubes = 9×3 = 27
∴ Total number of faces = 27×6 = 162
∴ Total number of non visible faces = 162-54 = 108
∴
7.
Number of visible faces
54 1


Number of non visible faces 108 2
Fill in the missing value
1
6
5
4
7
4
7
2
9
2
8
1
4
1
5
2
3
Answer:
Exp:
1
2
1
3
3
3
Middle number is the average of the numbers on both sides.
Average of 6 and 4 is 5
Average of (7+4) and (2+1) is 7
written permission.
2
www.gateforum.com
Average of (1+9+2) and (1+2+1) is 8
Average of (4+1) and (2+3) is 5
Therefore, Average of (3) and (3) is 3
8.
Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A
person sitting on the wall falls if the wall breaks.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
(A) Humpty Dumpty always falls while having lunch
(B) Humpty Dumpty does not fall sometimes while having lunch
(C) Humpty Dumpty never falls during dinner
(D) When Humpty Dumpty does not sit on the wall, the wall does not break
Answer:
9.
(B)
The following question presents a sentence, part of which is underlined. Beneath the sentence
you find four ways of phrasing the underline part. Following the requirements of the standard
written English, select the answer that produces the most effective sentence.
Tuberculosis, together with its effects, ranks one of the leading causes of death in India.
(A) ranks as one of the leading causes of death
(B) rank as one of the leading causes of death
(C) has the rank of one of the leading causes of death
(D) are one of the leading causes of death
Answer:
10.
(A)
Read the following paragraph and choose the correct statement.
Climate change has reduced human security and threatened human well being. An ignored
reality of human progress is that human security largely depends upon environmental
security. But on the contrary, human progress seems contradictory to environmental security.
To keep up both at the required level is a challenge to be addressed by one and all. One of the
ways to curb the climate change may be suitable scientific innovations, while the other may
be the Gandhian perspective on small scale progress with focus on sustainability.
(A) Human progress and security are positively associated with environmental security.
(B) Human progress is contradictory to environmental security.
(C) Human security is contradictory to environmental security.
(D) Human progress depends upon environmental security.
Answer:
(B)
written permission.
3
www.gateforum.com
Electronics and Communication Engineering
Q. No. 1 – 25 Carry One Mark Each
1.
A region of negative differential resistance is observed in the current voltage characteristics
of a silicon PN junction if
(A) Both the P-region and the N-region are heavily doped
(B) The N-region is heavily doped compared to the P-region
(C) The P-region is heavily doped compared to the N-region
(D) An intrinsic silicon region is inserted between the P-region and the N-region
Answer: (A)
2.
A silicon sample is uniformly doped with donor type impurities with a concentration of
1016 / cm3 . The electron and hole mobilities in the sample are
1200cm2 / V  s and 400cm2 / V  s respectively. Assume complete ionization of impurities.
The charge of an electron is 1.6 1019 C. The resistivity of the sample
____________.
Answer: 0.52
1
1
Exp: P 

N ND q n
 in  cm  is
1
10  1.6  1019  1200
 0.52   cm

16
K
.
s  s  1 s  3
The value of the gain K (>0) at which the root locus crosses the imaginary axis is
_________________.
Answer: 12
3.
A unity negative feedback system has the open-loop transfer function G  s  
Exp:
C.Eis1 
k
0
s  s  1 s  3
s3  4s2  3s  k  0
By using Routh Table, s1 row should be zero. For poles to be on imaginary axis
12  k
 0 ; k should be 12.
4
4.
Suppose
A
and
B
are
two
independent
events
with
probabilities
P  A   0 and P  B  0. Let A and B be their complements. Which one of the following
statements is FALSE?
(A) P  A  B  P  A  P  B
(B) P  A \ B  P  A 
(C) P  A  B  P  A   P  B


 
(D) P A  B  P A P  B
Answer: (C)
Exp: We know that A and B are independent
then P(A∩B) = P(A) P(B)
written permission.
4
www.gateforum.com
A and B are independent then P(A/B) = P(A) and P(B/A) = P(B)
Also if A and B are independent then Aand B are also independent

    
i.e., P A  B  P A P B
∴ (A), (B), (D) are correct
(C) is false
Since P(A∪B) = P(A)+P(B)-P(A∩B)
= P(A)+P(B)-P(A)P(B)
5.
The waveform of a periodic signal x(t) is shown in the figure.
xt
3
2
1
4 3
1
4
2
t
3
3
A signal g(t) is defined by
 t 1 
gt  x 
 . The average power of g(t) is
 2 
__________________.
Answer: 1.5
 t 1 
Exp: g  t   x 

 2 
The average power of x(t) and g(t) is same because the signal g(t) is scaled and shifted
version of x(t).
1
1
2
3t  dt

T  4
1
Power of x  t   lim

1
9  t3 
9 2 3
 lim     
T  4 3
  1 4 2 2
3
2
In the network shown in the figure, all resistors are identical with R  300  . The resistance
 Power of g  t  
6.
R ab  in   of the network is___________.
a
R
R
Answer: 100
R
R
R
R
R ab
R
R
R
R
R  300
R
R
R
R
R
b
written permission.
5
www.gateforum.com
Exp:
R
R
R
R
2
R
R
R
R eq
R
2
R
2
2
R
By bridge condition
2R
R
R
2R
R eq
R eq  R  100
3
7.
Consider a system of linear equations:
x  2y  3z  1
x  3y  4z  1 and
2x  4y  6z  k.
The value of k for which the system has infinitely many solutions is ________________.
Answer:
Exp:
2
x-2y+3z = -1
x-3y+4z = 1
-2x+4y-6z = k
 1 2 3 1
Augmented matrix  A B    1 3 4 1 
 2 4 6 K 
R 2  R 2  R1 , R 3  R 3  2R1
1 
1 2 3
0 1 1
2 

0 0 0 K  2 
The system will have infinitely many solutions if p(A/B) = p(A) = r < number of variables
 k-2 = 0
k=2
written permission.
6
8.
The polar plot of the transfer function G  s  
10  s  1
(A) first quadrant
for 0     will be in the
s  10
(B) second quadrant
(C) third quadrant
(D) fourth quadrant
Answer:
Exp:
www.gateforum.com
(A)
G s 
10  s  1
s  10
Put s  j
G  j 
10  j  1
 j  10 
  0, M  1  0
  , M  10  0
j

10
0

So, zero is nearer to imaginary axis. Hence plot will move clockwise direction.
It is first quadrant.
9.
Let z  x  iy be a complex variable. Consider that contour integration is performed along
the unit circle in anticlockwise direction. Which one of the following statements is NOT
TRUE?
(A) The residue of
(B)

C
z
at z  1 is 1 / 2
z2  1
z 2 dz  0
1
1
dz  1


C
2i z
(D) z (complex conjugate of z) is an analytical function
(C)
Answer:
Exp:
(D)
f z  z
 x  iy
u  x, v   y
 u x  1and v x  0
written permission.
7
www.gateforum.com
u y  0 and v y  1
 u x  v y i.e., C  R equations not satisfied
 z is not analytic
(A) z = 1 is a simple pole
z
z
1
 z 
Residue  2

 z  1. 2  lim
 at z  1 is lim
z

1
z

1
z 1
z 1 2
 z 1 
(B) Since z2 is analytic everywhere
∴ Using Cauchy’s integral theorem,
 z dz  0 y
2
C
10.
ˆ  t  2f c t  where m
ˆ  t  denotes the Hilbert
Consider the signal s  t   m  t  cos  2f c t   m
transform of m(t) and the bandwidth of m(t) is very small compared to f c . The signal s(t) is a
(A) high-pass signal
(B) low-pass signal
(C) band-pass signal
(D) double sideband suppressed carrier signal
Answer:
Exp:
(C)
Given s(t) is the equation for single side band modulation (lower side band).
Thus it is a Band pass signal.
11.
For the circuit with ideal diodes shown in the figure, the shape of the output  vout  for the
given sine wave input  vin  will be
0
T
0.5T
(A)
0
(C)
Answer:
0
0.5T
0.5T


 in
 out


T
T
(B)
0
0.5T
0
0.5T
T
(D)
T
(C)
written permission.
8
Exp:
www.gateforum.com
The circuit can be re drawn as

a
d

D1

Vo


b
R
c
D2
D2

During positive pulse, both diodes are forward biased. So output pulse of +ve polarity is
produced. As polarity at ‘d’ and ‘c’ is given opposite to input terminals, hence +ve pulse is
inverted. During negative pulse, both diodes are reverse biased. So, V0 = 0V
12.
The result of the convolution x  t     t  t 0  is
(A) x  t  t 0 
Answer:
Exp:
(B) x  t  t 0 
(C) x  t  t 0 
(D) x  t  t 0 
(D)
x(t) *   t  t 0   x(t) * (t  t 0 )
 x  t  t  t 0 
 x  t  t 0 
13.
1 
4


The value of p such that the vector  2  is an eigenvector of the matrix  p
3 
14
___________.
1
2
4
2
1  is
10 
Answer: 17
Exp:
4 1 2
1 


AX  X   P 2 1     2 
14 4 10 
 3 
 12    
  P  7    2     12      1
 36   3 
2  P  7
      2
and 3  36 i.e.,   12
 Equation  2  gives P  7  24  P  17
written permission.
9
14.
www.gateforum.com
In the given circuit, the values of V1 and V2 respectively are
4
I

2I
V2
5A
4
4

(A) 5V, 25V
Answer:
Exp:
(B) 10V, 30V

V1

(C) 15V, 35V
(D) 0V, 20V
(A)
By nodal analysis
5  I  I  2I  0
4I  5
5
I A
4
V1  4I  5volts
V2  4(5)  V1
 20  V1  25 volts
15.
In an 8085 microprocessor, the shift registers which store the result of an addition and the
overflow bit are, respectively
(A) B and F
Answer:
(B) A and F
(C) H and F
(D) A and C
(B)
Exp:
In an 8085 microprocessor, after performing the addition, result is stored in accumulator and
if any carry (overflow bit) is generated it updates flags.
16.
Negative feedback in a closed-loop control system DOES NOT
(A) reduce the overall gain
(B) reduce bandwidth
(C) improve disturbance rejection
(D) reduce sensitivity to parameter variation
Answer:
Exp:
(B)
Negative feedback in a closed loop
(i) Increases bandwidth
(ii) Reduces gain
(iii) Improve distance rejection
written permission.
10
17.
A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one
(number of rows is equal to the number of columns). The minimum number of address lines
needed for the row decoder is ___________________.
Answer:
Exp:
www.gateforum.com
7
Generally the structure of a memory chip = Number of Row × Number of column
= M×N
 The number of address line required for row decoder is n where M = 2n or
n = log2M
 As per information given in question : M = N
So M×N = M×M = M2 = 16k = 24×210
 M2 = 214
 M = 128
 n = log2128 = 7
18.
A function f (x)  1  x 2  x 3 is defined in the closed interval [-1, 1]. The value of x, in the
open interval (-1, 1) for which the mean value theorem is satisfied, is
(A) -1/2
(B) -1/3
(C) 1/3
(D) 1/2
Answer:
Exp:
(B)
By Lagrange’s mean value theorem
f ' x  
f 1  f  1
1   1

2
1
2
-2x+3x2 = 1
3x2-2x-1 = 0
So x = 1, -1/3
x= -1/3 only lies in (-1,1)
19.
The electric field component of a plane wave traveling in a lossless dielectric medium is

z 

given by E  z, t   aˆ y 2cos 108 t 
 V/ m . The wavelength (in m) for the wave is
2

_____________________.
Answer:
Exp:
8.885
z 

E  z, t   2cos 108 t 
ay
2

2

 2 2

  8.885m
written permission.
11
20.
www.gateforum.com
In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The
energy  in J  taken from the 3V source to charge the 0.1F capacitor from 0V to 3V is
3V
SW
120
B
A
t 0
0.1F
(A) 0.3
(B) 0.45
(C) 0.9
Answer: (C)
Exp: So the capacitor in initially uncharged i.e. VC(0) = 0
(D) 3
 The capacitor will be charged to supply voltage 3V when the switch is in position B
for ∞ time.
 So we need to find capacitor voltage
Vc  t   Vc      Vc  0   Vc     e  t 
 3  3e  t 
  RC  120  0.1  106  12  sec
ic  C
dVc
dt

 0.1  106

 dtd 3  3e
t 


3  0.1  t  0.3  t 
e 
e

12
 So instantaneous power of source = V(t)i(t)
 0.3
 0.9  t 
P  t    3  .e t   
e
 12
 12

 E  Pdt

0


0.9
 12 e
t 
dt
0
   
0.9  t  
0.9 
e    



0
12
 12 
 12  106 
0.9
12
 0.9 J
written permission.
12
21.
www.gateforum.com
In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6V. The output
voltage V0 (in volts) is ________________.
1k

10V
1k
V0

Answer: 5
Exp: Zener is not Breakdown
Hence
Vo  10 
22.
Consider a four bit D to A converter. The analog value corresponding to digital signals of
values 0000 and 0001 are 0V and 0.0625V respectively. The analog value (in Volts)
corresponding to the digital signal 1111 is ___________________.
Answer:
Exp:
1
 5V
2
0.9225
Analog output = [Resolution] × [Decimal equivalent of Binary]
= (0.0615) (15) = 0.9225V
23.
In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across
the capacitor is ___________________.
4
10cos  t 
 Volts 
Answer:
Exp:
0.1mH
1F

25
VC  QV  90
Q
0 L 1 L 10

  2.5
R
R C 4
VC = 25-90°
|VC| = 25V
written permission.
13
24
A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size  of the delta modulator are 20,000 samples per second and 0.1V, respectively. To
prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
(A)
Answer:
Exp:
www.gateforum.com
1
2
(A)
(B)
1

(C)
2

(D) 
To avoid slope overload,
.Ts 
d
x(t)
dt
max
x(t)  E m sin  2f m t 
d
x(t)
 E m .2f m
dt
max
0.1  20,000  E m .2.2000
 Em 
25.
1
2
Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one
of the following plots (in linear scale) qualitatively represents the dependence of H  on r,
where H  is the magnitude of the azimuthal component of magnetic field outside the
conductor and r is the radial distance from the conductor?
A
 B
H
H
r
C
Answer:
Exp:
H 
 D
H
(C)
r
r
H
r
I
2r
r is the distance from current element.
H 
1
r
written permission.
14
www.gateforum.com
Q. No. 26 – 55 carry Two Marks Each
26.
The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with
probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional
probability that ‘1’ was transmitted is ______________________.
X
0
Y
0
6 7
P[X  0]  0.2
17
17
P[X  1]  0.8
1
Answer:
Exp:
6 7
1
0.4
X
0
617
Y
0
Px  0  0.2
1/ 7
1/ 7
Px  1  0.8
1
1
6/7
P x  1 / y  0 
P y  0 / x  1 
P y  0 / x  1 P x  1
P{y  0}
1
7
P{x  1}  0.8
6
1 2
P{y  0}  0.2   0.8  
7
7 7
1
 0.8
 P x  1 / y  0  7
 0.4
2
7
27.
The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a
common bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total
bandwidth of the signal received by the base station of the cell will be at least (in kHz)
__________________.
Answer:
400
written permission.
15
Exp:
www.gateforum.com
Since GSM requires 200 KHz and only 8 users can use it using TDMA, 9th
another 200 KHz.
user
needs
9th, 10th, 11th, 12th user can use another 200 KHz bandwidth on time share basis.
Thus for 12 user we need 400 KHz bandwidth.
28.
For the discrete-time system shown in the figure, the poles of the system transfer function are
located at
Xn
Yn
1
6
5
6
Z1
Z1
(A) 2, 3
Answer:
(B)
1
, 3
2
(C)
1 1
,
2 3
(D) 2,
1
3
(C)
Exp:
Y(z)
 H(z) 
X(z)
1
5
z 2
1  z 1 
6
6
2
z

1
1


 z   z  
2 
3


z2
5
1
z2  z 
6
6
1
1
So, poles are z  , z  .
2
3
29.
The circuit shown in the figure has an ideal opamp. The oscillation frequency and the
condition to sustain the oscillations, respectively, are
R1
R2

 out

2C
1
and R1  R 2
CR
1
(C)
and R1  R 2
2CR
Answer: (D)
(A)
R
C
2R
1
and R1  4R 2
CR
1
(D)
and R1  4R 2
2CR
(B)
written permission.
16
Exp:
Frequency of Wein bridge oscillator is 0 
www.gateforum.com
1
, but in the question time constant is
RC
doubled so, frequency becomes half.
0 
1
2RC
Z1  2R 
1
 2  R  jR 
j c
1
R2
2 j c
j
Z2 

1
R

jR
R
2 jc
Z2
1


Z1  Z2 5
R
1
30.
R1
 5  R1  4R 2
R2
1
2
and bit 1 with probability . The emitted bits are
3
3
communicated to the receiver. The receiver decides for either 0 or 1 based on the received
value R. It is given that the conditional density functions of R are as
A source emits bit 0 with probability
1
1
 ,  3  x  1,
 ,  1  x  5,
f R|0 (r)   4
and f R|1 (r)   6

 0, otherwise.
 0, otherwise,

The minimum decision error probability is
(A) 0
Answer:
31.
(B) 1/12
(C) 1/9
(D) 1/6
(B)
For a silicon diode with long P and N regions, the accepter and donor impurity concentrations
are 11017 cm3 and 11015 cm3 , respectively. The lifetimes of electrons in P region and
holes in N region are both 100 s . The electron and hole diffusion coefficients are
49cm2 / s and 36cm2 / s,
respectively. Assume
kT / q  26mV , the intrinsic carrier
concentration is 110 cm and q  1.6 10 C . When a forward voltage of 208 mV is
10
3
19
applied across the diode, the hole current density  in nA / cm2  injected from P region to N
regions is __________.
Answer:
written permission.
17
32.
www.gateforum.com
For the NMOSFET in the circuit shown, the threshold voltage is Vth , where Vth  0 . The
source voltage Vss is varied from 0 to VDD . Neglecting the channel length modulation, the
drain current I D as a function Vss is represented by.
VDD
VSS
A
 B
ID
ID
VSS
VSS
VDD  Vth
C
Vth
 D
ID
VSS
VDD  Vth
VDD  Vth
Answer:
Exp:
ID
VSS
(A)
VGS = VDS
Hence MOS Transistor is in saturation.
In saturation,
ID  k  VGS  Vr   k  VDD  VSS  VT 
2
2
As VSS  ID   Not linearly because square factor 
Hence option (A) correct
written permission.
18
33.
www.gateforum.com
In the system shown in figure (a), m(t) is a low-pass signal with bandwidth W Hz. The
frequency response of the band-pass filter H(f) is shown in figure (b). If it is desired that the
output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than
____________________.
x  t   m  t  cos  2400t 
Amplifier
y  t   10x  t   x 2  t 
H f 
Band  pass
filter
zt
a 
H f 
1
1700
Answer:
Exp:
700
0
700
1700
f  Hz 
350
x(t)  m(t).cos  2400t 
Spectrum of x(t)
X(f )
1200  w 1200 1200  w
1200  w 1200 1200  w
f
y(t) =10x(t)+x2(t)
Let us draw the spectrum of positive frequencies of y(t).
y(t)  10m(t)cos  2400t  m 2 (t)cos 2 (2400t)
1  cos 4800t 
 10m(t)cos  2400t   m 2 (t) 

2


y(t) 
m2 (t)
m2 (t)
 10m(t)cos  2400t  
cos  4800t 
2
2
written permission.
19
www.gateforum.com
m2 (t)

2w
2w
y(t) 
 Y(f )
2w
2w 1200  w 1200 1200  w 2400  2w 1200 2400  2w
 2w  700
2400  2w  1700
 w  350
34.
In the circuit shown, I1  80mA and I2  4mA . Transistors T1 and T2 are identical. Assume
that the thermal voltage VT is 26mV at 27o C. At 50o C , the value of the voltage
V12  V1  V2 (in mV) is ________________.
Vs
I2
V2
T2
Answer:
 
V12
I1
V1
T1
-19.2
written permission.
20
Exp:
I2  ISe
www.gateforum.com
VBE2 VT
VBE2  V2
I1  ISe
VBE1 VT
VBE  V1
I1
e
I2
V1  V2
VT
VT  at 50C  
50  273
 27.8mV
11,600
V V
1
2
1
 e 27.8m
2
V1  V2  19.2 mV
35.
The electric field intensity of a plane wave traveling in free space is give by the following
expression
E  x, t   a y 24 cos  t  k 0 x  V / m 
In this field, consider a square area 10cm x 10 cm on a plane x + y = 1. The total timeaveraged power (in mW) passing through the square area is __________________.
Answer: 53.3
Exp:
E(x,t) = 24π cos(  t - k0x)V/m
Pavg 
1 E 02
ax
2 
1  24 
ax
2 120
 7.53a x
2

Power  P   Pavg .ds

s
x  y 1
ax  ay
2

 unit vector normal to thesurface
P  7.53a x .
s
ax
2
dydz
7.53

 10  10  102  102
2
P  53.3mW
P  53.3  103 W
36.
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
x 2  4y2  1 is ____________________.
Answer:
1
written permission.
21
Exp:
www.gateforum.com
rectangle
ellipse
o
Let 2x, 2y be the length, breadth respectively of the rectangle inscribed in the ellipse
x 2  4y2  1, then
Area of the rectangle (2x) (2y) i.e., 4xy
Consider, f   Area 
2
 16x 2 y2

1  x2 
 4x 2 1  x 2   y 2 

4 

f '  x   0  x 1  2x 2   0  x 
1
2
1
1
 y2   y 
8
8
f ''  x   8  48x 2  0 when x 
 f is maximum at x =
1
2
1
2
 1  1 
∴ Area is maximum and the maximum area is 4 
 i.e., 1

 2  8 
37.
In the given circuit, the maximum power (in Watts) that can be transferred to the load R L is
___________________.
2
40 Vrms
Answer:
Exp:
j2
RL
1.66
VTh(rms) 
4  2j
 2 245 ; VTh(mq)  24
2  2j
written permission.
22
www.gateforum.com
ZTh  2 || 2 j  1  j
R L  Zth  2 
Maximum power transfer to RL is
2
Pmax
38.
A lead compensator network includes a parallel combination of R and C in the feed-forward
s2
path. If the transfer function of the compensator is G c  s  
, the value of RC is
s4
______________.
Answer:
Exp:
2 245
 I  RL 
 2 1.66W
2 1 j
2
0.5
Given G(s) 
s2
s4
1
1
Zero = 2 = 
 RC
Pole = 4 =
1
1

 RC
So, RC = 0.5
39.
A MOSFET in saturation has a drain current of 1mA for VDS  0.5V . If the channel length
modulation coefficient is 0.05 V1 , the output resistance
_______________.
Answer: 20
Exp:
 in k 
of the MOSFET is
Under channel length modulation
I D  I Dsat 1  VDS 
dI D
1
  I Dsat
dVDS r0
r0 
1
1

I Dsat 0.05  103
 20 k
40.
The built-in potential of an abrupt p-n junction is 0.75V. If its junction capacitance  CJ  at
a reverse bias  VR  of 1.25V is 5pF , the value of CJ  in pF when
VR  7.25V is ___________ .
Answer:
Exp:
2.5
Cj 
1
Vbi  VR
written permission.
23
C2 j
C1j

www.gateforum.com
Vbi  VR1
Vbi  VR 2
2 C1j

 2.5 pF
8
2
So, answer is 2.5
C2 j  C1j
41.
In the circuit shown, assume that the opamp is ideal. The bridge output voltage V0 (in mV)
for   0.05 is _______________________.
100 
250 1 
+
1V
250 1 

-

V0
250 1 
250 1 
100 
250
1
I50  A  I100
50

Vo 
1
A
100
1
A
100
Answer:
Exp:
50 
Vo

1
 250 1     250 1   
100 
1
 250  2
100
1

 250  0.25V
1000
 250mV

42.
The damping ratio of a series RLC circuit can be expressed as
(A)
Answer:
Exp:
R 2C
2L
(C)
' ' 
(B)
2L
R 2C
(C)
R
2
C
L
(D)
2
R
L
C
1
(In series RLC circuit)
2Q
1

2
1 L
R C

R C
2 L
written permission.
24
43.
www.gateforum.com
In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value
of vc  t  (in Volts) at t= 1 sec is ___________________.
t 0
3

SW
2
10V
Answer:
5
F
6
v c t 

2.528
Exp:
3

Vc     4V

2
10
VC(0-) = 0V
At t = ∞, C is open circuit
Vc (∞) = 4V
  R th C   3 || 2  
5 6 5
   1sec
6 5 6
 
VC  t   VC      VC 0  VC     e  t 


 4  4e  t
VC 1  4  4e 1  2.528V
44.
Consider a uniform plane wave with amplitude  E0  of 10V / m and 1.1GHz frequency
travelling in air, and incident normally on a dielectric medium with complex relative
permittivity   r  and permeability   r  as shown in the figure.
Air
120
Dielectric
 r 1 j2
 r 1 j2
E ?
10cm
E 0 10V/m
Freq1.1GHz
The magnitude of the transmitted electric field component (in V/m) after it has travelled a
distance of 10 cm inside the dielectric region is __________________.
Answer: 0.1
written permission.
25
Exp:
1
 2
www.gateforum.com
Dielectric    0 
 r  1  j2
r  1  j2
2  120
air
1  120
E1  10 V m
1 = 2
So, E2 = E1 = 10 V/m
E3 Electric field in the dielectric after travelling 10 cm
E3  E 2ez
r    j  j    j
  j  j  0 0  r r
  j  j  0 0 1  j2 
 j  0 0  2  0 0
  2 0 0 
2  2  1.1  109
 46.07
3  108
z  10cm
E 3  10e 1010
45.
2
46.07
 10e 4.6  0.1





A vector P is given by P  x 3 ya x  x 2 y2a y  x 2 yza z . Which one of the following statements
is TRUE?

(A) P is solenoidal, but not irrotational

(B) P is irrotational, but not solenoidal,

(C) P is neither solenoidal nor irrotational

(D) P is both solenoidal and irrotational
Answer: (A)
Exp:
P  x 3 ya x  x 2 y 2 a y  x 2 yza z
.P  3x  y  2x 2 y  x 2 y  0
It is solenoidal.
a x
a y


 P 
x
y
x 3 y x 2 y2
a z

z
 x 2 yz
 a x   x 2 y   a y  2xyz   a z  2xy 2  x 3   0
So P is solenoidal but not irrotational.
written permission.
26
46.
www.gateforum.com
All the logic gates shown in the figure have a propagation delay of 20 ns. Let A=C=0 and
B=1 until time t=0. At t= 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that
state. For t > 0, output Z = 1 for a duration (in ns) of
A
B
C
Answer:
Z
40
Exp:
A
Y
Z
B
X
C
As per information given on question the waveforms of A, B, C are as follows
A
B
C
t 0
 The logic to solve this question is first obtain X, Y waveform and using this obtain Z.
 To obtain X, initially assume delay of NOT gate is 0 and draw its waveform and finally
shift it by 20nsec to obtain actual X. Similar procedure to be followed for obtaining Y
and Z i.e., first draw waveform with 0 delay and at the end shift by the amount of delay
given in question.
 X  B  with 0 delay 
B
t 0
B
t 0
B
 with delay 
t  20nsec
written permission.
27
www.gateforum.com
 Y  B.A
A
t 0
B
t  20
 with delay 
Y  AB
 without delay 
t  20nsec
Y  AB
 with delay 
t  40nsec
 
 z  AB  C
AB
t  40
C
t 0
t  20
t  40
20
40
Z
 without delay 
t 0
Z
 with delay 
0
20
40
60
Clearly we can say that output is high during 20 nsec to 60 nsec i.e. a duration of 40 nsec
K  1

A plant transfer function is given as G  s    K p  I 
. When the plant operates in a
s  s s  2

unity feedback configuration, the condition for the stability of the closed loop system is
K
(A) K p  I  0
(B) 2K I  K p  0
(C) 2K I  K p
(D) 2K I  K p
2
Answer: (A)
47.
Exp:
G s 
 sK
s
3
p
 KI
 2s 2


C.E  s3  2s 2  s1K P  K I  0
written permission.
28
www.gateforum.com
R  H table
s3
1
2
s2

s1 2K p  K I

Kp
KI
0
0
0
0
2
KI
s0
For stable system
1st column elements must be positive
 KI  0
 2K P  K I 

0
2


K
K P  I  0
2
48.
A 3-input majority gate is defined by the logic function M  a,b,c   ab  bc  ca . Which one
of the following gates is represented by the function M(M(a,b,c),M(a,b,c),c)?
(A) 3-input NAND gate
(B) 3-input XOR gate
(C) 3-input NOR gate
Answer: (B) and (D)
Exp:
(D) 3-input XNOR gate
M  a, b,c   ab  bc  ac   m  3,5,6,7 
M  a, b,c    m  0,1, 2, 4   X  let say for simplicity 


M a, b,c  ab  bc  ac   m  2, 4,6,7   Y  let 
c   m 1,3,5,7   z  let 


f  M  a, b,c  , M a, b,c ,c  


 f  x, y, z 
 xy  yz  zx
   m  0,1, 2, 4     m  2, 4,6,7       m  2, 4,6,7  m 1,3,5,7   
  m  2, 4    m  7    m 1
   m 1,3,5,7   m  0,1, 2, 4  
 AND operater is like intersection 
  m 1, 2, 4,7  

 OR operator is like union

 A  B  C  A  B  C  standard result 
Both options  D  and  B  are correct
written permission.
29
49.
www.gateforum.com
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide
made of a perfect electric conductor is given by the following expression
Hz  x, y,z, t   0.1 cos  25x  cos 30.3 y  cos 12109 t  z   A / m 
The cross-sectional dimensions of the waveguide are given as a = 0.08m and b= 0.033m. The
mode of propagation inside the waveguide is
(A) TM12
(B) TM21
(C) TE21
(D) TE12
Answer: (C)
mx
Exp:
 25x  m  25a  2
a
ny
 30.3y  n  30.3b  1
b
Given is Hz means TE mode
 mode  TE21
50.
The open-loop transfer function of a plant in a unity feedback configuration is given as
K s  4
G s  
. The value of the gain K(>0) for which 1  j2 lies on the root locus
 s  8  s2  9 
is __________________.
Answer: 25.5
Exp: By magnitude condition
G  s  H  s  s 1 2 j  1
So,
K
k 2j  3
7  2j 2  2j 4  2j
1
20 8 53
13
 25.5
So K value is = 25.5
51.
Two sequences [a, b, c] and [A, B, C] are related as,
1
1  a 
 A  1
2
 B   1 W 1 W 2   b  where W  e j 3 .
3
3  
3
  
C  1 W32 W34  c 
If another squence  p,q, r  is derived as,
1
1  1 0
0   A / 3
 p  1

q   1 W1 W 2  0 W 2
0   B / 3  ,
3
3 
3
  
 r  1 W32 W34  0 0 W34  C / 3 
then the relationship between the sequences [p, q, r] and [a, b, c] is
(A)  p,q,r    b,a,c
(B)  p,q,r    b,c,a 
(C)  p,q,r   c,a,b
Answer: (C)
Exp: Consider,
(D)  p,q,r   c,b,a 
written permission.
30
1 1

1
1 w 3
1 w 2
3

1  1 0

w 32  0 w 32
w13  0 0
0  1 w 32
 
0   1 w 33

w 34  1 w 34
www.gateforum.com
w 34 

w 36 

w 35 
31
w 34  w 3   w13 ; w 36  w 33  w 30  1 ; w 35  w 32
1 w 32
1
1 1
3 
1
1 w 3
1 w 32
w13   A 

1
1   B   1 1
3
1
w 32   C 
1 w 3
w13  1 1

1  1 w 31
w 32  1 w 32
1  a 

w 32   b 
w 31   c 
1  w 32  w13 1  w 3  w 31 1  w 30  w 30   a 

1
1  w 31  w 32 1  w 32  w 31   b 
 111
3
1
2
0
0
1
1  
1  w 3  w 3 1  w 3  w 3 1  w 3  w 3   c 
 w3  e
j2 
3 ,
w 32  w13  w 3  w 31  w 31  w 32  1
p
0 0 3  a   c 
1


 q    3 0 0   b    a 
3
 r 
0 3 0   c   b 
52.
The solution of the differential equation
(A)  2  t  e t
Answer:
Exp:
(B) 1  2t  e t
d2 y
dy
 2  y  0 with y(0)  y'  0   1 is
2
dt
dt
(C)  2  t  e t
(D) 1  2t  e t
(B)
Differential equation is (D2+2D+1).y = 0
D2+2D+1 = 0(D+1)2 = 0  D = -1,-1
solution is y  t    c1  c 2 t  e  t  C.F
 y'  t   c2 e t   c1  c2 t   e  t 
y(0) = 1; y'  0   1 gives c1 = 1 and c2+c1(-1) = 1c2 = 2
∴ y(t) = (1+2t)e-t
written permission.
31
53.
www.gateforum.com
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The
zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1,
we can conclude
Imz
0.5
Rez
4
0.5
0.5
0.5
(A) h[n] is real for all n
(B) h[n] is purely imaginary for all n
(C) h[n] is real for only even n
(D) h[n] is purely imaginary for only odd n
Answer: (C)
54.
Which one of the following graphs describes the function f  x   e x  x 2  x  1 ?
A
 B
f (x)
f (x)
x
C
x
 D
f (x)
f (x)
x
Answer:
(B)
Exp:
f(1) = e-x (x2+x+1)
x
f(0) = 1
f(0.5) = 1.067
For positive values of x, function never goes negative.
written permission.
32
55.
www.gateforum.com
The Boolean expression F  X,Y, Z  XYZ  XYZ  XYZ  XYZ
canonical product of sum (POS) form is
converted into the
(A)  X  Y  Z  X  Y  Z X  Y  Z  X  Y  Z 
(B)  X  Y  Z X  Y  Z X  Y  Z  X  Y  Z 
(C)  X  Y  Z  X  Y  Z X  Y  Z  X  Y  Z 
(D)  X  Y  Z X  Y  Z X  Y  Z   X  Y  Z 
Answer:
Exp:
(A)
Given minterms are:
F  X, Y, Z   XYZ  XYZ  XYZ  XYZ
So, maxtermis F  X, Y, Z   m  0,1,3,5 



POS   X  Y  Z  X  Y  Z X  Y  Z X  Y  Z

written permission.
33

EC-GATE-2015 PAPER-01| General Aptitude Q. No. 1 – 5 Carry One

Transcription

Similar documents