Gate physics Sample Papers - 2008
GATE 2008
· Added August 2010
dy
Given y x2 2x 10, the value of is equal to
1.
dx x 1
(A) 0 (B) 4 (C) 12 (D) 13
sin x
lim is
2.
x
x 0
(D)
(A) Indeterminate (B) 0 (C) 1
3. The power supplied by the dc voltage source in the circuit shown below is
3
6
1
3V
(A) 0W (B) 1.0W (C) 2.5W (D) 3.0W
4. The current I supplied by the dc voltage source in the circuit shown below is
I
1
1A
1V
(A) 0A (B) 0.5A (C) 1A (D) 2A
5. For signal conditioning of a piezoelectric type transducer we require
(A) a charge amplifier (B) a differential amplifier
(C) an instrumentation amplifier (D) a transconductance amplifier
6. A linear variable differential transformer (LVDT) is
(A) a displacement transducer
(B) an impedance matching transformer
(C) a differential temperature sensor
(D) an auto transformer
7. The temperature being sensed by a negative temperature coefficient (NTC) type
thermistor is linearly increasing. Its resistance will
(A) linearly increase with temperature
(B) exponentially increase with temperature
(C) linearly decrease with temperature
(D) exponentially decrease with temperature
8. For a single stage BJT common base amplifier
(A) current gain as well as voltage gain can be greater than unity
(B) current gain can be greater than unity but voltage gain is always less than
unity
(C) voltage gain can be greater than unity but current gain is always less than
unity
(D) current gain as well as voltage gain is always less than unity
In the circuit shown below, the ideality factor of the diode is unity and the
9.
voltage drop across it is 0.7V. The dynamic resistance of the diode at room
temperature is approximately
1.7V
1k
(A) 15 (B) 25 (C) 50 (D) 700
10. An ideal op-amp has the characteristics of an ideal
(A) voltage controlled voltage source (B) voltage controlled current source
(C) current controlled voltage source (D) current controlled current source
11. The inverters in the ring oscillator circuit shown below are identical. If the output
waveform has a frequency of 10 MHz, the propagation delay pf each inverter is
output
(B) 10 ns (C) 20 ns (D) 50 ns
(A) 5 ns
12. A 2K×8 bit RAM is interfaced to an 8-bit microprocessor. If the address of the first
memory location in the RAM is 0800H, the address of the last memory location
will be
(A) 1000H (B) 0FFFH (C) 2848H (D) 47FFH
5
f n
6
The fundamental period of the discrete-time signal x n e
13. is
6 12
(A) (B) (C) 6 (D) 12
5 5
14. Which one of the following discrete-time systems is time invariant?
(A) y n nx n (B) y n x 3n (C) y n x n (D) y n x n 3
If a current of 6 2 sin 100t 6 2 cos 300t A is passed through a true
15.
4
RMS ammeter, the meter reading will be
(C) 12A
(A) 6 2A 126A (D) 216A
(B)
16. If the ac bridge circuit shown below is
balanced, the element Z can be a
(A) Pure capacitor :
Detector
(B) Pure inductor D
(C) R-L series combination
(D) R-L parallel combination Z
17. The Bode asymptotic plot of a transfer function is given below. In the frequency
range shown, the transfer function has
dB
20dB / decade
20dB / decade
0dB / decade
log
1 2
(A) 3 poles ands 1 zero (B) 1 pole and 2 zeros
(C) 2 poles and 1 zero (D) 2 poles and 2 zeros
18. For radioisotope imaging, an Anger camera is fitted with a parallel hole
collimator. If the thickness of the collimator is increased, the camera
(A) resolution and sensitivity will increase
(B) resolution and sensitivity will decrease
(C) resolution will increase and sensitivity will decrease
(D) resolution will decrease and sensitivity will increase
19. In the standard 12-lead ECG recording system, the minimum number of
electrodes required to be attached to a human subject for recording any one of
the unipolar chest lead signals is
(A) 1 (B) 2 (C) 4 (D) 5
20. A laser light with a wavelength of 633nm is passed through 1cm length of tissue
and 2cm length of glass. The refractive indices of tissue ad glass are 1.33 ad 1.5
respectively. The velocities of laser light in the tissue and in the glass are in the
ratio of
(A) 1.33:0.75 (B) 1.33:3.0 (C) 1.33:15 (D) 1.5:1.33
Q. No. 21 – 75 Carry Two Marks Each
The expression e ln x for x 0 is equal to
21.
(C) x-1 (D) -x-1
(A) -x (B) x
dy
1 y2 . Which one of the following can be
22. Consider the differential equation
dx
a particular solution of this differential equation?
(A) y tan x 3 (C) x tan y 3
(B) y tan x 3 (D) x tan y 3
Consider the function y=x2-6x+9. The maximum value of y obtained when x
23.
varies over the interval 2 to 5 is
(A) 1 (B) 3 (C) 4 (D) 9
It is known that two roots of the nonlinear equation x3 6x2 11x 6 0 are 1
24.
and 3. The third root will be
(A) j (B) - j (C) 2 (D) 4
25. Consider a Gaussian distributed random variable with zero mean and standard
deviation . The value of its cumulative distribution function at the origin will be
(A) 0 (B) 0.5 (C) 1 (D) 10
26. A random variable is uniformly distributed over the interval 2 to 10. Its variance
will be
16 256
(A) (B) 6 (C) (D) 36
3 9
The Fourier transform of x t e atu t , where u t is the unit step function
27.
(A) Exists for any real value of a
(B) Does not exist for any real value of a
(C) Exists if the real value of a is strictly negative
(D) Exists if the real value of a is strictly positive
28. In the circuit shown below the maximum power that can be transferred to the
load ZL is
i t 10 2 sin 1000t A
(A) 250W
A complete variable Z x j 0.1 has its real part x varying in the range
29.
to . Which one of the following is the locus (shown in thick lines) of 1/Z in
the complex plane?
(A)
Real axis
^ -j10
(C)
Image axis
10
ZL
10mH
(B) 500W (C) 1000W
(B)
(D)
Image axis
(D) 2000W
Image axis
Image axis
Real axis
^ -j10
Real axis Real axis
-j10 -j10
V1
For the circuit shown below the input resistance R11 is
30.
I1 I2 0
3I2
2
1 2V3
I1 I2
V1 V2
2 V3
(A) 3 (B) 2 (C) 3 (D) 13
In the circuit shown below the average power consumed by the 2 resistor is
31.
1
10 2 sin 1000t V :
1mH
100 2 sin 3000t V :
(A) 50W (B) 1050W (C) 5000W (D) 10100W
32. Which one of the following equations is valid for the circuit shown below?
1 1
I1 I3
1 1
I2 I6
1
I5
5V 1
1 I4
I7
(A) I3 I5 I6 I7 0 (B) I3 I5 I6 I7 0
(C) I3 I5 I6 I7 0 (D) I3 I5 I6 I7 0
33. For the circuit shown below the steady-state current I is
I
1
v t 5 2e5t cos 1000t V
1000 F
1mH
(B) 5 2 cos 1000t A
(A) 0 A
(D) 5 2 A
(C) 5 2 cos 1000t A
4
34. For the circuit shown below the voltage across the capacitor is
j100
10 j0 V
j100
10 j 0 V 100 j0 V 0 j100 V (D) 0 j100 V
(B) (C)
(A)
35. The speed of a gear having 60 teeth is measured using a proximity sensor. The
output of the proximity sensor is fed to a counter with a gating time of 1s. The
counter indicates a value of 120. The speed at which the gear is rotating is
(A) 60 rpm (C) 600 rpm (D) 1200 rpm
36. A piezoelectric type accelerometer has a sensitivity of 100mV/g. The transducer
is subjected to a constant acceleration of 5g. The steady state output of the
transducer will be
(A) 0V (C) 0.5V (D) 5V
37. A pair of identical thermocouples is employed for measuring the temperature of a
specimen as shown below. The characteristic is tabulated below. The reference
junction is at 20C. The meter reads 48 V . The correct temperature of the
specimen is
Specimen
10
:
(B) 120 rpm
(B) 100mV
+
V
meter
- - +
Reference junction
Temperature (0C) 0 10 20 30 40 50 60 70 80 90
Output ( V ) 35 45 55 65 75 85 95 105 115 125
(A) 130 C (B) 460 C (C) 480 C (D) 500 C
A strain gauge has a nominal resistance of 600 and a gauge factor of 2.5. The
38.
strain gauge is connected in a dc bridge with three other resistances of 600
each. The bridge is excited by a 4V battery. If the strain gauge is subjected to a
strain of 100 m / m , the magnitude of the bridge output will be
(B) 250V (C) 500V (D) 750V
(A) 0V
39. The torque in a rotating shaft is measured using strain gauges. The strain gauges
must be positioned on the shaft such that the axes of the strain gauges are at
(A) 00 with respect to the axis of the shaft
(B) 300 with respect to the axis of the shaft
(C) 450 with respect to the axis of the shaft
(D) 900 with respect to the axis of the shaft
40. To reduce the effect of fringing in a capacitive type transducer
(A) the transducer is shielded and the shield is kept at ground potential
(B) a guard ring is provided ad it is kept at ground potential
(C) the transducer is shielded and the shied is kept at the same potential as the
moving plate
(D) a guard ring is provided and it is kept at the same potential as the moving
plate
41. A differential amplifier shown below has a differential mode gain of 100 and a
CMRR of 40dB. If V1 0.55V and V2 0.45V, the output V0 is
V1
V0
V2
(A) 10V (B) 10.5V (C) 11V (D) 15V
42. The op-amp circuit shown below is that of a
Vin
1F
v0
1k
1k 1k
(A) low-pass filter with a maximum gain of 1
(B) low-pass filter with a maximum, gin of 2
(C) high-pass filter with a maximum gain of 1
(D) high-pass filter with a maximum gain of 2
In the op-amp circuit shown below is that of a vin is gradually increased from -10V
43.
to +10V. Assuming that the output voltage vout saturates at -10V and +10V,
vout will change from
Vin
v0
9k
1k
(A) 10V to +10V when vin 1V (B) 10V to +10V when vin 1V
(C) 10V to -10V when vin 1V (D) 10V to -10V when vin 1V
For the op-amp circuit shown below v0 is approximately equal to
44.
10V
1M
105 95
100k
v0
100k
95
105 1M
(A) -10V (B) -5V (C) +5v (D) +10V
In the amplifier circuit shown below, assume VBE 0.7V and the of the
45
transistor and the values of C1 and C2 are extremely high. If the amplifier is
VCC
designed such that at the quiescent point its VCE , where VCC is the power
2
vout
supply voltage, its small signal voltage gain will be
vin
10V
RC
8.8k
vout
C2
vin
C1
1.2k RE
(A) 3.75 (B) 4.5 (C) 9 (D) 19
46. The result of (45)10 – (45)16 expressed in 6-bit 2's complement representation is
(A) 011000 (B) 100111 (C) 101000 (D) 101001
47. The output F of the multiplexer circuit shown below expressed in terms of the
inputs P, Q and R is
R I0
I1
R
4 1 Y F
MUX
R I2
R I3 S1 S0
Q
P
(B) F PQ QR RP (C) F P Q R (D) F P Q R
(A) F P Q R
48. A part of a program written for an 8085 microprocessor is shown below. When
the program execution reaches LOOP2, the value of register C will be
SUB A
MOV C, A
LOOPI: INR A
DAA
JC LOOP2
INR C
JNC LOOPI
LOOP2: NOP
(A) 63H (B) 64H (C) 99H (D) 100H
49. The minimum sum of products form of the Boolean expression
Y P QR SP QR SP QR SP QR SP QR SP QR S is
(C) Y P Q QR S (D) Y QS PQR
(A) Y P Q Q S (B) Y P Q Q R S
50. An X-ray tube is operated at 80kV anode voltage. In order to filter the low
intensity X-rays, a 2.5mm thick aluminium filter is used. It is given that at 80kV
anode voltage, the mass attenuation coefficients and densities of aluminium are
0.02m2kg1 and 2699kgm3 respectively and for copper these are
0.075m2kg1 and 8960 kgm3 respectively. If a copper filter is to replace the
aluminium filter with the same effect, the thickness of the copper filter should be
(A) 0.2mm (B) 0.66mm (C) 1.5mm (D) 5mm
51. A 5 MHz acoustic pulse travels from a transducer through a 2cm thick fat tissue
before it encounters ad interface with a liver tissue at normal incidence. The
amplitude attenuation factors of fat and liver are
0.075 Npcm1 / MHz and 0.1Npcm1 / MHz respectively. The amplitude reflectivity
coefficient of fat-liver interface is 0.1. Taking both attenuation and reflection
losses into a account, the amplitude loss (in dB) of echo pulse when it returns to
the transducers is
(A) 0.74 (B) -2.6 (C) -6 (D) -33
Consider a discrete-time LTI system with input x n n n 1 and impulse
52.
response h n n n 1 . The output of the system will be given by
(A) n n 2 (B) n n 1
(C) n 1 n 2 (D) n n 1 n 2
53. Consider a discrete-time system for which the input x[n] and the output y[n] are
1
related as y n x n y n 1 . If y n 0 for n 0 and x n n , then y n
3
can be expressed in terms of the unit step u[n] as
n n
1 1
3n u n n
(D) 3 u n
u n (B) u n (C)
(A)
3 3
If the bandwidth of a low-pass signal g(t) is 3kHz, the bandwidth of g2 t will be
54.
3
kHz (B) 3kHz (C) 6kHz (D) 9kHz
(A)
2
Consider the AM signal s t 1 m t cos 2fc t . It is given that the bandwidth
55.
of the real, low-pass message signal m(t) is 2kHz. If fc 2MHz , the bandwidth of
the band-pass signal s(t) will be
(A) 2.004MHz (B) 2MHz (C) 4kHz (D) 2kHz
56. Ten, real, band-pass message signals, each of bandwidth 3kHz, are to be
frequency division multiplexed over a band-pass channel with bandwidth B kHz.
If the guard band in between any two adjacent signals should be of 500 Hz width
and there is no need to provide any guard band at the edges of the band-pass
channel, the value of B should be at least
(A) 30 (B) 34.5 (C) 35 (D) 35.5
57. The region of convergence of the z-transform of the discrete-time signal
x n 2n u n will be
1 1
(A) z 2 (B) z 2 (C) z (D) z
2 2
The step response of a linear invariant system is y t 5e10tu t , where u(t) is
58.
the unit step function. If the output of the system corresponding to an impulse
input t is h t , then h t is
(A) 50e10tu t (B) 5e10t t
(C) 5u t 50e10t t (D) 5 t 50e10tu t
59. A 2A full-scale PMMC type dc ammeter has a voltage drop of 100 mV at 2A. The
meter can be converted into a 10A full-scale dc ammeter by connecting a
(A) 12.5 m resistor in parallel with the meter
(B) 12.5 m resistor in series with the meter
(C) 50.0 m resistor in parallel with the meter
(D) 50.0 m resistor in series with the meter
A 31⁄2 digit, 200 mV full scale DVM has an accuracy specification of 0.5% of
60.
reading plus 5 counts. When the meter reads 100 mV, the voltage being
measured is
(A) Any value between 99.5 mV and 100.5 mV
(B) Any value between 99.0 mV and 101.0 mV
(C) Exactly 99.5 mV (D) Exactly 100 mV
61. A 230 V, 5A, 50 Hz single phase house service energy meter has a meter
constant of 360 rev/kWhr. The meter takes 50 s for making 51 revolutions of the
disc when connected to a 10 kW, unity power factor load. The error in the
reading of the meter is
(A) 0% (B) +0.5% (C) -2.0% (D) +2.0%
62. The op-amp based circuit of a half wave rectifier electronic voltmeter shown
below uses a PMMC ammeter with a full scale deflection (FSD) current of 1 mA
and a coil resistance of 1k . The value of R that gives FSD for a sinusoidal input
voltage of 100 mV (RMS) is
Sinusoidal
input
1k
PMMC
ameter
R
(A) 45 (B) 67.5 (C) 100 (D) 144.4
63. The x and y sensitivities of an analog oscilloscope are set as 2 ms/cm and 1V/cm
respectively. The trigger is set at 0V with negative slope. An input of
2 cos 100t 300 V is fed to the y input of the oscilloscope. The waveform seen
on the oscilloscope will be
(A) (B)
(C) (D)
64. The open loop transfer function of a unity feedback system is
K s 2
G s . The root locus plot of the system has
s 1 j1 s 1 j1
(A) two breakaway points located at s 0.59 and s 3.41
(B) one breakaway point located at s 0.59
(C) one breakaway point located at s 3.41
(D) one breakaway point located at s 1.41
65. If a first order system and its time response to a unit step input are as shown
below, the gain K is
y
K
r t y t 0.8
1 ST
t
(A) 0.25 (B) 0.8 (C) 1 (D) 4
x 0 1 1
x u
0 3 0 .
66. The state space representation of a system is given by
y 1 0 x
Y s
The transfer function of the system will be
U s
1
1
1 1
(A) (B) (C) (D)
s s 3 s2
s s3
A closed loop control system is shown below. The range of the controller gain KC
67.
which will make the real parts of all the closed loop poles more negative than -1
is
1
KC s s 3 Y s
R s
(A) KC 4 (B) KC 0 (C) KC 2 (D) KC 2
68. For the closed loop system shown below to be sable, the value of time delay
TD (in seconds) should be less than
1
Y s
R s s
esTD
(A) (B) (C) (D)
4 2
3
69. A tissue with a refractive index 1.33 is introduced on one of the light paths of a
Michelson interferometer operating with a monochromatic coherent light source
of wavelength 589nm. After the introduction of a tissue sample of thickness t ,
the fringe pattern is observed to shift by 50 fringes. If the thickness is 2t , the
fringe pattern will shift by
(A) 25 fringes (B) 50 fringes (C) 100 fringes (D) 200 fringes
70. In the process of non-destructive testing of a 10cm diameter cylinder, a cross-
sectional (trans-axial) image of the cylinder is reconstructed with the help of
parallel beam computer tomography technique. To realize a spatial resolution of
1mm in the image, the minimum number of ray sample in each projection set
and the minimum number of projection sets required are
(A) 200 and 315 respectively (B) 100 and 315 respectively
(C) 200 and 629 respectively (D) 100 and 629 respectively
Common Data Questions 71, 72 & 73
A data acquisition system (DAS) shown below employs a successive
approximation type 12-bit ADC having a conversion time of 5 s.
A B
Filter
Filter
Y
Filter
Filter
71. The quantization error of the ADC is
(B) 0.012% (C) 0.024% (D) 0.048%
(A) 0%
72. The system is used as a single channel DAS with channel 1 selected as input to
the ADC which is set in the continuous conversion mode. For avoiding aliasing
error, the cutoff frequency fc of the filter in channel 1 should be
(A) fc 100kHz (B) fc 100kHz
(C) 100kHz fc 200kHz (D) fc 200kHz
73. If the multiplexer is controlled such that the channels are sequenced every 5 s
as 1, 2, 1, 3, 1, 4, 1, 2, 1, 3, 1, 4, 1......, the input connected to channel 1 will be
sampled at the rate of
(A) 25k samples/s (B) 50k samples/s
(C) 100k samples/s (D) 200k samples/s
Common Data Questions: 74 & 75
Laser light is generated by energizing helium-neon gas in a chamber. The ground
and metastable states of helium are 0eV and 20.61eV respectively. The ground,
higher and metastable energies of neon is 0eV, 18.70eV and 20.66eV
respectively. The values of speed of light, Planks constant and charge of electron
are 3 108 m / s, 6.625 1034 Js and 1.6 1019 C respectively
74. In this process, helium molecules
(A) play no role
(B) produce laser light
(C) give energy to neon molecules
(D) absorb energy from neon molecules
75. Wavelength of laser light generated in this process is
(A) 61.6nm (B) 66.4nm (C) 633.8nm (D) 650.3nm
Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each
Statement for Linked Answer Questions: 76 & 77
In the Wheatstone bridge shown below the galvanometer G has a current
sensitivity of 1 A / mm , a resistance of 2.5k and a scale resolution of 1 mm. Let
R be the minimum increase in R from its nominal value of 2 k that can be
detected by this bridge.
3k 6k
15V G
A
R
VAN
4k
N
When R is 2 k R, VAN is
76.
(A) 6 V (B) 6.0024 V (C) 6.0038V (D) 6.005 V
The value of R is approximately
77.
(A) 2.8 (B) 3.4 (C) 5.2 (D) 12
Statement for Linked Answer Questions 78 & 79
In the circuit shown below the steady-state is reached with the switch K open.
Subsequently the switch is closed at time t = 0
1 I2
K I
t0 I1
2
1H
5V
10V
1F
At time t 0 , current I is
78.
5 5
(D) A
(A) A A
(B) 0A (C)
3 3
dI2
At time t 0 , is
79.
dt
10
(B) A /s
(A) 5A / s (C) 0A / s (D) 5A / s
3
Given y x2 2x 10, the value of is equal to
1.
dx x 1
(A) 0 (B) 4 (C) 12 (D) 13
sin x
lim is
2.
x
x 0
(D)
(A) Indeterminate (B) 0 (C) 1
3. The power supplied by the dc voltage source in the circuit shown below is
3
6
1
3V
(A) 0W (B) 1.0W (C) 2.5W (D) 3.0W
4. The current I supplied by the dc voltage source in the circuit shown below is
I
1
1A
1V
(A) 0A (B) 0.5A (C) 1A (D) 2A
5. For signal conditioning of a piezoelectric type transducer we require
(A) a charge amplifier (B) a differential amplifier
(C) an instrumentation amplifier (D) a transconductance amplifier
6. A linear variable differential transformer (LVDT) is
(A) a displacement transducer
(B) an impedance matching transformer
(C) a differential temperature sensor
(D) an auto transformer
7. The temperature being sensed by a negative temperature coefficient (NTC) type
thermistor is linearly increasing. Its resistance will
(A) linearly increase with temperature
(B) exponentially increase with temperature
(C) linearly decrease with temperature
(D) exponentially decrease with temperature
8. For a single stage BJT common base amplifier
(A) current gain as well as voltage gain can be greater than unity
(B) current gain can be greater than unity but voltage gain is always less than
unity
(C) voltage gain can be greater than unity but current gain is always less than
unity
(D) current gain as well as voltage gain is always less than unity
In the circuit shown below, the ideality factor of the diode is unity and the
9.
voltage drop across it is 0.7V. The dynamic resistance of the diode at room
temperature is approximately
1.7V
1k
(A) 15 (B) 25 (C) 50 (D) 700
10. An ideal op-amp has the characteristics of an ideal
(A) voltage controlled voltage source (B) voltage controlled current source
(C) current controlled voltage source (D) current controlled current source
11. The inverters in the ring oscillator circuit shown below are identical. If the output
waveform has a frequency of 10 MHz, the propagation delay pf each inverter is
output
(B) 10 ns (C) 20 ns (D) 50 ns
(A) 5 ns
12. A 2K×8 bit RAM is interfaced to an 8-bit microprocessor. If the address of the first
memory location in the RAM is 0800H, the address of the last memory location
will be
(A) 1000H (B) 0FFFH (C) 2848H (D) 47FFH
5
f n
6
The fundamental period of the discrete-time signal x n e
13. is
6 12
(A) (B) (C) 6 (D) 12
5 5
14. Which one of the following discrete-time systems is time invariant?
(A) y n nx n (B) y n x 3n (C) y n x n (D) y n x n 3
If a current of 6 2 sin 100t 6 2 cos 300t A is passed through a true
15.
4
RMS ammeter, the meter reading will be
(C) 12A
(A) 6 2A 126A (D) 216A
(B)
16. If the ac bridge circuit shown below is
balanced, the element Z can be a
(A) Pure capacitor :
Detector
(B) Pure inductor D
(C) R-L series combination
(D) R-L parallel combination Z
17. The Bode asymptotic plot of a transfer function is given below. In the frequency
range shown, the transfer function has
dB
20dB / decade
20dB / decade
0dB / decade
log
1 2
(A) 3 poles ands 1 zero (B) 1 pole and 2 zeros
(C) 2 poles and 1 zero (D) 2 poles and 2 zeros
18. For radioisotope imaging, an Anger camera is fitted with a parallel hole
collimator. If the thickness of the collimator is increased, the camera
(A) resolution and sensitivity will increase
(B) resolution and sensitivity will decrease
(C) resolution will increase and sensitivity will decrease
(D) resolution will decrease and sensitivity will increase
19. In the standard 12-lead ECG recording system, the minimum number of
electrodes required to be attached to a human subject for recording any one of
the unipolar chest lead signals is
(A) 1 (B) 2 (C) 4 (D) 5
20. A laser light with a wavelength of 633nm is passed through 1cm length of tissue
and 2cm length of glass. The refractive indices of tissue ad glass are 1.33 ad 1.5
respectively. The velocities of laser light in the tissue and in the glass are in the
ratio of
(A) 1.33:0.75 (B) 1.33:3.0 (C) 1.33:15 (D) 1.5:1.33
Q. No. 21 – 75 Carry Two Marks Each
The expression e ln x for x 0 is equal to
21.
(C) x-1 (D) -x-1
(A) -x (B) x
dy
1 y2 . Which one of the following can be
22. Consider the differential equation
dx
a particular solution of this differential equation?
(A) y tan x 3 (C) x tan y 3
(B) y tan x 3 (D) x tan y 3
Consider the function y=x2-6x+9. The maximum value of y obtained when x
23.
varies over the interval 2 to 5 is
(A) 1 (B) 3 (C) 4 (D) 9
It is known that two roots of the nonlinear equation x3 6x2 11x 6 0 are 1
24.
and 3. The third root will be
(A) j (B) - j (C) 2 (D) 4
25. Consider a Gaussian distributed random variable with zero mean and standard
deviation . The value of its cumulative distribution function at the origin will be
(A) 0 (B) 0.5 (C) 1 (D) 10
26. A random variable is uniformly distributed over the interval 2 to 10. Its variance
will be
16 256
(A) (B) 6 (C) (D) 36
3 9
The Fourier transform of x t e atu t , where u t is the unit step function
27.
(A) Exists for any real value of a
(B) Does not exist for any real value of a
(C) Exists if the real value of a is strictly negative
(D) Exists if the real value of a is strictly positive
28. In the circuit shown below the maximum power that can be transferred to the
load ZL is
i t 10 2 sin 1000t A
(A) 250W
A complete variable Z x j 0.1 has its real part x varying in the range
29.
to . Which one of the following is the locus (shown in thick lines) of 1/Z in
the complex plane?
(A)
Real axis
^ -j10
(C)
Image axis
10
ZL
10mH
(B) 500W (C) 1000W
(B)
(D)
Image axis
(D) 2000W
Image axis
Image axis
Real axis
^ -j10
Real axis Real axis
-j10 -j10
V1
For the circuit shown below the input resistance R11 is
30.
I1 I2 0
3I2
2
1 2V3
I1 I2
V1 V2
2 V3
(A) 3 (B) 2 (C) 3 (D) 13
In the circuit shown below the average power consumed by the 2 resistor is
31.
1
10 2 sin 1000t V :
1mH
100 2 sin 3000t V :
(A) 50W (B) 1050W (C) 5000W (D) 10100W
32. Which one of the following equations is valid for the circuit shown below?
1 1
I1 I3
1 1
I2 I6
1
I5
5V 1
1 I4
I7
(A) I3 I5 I6 I7 0 (B) I3 I5 I6 I7 0
(C) I3 I5 I6 I7 0 (D) I3 I5 I6 I7 0
33. For the circuit shown below the steady-state current I is
I
1
v t 5 2e5t cos 1000t V
1000 F
1mH
(B) 5 2 cos 1000t A
(A) 0 A
(D) 5 2 A
(C) 5 2 cos 1000t A
4
34. For the circuit shown below the voltage across the capacitor is
j100
10 j0 V
j100
10 j 0 V 100 j0 V 0 j100 V (D) 0 j100 V
(B) (C)
(A)
35. The speed of a gear having 60 teeth is measured using a proximity sensor. The
output of the proximity sensor is fed to a counter with a gating time of 1s. The
counter indicates a value of 120. The speed at which the gear is rotating is
(A) 60 rpm (C) 600 rpm (D) 1200 rpm
36. A piezoelectric type accelerometer has a sensitivity of 100mV/g. The transducer
is subjected to a constant acceleration of 5g. The steady state output of the
transducer will be
(A) 0V (C) 0.5V (D) 5V
37. A pair of identical thermocouples is employed for measuring the temperature of a
specimen as shown below. The characteristic is tabulated below. The reference
junction is at 20C. The meter reads 48 V . The correct temperature of the
specimen is
Specimen
10
:
(B) 120 rpm
(B) 100mV
+
V
meter
- - +
Reference junction
Temperature (0C) 0 10 20 30 40 50 60 70 80 90
Output ( V ) 35 45 55 65 75 85 95 105 115 125
(A) 130 C (B) 460 C (C) 480 C (D) 500 C
A strain gauge has a nominal resistance of 600 and a gauge factor of 2.5. The
38.
strain gauge is connected in a dc bridge with three other resistances of 600
each. The bridge is excited by a 4V battery. If the strain gauge is subjected to a
strain of 100 m / m , the magnitude of the bridge output will be
(B) 250V (C) 500V (D) 750V
(A) 0V
39. The torque in a rotating shaft is measured using strain gauges. The strain gauges
must be positioned on the shaft such that the axes of the strain gauges are at
(A) 00 with respect to the axis of the shaft
(B) 300 with respect to the axis of the shaft
(C) 450 with respect to the axis of the shaft
(D) 900 with respect to the axis of the shaft
40. To reduce the effect of fringing in a capacitive type transducer
(A) the transducer is shielded and the shield is kept at ground potential
(B) a guard ring is provided ad it is kept at ground potential
(C) the transducer is shielded and the shied is kept at the same potential as the
moving plate
(D) a guard ring is provided and it is kept at the same potential as the moving
plate
41. A differential amplifier shown below has a differential mode gain of 100 and a
CMRR of 40dB. If V1 0.55V and V2 0.45V, the output V0 is
V1
V0
V2
(A) 10V (B) 10.5V (C) 11V (D) 15V
42. The op-amp circuit shown below is that of a
Vin
1F
v0
1k
1k 1k
(A) low-pass filter with a maximum gain of 1
(B) low-pass filter with a maximum, gin of 2
(C) high-pass filter with a maximum gain of 1
(D) high-pass filter with a maximum gain of 2
In the op-amp circuit shown below is that of a vin is gradually increased from -10V
43.
to +10V. Assuming that the output voltage vout saturates at -10V and +10V,
vout will change from
Vin
v0
9k
1k
(A) 10V to +10V when vin 1V (B) 10V to +10V when vin 1V
(C) 10V to -10V when vin 1V (D) 10V to -10V when vin 1V
For the op-amp circuit shown below v0 is approximately equal to
44.
10V
1M
105 95
100k
v0
100k
95
105 1M
(A) -10V (B) -5V (C) +5v (D) +10V
In the amplifier circuit shown below, assume VBE 0.7V and the of the
45
transistor and the values of C1 and C2 are extremely high. If the amplifier is
VCC
designed such that at the quiescent point its VCE , where VCC is the power
2
vout
supply voltage, its small signal voltage gain will be
vin
10V
RC
8.8k
vout
C2
vin
C1
1.2k RE
(A) 3.75 (B) 4.5 (C) 9 (D) 19
46. The result of (45)10 – (45)16 expressed in 6-bit 2's complement representation is
(A) 011000 (B) 100111 (C) 101000 (D) 101001
47. The output F of the multiplexer circuit shown below expressed in terms of the
inputs P, Q and R is
R I0
I1
R
4 1 Y F
MUX
R I2
R I3 S1 S0
Q
P
(B) F PQ QR RP (C) F P Q R (D) F P Q R
(A) F P Q R
48. A part of a program written for an 8085 microprocessor is shown below. When
the program execution reaches LOOP2, the value of register C will be
SUB A
MOV C, A
LOOPI: INR A
DAA
JC LOOP2
INR C
JNC LOOPI
LOOP2: NOP
(A) 63H (B) 64H (C) 99H (D) 100H
49. The minimum sum of products form of the Boolean expression
Y P QR SP QR SP QR SP QR SP QR SP QR S is
(C) Y P Q QR S (D) Y QS PQR
(A) Y P Q Q S (B) Y P Q Q R S
50. An X-ray tube is operated at 80kV anode voltage. In order to filter the low
intensity X-rays, a 2.5mm thick aluminium filter is used. It is given that at 80kV
anode voltage, the mass attenuation coefficients and densities of aluminium are
0.02m2kg1 and 2699kgm3 respectively and for copper these are
0.075m2kg1 and 8960 kgm3 respectively. If a copper filter is to replace the
aluminium filter with the same effect, the thickness of the copper filter should be
(A) 0.2mm (B) 0.66mm (C) 1.5mm (D) 5mm
51. A 5 MHz acoustic pulse travels from a transducer through a 2cm thick fat tissue
before it encounters ad interface with a liver tissue at normal incidence. The
amplitude attenuation factors of fat and liver are
0.075 Npcm1 / MHz and 0.1Npcm1 / MHz respectively. The amplitude reflectivity
coefficient of fat-liver interface is 0.1. Taking both attenuation and reflection
losses into a account, the amplitude loss (in dB) of echo pulse when it returns to
the transducers is
(A) 0.74 (B) -2.6 (C) -6 (D) -33
Consider a discrete-time LTI system with input x n n n 1 and impulse
52.
response h n n n 1 . The output of the system will be given by
(A) n n 2 (B) n n 1
(C) n 1 n 2 (D) n n 1 n 2
53. Consider a discrete-time system for which the input x[n] and the output y[n] are
1
related as y n x n y n 1 . If y n 0 for n 0 and x n n , then y n
3
can be expressed in terms of the unit step u[n] as
n n
1 1
3n u n n
(D) 3 u n
u n (B) u n (C)
(A)
3 3
If the bandwidth of a low-pass signal g(t) is 3kHz, the bandwidth of g2 t will be
54.
3
kHz (B) 3kHz (C) 6kHz (D) 9kHz
(A)
2
Consider the AM signal s t 1 m t cos 2fc t . It is given that the bandwidth
55.
of the real, low-pass message signal m(t) is 2kHz. If fc 2MHz , the bandwidth of
the band-pass signal s(t) will be
(A) 2.004MHz (B) 2MHz (C) 4kHz (D) 2kHz
56. Ten, real, band-pass message signals, each of bandwidth 3kHz, are to be
frequency division multiplexed over a band-pass channel with bandwidth B kHz.
If the guard band in between any two adjacent signals should be of 500 Hz width
and there is no need to provide any guard band at the edges of the band-pass
channel, the value of B should be at least
(A) 30 (B) 34.5 (C) 35 (D) 35.5
57. The region of convergence of the z-transform of the discrete-time signal
x n 2n u n will be
1 1
(A) z 2 (B) z 2 (C) z (D) z
2 2
The step response of a linear invariant system is y t 5e10tu t , where u(t) is
58.
the unit step function. If the output of the system corresponding to an impulse
input t is h t , then h t is
(A) 50e10tu t (B) 5e10t t
(C) 5u t 50e10t t (D) 5 t 50e10tu t
59. A 2A full-scale PMMC type dc ammeter has a voltage drop of 100 mV at 2A. The
meter can be converted into a 10A full-scale dc ammeter by connecting a
(A) 12.5 m resistor in parallel with the meter
(B) 12.5 m resistor in series with the meter
(C) 50.0 m resistor in parallel with the meter
(D) 50.0 m resistor in series with the meter
A 31⁄2 digit, 200 mV full scale DVM has an accuracy specification of 0.5% of
60.
reading plus 5 counts. When the meter reads 100 mV, the voltage being
measured is
(A) Any value between 99.5 mV and 100.5 mV
(B) Any value between 99.0 mV and 101.0 mV
(C) Exactly 99.5 mV (D) Exactly 100 mV
61. A 230 V, 5A, 50 Hz single phase house service energy meter has a meter
constant of 360 rev/kWhr. The meter takes 50 s for making 51 revolutions of the
disc when connected to a 10 kW, unity power factor load. The error in the
reading of the meter is
(A) 0% (B) +0.5% (C) -2.0% (D) +2.0%
62. The op-amp based circuit of a half wave rectifier electronic voltmeter shown
below uses a PMMC ammeter with a full scale deflection (FSD) current of 1 mA
and a coil resistance of 1k . The value of R that gives FSD for a sinusoidal input
voltage of 100 mV (RMS) is
Sinusoidal
input
1k
PMMC
ameter
R
(A) 45 (B) 67.5 (C) 100 (D) 144.4
63. The x and y sensitivities of an analog oscilloscope are set as 2 ms/cm and 1V/cm
respectively. The trigger is set at 0V with negative slope. An input of
2 cos 100t 300 V is fed to the y input of the oscilloscope. The waveform seen
on the oscilloscope will be
(A) (B)
(C) (D)
64. The open loop transfer function of a unity feedback system is
K s 2
G s . The root locus plot of the system has
s 1 j1 s 1 j1
(A) two breakaway points located at s 0.59 and s 3.41
(B) one breakaway point located at s 0.59
(C) one breakaway point located at s 3.41
(D) one breakaway point located at s 1.41
65. If a first order system and its time response to a unit step input are as shown
below, the gain K is
y
K
r t y t 0.8
1 ST
t
(A) 0.25 (B) 0.8 (C) 1 (D) 4
x 0 1 1
x u
0 3 0 .
66. The state space representation of a system is given by
y 1 0 x
Y s
The transfer function of the system will be
U s
1
1
1 1
(A) (B) (C) (D)
s s 3 s2
s s3
A closed loop control system is shown below. The range of the controller gain KC
67.
which will make the real parts of all the closed loop poles more negative than -1
is
1
KC s s 3 Y s
R s
(A) KC 4 (B) KC 0 (C) KC 2 (D) KC 2
68. For the closed loop system shown below to be sable, the value of time delay
TD (in seconds) should be less than
1
Y s
R s s
esTD
(A) (B) (C) (D)
4 2
3
69. A tissue with a refractive index 1.33 is introduced on one of the light paths of a
Michelson interferometer operating with a monochromatic coherent light source
of wavelength 589nm. After the introduction of a tissue sample of thickness t ,
the fringe pattern is observed to shift by 50 fringes. If the thickness is 2t , the
fringe pattern will shift by
(A) 25 fringes (B) 50 fringes (C) 100 fringes (D) 200 fringes
70. In the process of non-destructive testing of a 10cm diameter cylinder, a cross-
sectional (trans-axial) image of the cylinder is reconstructed with the help of
parallel beam computer tomography technique. To realize a spatial resolution of
1mm in the image, the minimum number of ray sample in each projection set
and the minimum number of projection sets required are
(A) 200 and 315 respectively (B) 100 and 315 respectively
(C) 200 and 629 respectively (D) 100 and 629 respectively
Common Data Questions 71, 72 & 73
A data acquisition system (DAS) shown below employs a successive
approximation type 12-bit ADC having a conversion time of 5 s.
A B
Filter
Filter
Y
Filter
Filter
71. The quantization error of the ADC is
(B) 0.012% (C) 0.024% (D) 0.048%
(A) 0%
72. The system is used as a single channel DAS with channel 1 selected as input to
the ADC which is set in the continuous conversion mode. For avoiding aliasing
error, the cutoff frequency fc of the filter in channel 1 should be
(A) fc 100kHz (B) fc 100kHz
(C) 100kHz fc 200kHz (D) fc 200kHz
73. If the multiplexer is controlled such that the channels are sequenced every 5 s
as 1, 2, 1, 3, 1, 4, 1, 2, 1, 3, 1, 4, 1......, the input connected to channel 1 will be
sampled at the rate of
(A) 25k samples/s (B) 50k samples/s
(C) 100k samples/s (D) 200k samples/s
Common Data Questions: 74 & 75
Laser light is generated by energizing helium-neon gas in a chamber. The ground
and metastable states of helium are 0eV and 20.61eV respectively. The ground,
higher and metastable energies of neon is 0eV, 18.70eV and 20.66eV
respectively. The values of speed of light, Planks constant and charge of electron
are 3 108 m / s, 6.625 1034 Js and 1.6 1019 C respectively
74. In this process, helium molecules
(A) play no role
(B) produce laser light
(C) give energy to neon molecules
(D) absorb energy from neon molecules
75. Wavelength of laser light generated in this process is
(A) 61.6nm (B) 66.4nm (C) 633.8nm (D) 650.3nm
Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each
Statement for Linked Answer Questions: 76 & 77
In the Wheatstone bridge shown below the galvanometer G has a current
sensitivity of 1 A / mm , a resistance of 2.5k and a scale resolution of 1 mm. Let
R be the minimum increase in R from its nominal value of 2 k that can be
detected by this bridge.
3k 6k
15V G
A
R
VAN
4k
N
When R is 2 k R, VAN is
76.
(A) 6 V (B) 6.0024 V (C) 6.0038V (D) 6.005 V
The value of R is approximately
77.
(A) 2.8 (B) 3.4 (C) 5.2 (D) 12
Statement for Linked Answer Questions 78 & 79
In the circuit shown below the steady-state is reached with the switch K open.
Subsequently the switch is closed at time t = 0
1 I2
K I
t0 I1
2
1H
5V
10V
1F
At time t 0 , current I is
78.
5 5
(D) A
(A) A A
(B) 0A (C)
3 3
dI2
At time t 0 , is
79.
dt
10
(B) A /s
(A) 5A / s (C) 0A / s (D) 5A / s
3