GATE IN 2012: Instrumentation Engineering
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2012 INSTRUMENTATION ENGINEERING - IN
IN : INSTRUMENTATION ENGINEERING
Duration: Three Hours Maximum Marks: 100
Read the following instructions carefully.
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator.
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal
and read the instructions printed on the ORS carefully.
3. On the right half of the ORS, using ONLY a black ink ball point pen, (i) darken the bubble
corresponding to your test paper code and the appropriate bubble under each digit of your registration
number and (ii) write your registration number, your name and name of the examination centre and
put your signature at the specified location.
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are
permitted to open the seal, please check all pages and report discrepancies, if any, to the invigilator.
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each
question has only one correct answer. Questions must be answered on the left hand side of the ORS
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ball point pen
against the question number. For each question darken the bubble of the correct answer. More
than one answer bubbled against a question will be treated as an incorrect response.
6. Since bubbles darkened by the black ink ball point pen cannot be erased, candidates should darken
the bubbles in the ORS very carefully.
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is unattempted, then
the answer to the second question in the pair will not be evaluated.
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each.
9. Unattempted questions will result in zero mark and wrong answers will result in NEGATIVE marks.
For all 1 mark questions, ⅓ mark will be deducted for each wrong answer. For all 2 marks questions,
⅔ mark will be deducted for each wrong answer. However, in the case of the linked answer question
pair, there will be negative marks only for wrong answer to the first question and no negative marks
for wrong answer to the second question.
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall.
11. Rough work can be done on the question paper itself. Blank pages are provided at the end of the
question paper for rough work.
12. Before the start of the examination, write your name and registration number in the space provided
below using a black ink ball point pen.
Name
Registration Number IN
IN 1/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q. 1 – Q. 25 carry one mark each.
Q.1 If x 1 , then the value of x x is
(A) e / 2 (B) e / 2 (C) x (D) 1
Q.2 With initial condition x(1) 0.5 , the solution of the differential equation,
dx
t x t is
dt
(A) x t
1
(B) x t 2
1 t2 (D) x
t
(C) x
2 2 2 2
Q.3 Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The
probability that max[X, Y] is less than 1 2 is
(A) 3 4 (B) 9 16 (C) 1 4 (D) 2 3
1
Q.4 The unilateral Laplace transform of f (t) is . The unilateral Laplace transform of t f (t ) is
s s 1
2
s 2s 1
(A) (B) 2
( s s 1)
2 2
( s s 1) 2
s 2s 1
(C) (D)
( s s 1)
2 2
( s s 1) 2
2
Q.5 Given
1 2
f ( z) . If C is a counterclockwise path in the z-plane such that z 1 1 , the value of
z 1 z 3
1
2 j C
f ( z ) dz is
(A) –2 (B) –1 (C) 1 (D) 2
Q.6 The average power delivered to an impedance (4 j3) by a current 5cos(100 t 100) A is
(A) 44.2 W (B) 50 W (C) 62.5 W (D) 125 W
Q.7 In the circuit shown below, the current through the inductor is
j1
1
1 0A
1 0V 1 0V
- + + -
1 0A
- j1 1
2 1 1
(A) A (B) A (C) A (D) 0 A
1 j 1 j 1 j
IN 2/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.8 In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal
switch S is closed at t = 0. The current i(t) for all t is
S t =0
C1 C2
i(t)
(A) zero (B) a step function
(C) an exponentially decaying function (D) an impulse function
Q.9 The impedance looking into nodes 1 and 2 in the given circuit is
ib
1k 99ib
9k
1
100
2
(A) 50 (B) 100 (C) 5 k (D) 10.1 k
Q.10 The i-v characteristics of the diode in the circuit given below are
v 0.7
A, v 0.7 V
i 500
0 A, v 0.7 V
1k
i
+ +
v
- 10V -
The current in the circuit is
(A) 10 mA (B) 9.3 mA (C) 6.67 mA (D) 6.2 mA
Q.11 A system with transfer function
( s 2 9 ) ( s 2)
G( s)
( s 1) ( s 3) ( s 4)
is excited by sin ( t ) . The steady-state output of the system is zero at
(A) 1 rad/s (B) 2 rad/s
(C) 3 rad/s (D) 4 rad/s
IN 3/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.12 The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit
input B. The number of combinations for which the output is logic 1, is
(A) 4 (B) 6 (C) 8 (D) 10
Q.13 In the sum of products function f ( X , Y , Z ) (2, 3, 4, 5) , the prime implicants are
(A) X Y , X Y (B) X Y , X Y Z , X Y Z
(C) X Y Z , X Y Z , X Y (D) X Y Z , X Y Z , X Y Z , X Y Z
Q.14 Consider the given circuit.
A
CLK
B
In this circuit, the race around
(A) does not occur (B) occurs when CLK = 0
(C) occurs when CLK = 1 and A = B = 1 (D) occurs when CLK = 1 and A = B = 0
If x [n] (1 / 3) (1 / 2) n u[n] , then the region of convergence (ROC) of its Z-transform in the
n
Q.15
Z-plane will be
(A) 1
3
z 3 (B) 1
3
z 12 (C) 1
2
z 3 (D) 1
3
z
Q.16 A capacitive motion transducer circuit is shown. The gap d between the parallel plates of the
capacitor is varied as d (t ) 103 [1 0.1sin (1000 t )] m . If the value of the capacitance is 2pF at
t 0 ms , the output voltage VO at t 2 ms is
1M
5 Volts DC
d
Capacitive
transducer VO
(A) mV (B) mV (C) 2 mV (D) 4 mV
2
Q.17 A psychrometric chart is used to determine
(A) pH (B) Sound velocity in glasses
(C) CO 2 concentration (D) Relative humidity
IN 4/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.18 A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates
according to the equation x(t ) sin 1t sin 2 t , where 2 rad/s 1 , 2 3 rad/s , then the output
of the strain gauge is proportional to
x
Cantilever beam:
Stiffness=8N/m y
Damping=0.1Ns/m
Base
Strain gauge Mass=0.001Kg
dx d 2x d ( x y)
(A) x (B) (C) (D)
dt dt 2 dt
Q.19 The transfer function of a Zero-Order-Hold system with sampling interval T is
1 1 1 T s 1 T s
(A) (1 e T s ) (B) (1 e T s ) 2 (C) e (D) e
s s s s2
Q.20 An LED emitting at 1 m with a spectral width of 50 nm is used in a Michelson interferometer. To
obtain a sustained interference, the maximum optical path difference between the two arms of the
interferometer is
(A) 200 m (B) 20 m (C) 1 m (D) 50 nm
Q.21 Light of wavelength 630 nm in vacuum, falling normally on a biological specimen of thickness
10 m, splits into two beams that are polarized at right angles. The refractive index of the tissue for
the two polarizations are 1.32 and 1.333. When the two beams emerge, they are out of phase by
(A) 0.13 (B) 74.3 (C) 90.0 (D) 128.6
Q.22 The responsivity of the PIN photodiode shown is 0.9 A/W. To obtain Vout of –1 V for an incident
optical power of 1 mW, the value of R to be used is
R
+5V
Vout
-5V
(A) 0.9 (B) 1.1 (C) 0.9 k (D) 1.1 k
IN 5/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.23 A periodic voltage waveform observed on an oscilloscope across a load is shown. A permanent
magnet moving coil (PMMC) meter connected across the same load reads
v(t)
10V
5V
0 10 12 20
time (ms)
-5V
(A) 4 V (B) 5 V (C) 8 V (D) 10 V
Q.24 For the circuit shown in the figure, the voltage and current expressions are
v(t ) E1 sin ( t ) E3 sin (3 t ) and i (t ) I1 sin ( t 1 ) I 3 sin (3 t 3 ) I 5 sin (5 t ) .
The average power measured by the Wattmeter is
i(t)
+ Wattmeter
v(t) Load
1 1
(A) E1 I 1 cos1 (B) [ E1 I 1 cos1 E1 I 3 cos3 E1 I 5 ]
2 2
1 1
(C) [ E1 I 1 cos1 E3 I 3 cos3 ] (D) [ E1 I 1 cos1 E3 I 1 cos1 ]
2 2
Q.25 The bridge method commonly used for finding mutual inductance is
(A) Heaviside Campbell bridge (B) Schering bridge
(C) De Sauty bridge (D) Wien bridge
Q. 26 to Q. 55 carry two marks each.
Q.26 A fair coin is tossed till a head appears for the first time. The probability that the number of
required tosses is odd, is
(A) 1/3 (B) 1/2 (C) 2/3 (D) 3/4
Q.27 Given that
5 3 1 0
A and I , the value of A 3 is
2 0 0 1
(A) 15 A + 12 I (B) 19 A + 30 I
(C) 17 A + 15 I (D) 17 A + 21 I
Q.28 The direction of vector A is radially outward from the origin, with A k r n where
r 2 x 2 y 2 z 2 and k is a constant. The value of n for which A 0 is
(A) –2 (B) 2 (C) 1 (D) 0
IN 6/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.29 The maximum value of f ( x) x 3 9 x 2 24 x 5 in the interval [1, 6] is
(A) 21 (B) 25 (C) 41 (D) 46
Q.30 Consider the differential equation
d 2 y (t ) dy(t ) dy
2
2 y (t ) (t ) with y (t ) t 0 2 and 0.
dt dt dt t 0
dy
The numerical value of is
dt t 0
(A) –2 (B) –1 (C) 0 (D) 1
Q.31 If VA VB 6 V, then VC VD is
R VA 2 VB R
R
R R -
10 V
R 1 R +
R
+ - VC VD
5V 2A
(A) –5 V (B) 2 V (C) 3 V (D) 6 V
Q.32 Assuming both the voltage sources are in phase, the value of R for which maximum power is
transferred from circuit A to circuit B is
2 R
+ - j1 +
10 V 3V
- -
Circuit A Circuit B
(A) 0.8 (B) 1.4 (C) 2 (D) 2.8
Q.33 The voltage gain Av of the circuit shown below is
13.7 Volts
12k
C vo
100k
C
b=100
vi 10k
(A) Av 200 (B) Av 100 (C) Av 20 (D) Av 10
IN 7/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.34 The state variable description of an LTI system is given by
x1 0 a1 0 x1 0
x 2 0 0 a2 x2 0 u
x a 0 x3 1
3 3 0
x1
y 1 0 0 x2
x
3
where y is the output and u is the input. The system is controllable for
(A) a1 0 , a 2 0 , a3 0 (B) a1 0 , a 2 0 , a3 0
(C) a1 0 , a 2 0 , a3 0 (D) a1 0 , a 2 0 , a3 0
Q.35 The state transition diagram for the logic circuit shown is
2-1 MUX
D Q
X1
Y
CLK X0
Q Select
A
A=1 A=0 A=0 A=0
A=1 A=1
(A) (B)
Q=0 Q=1 Q=0 Q=1
A=0 A=1
A=0 A=1 A=1 A=1
A=0 A=0
(C) (D)
Q=0 Q=1 Q=0 Q=1
A=1 A=0
Q.36 The Fourier transform of a signal h(t) is H ( j ) (2 cos) (sin 2) / . The value of h(0) is
(A) 1/4 (B) 1/2 (C) 1 (D) 2
Q.37 Let y[n] denote the convolution of h[n] and g[n], where h [n] (1 / 2) n u[n] and g[n] is a causal
sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals
(A) 0 (B) 1/2 (C) 1 (D) 3/2
IN 8/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.38 The feedback system shown below oscillates at 2 rad/s when
R(s) + K ( s 1) Y(s)
s as 2 2 s 1
3
-
(A) K = 2 and a = 0.75 (B) K = 3 and a = 0.75
(C) K = 4 and a = 0.5 (D) K = 2 and a = 0.5
Q.39 The circuit shown is a
R2
C R1 +5V
+ - +
Input Output
- + -
-5V
1
(A) low pass filter with f3dB = rad/s
( R1 R2 ) C
1
(B) high pass filter with f3dB = rad/s
R1C
1
(C) low pass filter with f3dB = rad/s
R1C
1
(D) high pass filter with f3dB = rad/s
( R1 R2 ) C
t
Q.40 The input x(t) and output y(t) of a system are related as y (t ) x( ) cos(3 ) d . The system is
(A) time-invariant and stable (B) stable and not time-invariant
(C) time-invariant and not stable (D) not time-invariant and not stable
Q.41 A double convex lens is used to couple a laser beam of diameter 5 mm into an optical fiber with a
numerical aperture of 0.5. The minimum focal length of the lens that should be used in order to
focus the entire beam into the fiber is
(A) 1.44 mm (B) 2.50 mm (C) 4.33 mm (D) 5.00 mm
Q.42 An analog voltmeter uses external multiplier settings. With a multiplier setting of 20 kit reads
440 V and with a multiplier setting of 80 kit reads 352 V. For a multiplier setting of 40 k the
voltmeter reads
(A) 371 V (B) 383 V (C) 394 V (D) 406 V
Q.43 The open loop transfer function of a unity negative feedback control system is given by
150
G( s) . The gain margin of the system is
s ( s 9) ( s 25)
(A) 10.8 dB (B) 22.3 dB (C) 34.1 dB (D) 45.6 dB
IN 9/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.44 A dynamometer arm makes contact with the piezoelectric load cell as shown. The g-constant of the
piezoelectric material is 50 103 Vm/N and the surface area of the load cell is 4 cm2. If a torque
20 Nm is applied to the dynamometer, the output voltage VO of the load cell is
0.5 m
Area A=4cm2
VO
Torque τ d= 1mm Load cell
Dynamometer
(A) 4 V (B) 5 V (C) 10 V (D) 16 V
Q.45 Water (density: 1000 kgm–3) stored in a cylindrical drum of diameter 1 m is emptied through a
horizontal pipe of diameter 0.05 m. A pitot-static tube is placed inside the pipe facing the flow.
At the time when the difference between the stagnation and static pressures measured by the pitot-
static tube is 10 kPa, the rate of reduction in water level in the drum is,
1 1 1 1
(A) ms1 (B) ms1 (C) ms1 (D) ms1
200 5 75 10 50 10 40 5
Q.46 A U-tube manometer of tube diameter D is filled with a liquid of zero viscosity. If the volume of
the liquid filled is V, the natural frequency of oscillations in the liquid level about its mean position,
due to small perturbations, is
D g 2 2 gV 1 gD 1 g
(A) (B) (C) (D)
2 2 V D 2
2 V
1/ 3
D
Q.47 The open loop transfer function of a unity gain negative feedback control system is given by
s 2 4s 8
G( s) . The angle , at which the root locus approaches the zeros of the system,
s ( s 2) ( s 8)
satisfies
1 3 1
(A) tan1 (B) tan1
4 4 3
1 1
(C) tan1 (D) tan1
2 4 4 3
IN 10/20
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2012 INSTRUMENTATION ENGINEERING - IN
Common Data Questions
Common Data for Questions 48 and 49:
With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following
were observed:
(i) 1 connected at port B draws a current of 3 A
(ii) 2.5 connected at port B draws a current of 2 A
+
A B
-
Q.48 With 10 V dc connected at port A, the current drawn by 7 connected at port B is
(A) 3/7 A (B) 5/7 A (C) 1 A (D) 9/7 A
Q.49 For the same network, with 6 V dc connected at port A, 1 connected at port B draws 7/3 A.
If 8 V dc is connected to port A, the open circuit voltage at port B is
(A) 6 V (B) 7 V (C) 8 V (D) 9 V
Common Data for Questions 50 and 51:
The deflection profile y (x ) of a cantilever beam due to application of a point force F (in Newton), as a
x
function of distance x from its base, is given by y ( x ) 0.001F x 2 1 m . The angular deformation
3
at the end of the cantilever is measured by reflecting a laser beam off a mirror M as shown in the figure.
S
90°
Photodetector
Laser θ
3m
y(x) M
x Cantilever
beam
F
1m
Q.50 The translation S of the spot of laser light on the photodetector when a force of F 1 N is applied
to the cantilever is
(A) 1 mm (B) 3 mm (C) 6 mm (D) 12 mm
1 1
Q.51 If linear variable differential transformers (LVDTs) are mounted at x m and x m on the
2 4
cantilever to measure the effect of time varying forces, the ratio of their outputs is
(A) 12/7 (B) 40/11 (C) 176/23 (D) 112/15
IN 11/20
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2012 INSTRUMENTATION ENGINEERING - IN
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
The transfer function of a compensator is given as
sa
Gc ( s ) .
sb
Q.52 Gc (s) is a lead compensator if
(A) a =1, b = 2 (B) a = 3, b = 2
(C) a = –3, b = –1 (D) a = 3, b = 1
Q.53 The phase of the above lead compensator is maximum at
(A) 2 rad/s (B) 3 rad/s (C) 6 rad/s (D) 1 / 3 rad/s
Statement for Linked Answer Questions 54 and 55:
In the circuit shown, the three voltmeter readings are V1 220 V , V2 122 V , V3 136 V .
R I
V2
RL
V1 V3 Load
X
Q.54 The power factor of the load is
(A) 0.45 (B) 0.50 (C) 0.55 (D) 0.60
Q.55 If RL 5 , the approximate power consumption in the load is
(A) 700 W (B) 750 W (C) 800 W (D) 850 W
IN 12/20
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2012 INSTRUMENTATION ENGINEERING - IN
General Aptitude (GA) Questions (Compulsory)
Q. 56 – Q. 60 carry one mark each.
Q.56 Choose the most appropriate alternative from the options given below to complete the following
sentence:
If the tired soldier wanted to lie down, he ___ the mattress out on the balcony.
(A) should take
(B) shall take
(C) should have taken
(D) will have taken
Q.57 If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =
(A) 2.23 (B) 4.33 (C) 11.37 (D) 27.64
Q.58 One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the
following is INCORRECT?
I requested that he should be given the driving test today instead of tomorrow.
(A) requested that
(B) should be given
(C) the driving test
(D) instead of tomorrow
Q.59 Which one of the following options is the closest in meaning to the word given below?
Latitude
(A) Eligibility (B) Freedom (C) Coercion (D) Meticulousness
Q.60 Choose the most appropriate word from the options given below to complete the following
sentence:
Given the seriousness of the situation that he had to face, his ___ was impressive.
(A) beggary (B) nomenclature (C) jealousy (D) nonchalance
Q. 61 - Q. 65 carry two marks each.
Q.61 Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total
money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is
(A) 5 (B) 6 (C) 9 (D) 10
IN 13/20
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2012 INSTRUMENTATION ENGINEERING - IN
Q.62 One of the legacies of the Roman legions was discipline. In the legions, military law prevailed
and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting,
even when the odds and conditions were against them.
Which one of the following statements best sums up the meaning of the above passage?
(A) Thorough regimentation was the main reason for the efficiency of the Roman legions even in
adverse circumstances.
(B) The legions were treated inhumanly as if the men were animals.
(C) Discipline was the armies’ inheritance from their seniors.
(D) The harsh discipline to which the legions were subjected to led to the odds and conditions being
against them.
Q.63 A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a
condition that whoever arrives first will not wait for the other for more than 15 minutes. The
probability that they will meet on that day is
(A) 1/4 (B) 1/16 (C) 7/16 (D) 9/16
Q.64 The data given in the following table summarizes the monthly budget of an average household.
Category Amount (Rs.)
Food 4000
Clothing 1200
Rent 2000
Savings 1500
Other expenses 1800
The approximate percentage of the monthly budget NOT spent on savings is
(A) 10% (B) 14% (C) 81% (D) 86%
Q.65 There are eight bags of rice looking alike, seven of which have equal weight and one is slightly
heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number
of weighings required to identify the heavier bag is
(A) 2 (B) 3 (C) 4 (D) 8
END OF THE QUESTION PAPER
IN 14/20
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GATE 2012 ‐ Answer Key ‐ Paper : IN Paper Question no. Key Paper Question no. Key IN 1 A IN 46 A IN 2 D IN 47 D IN 3 B IN 48 C IN 4 D IN 49 C IN 5 C IN 50 C IN 6 B IN 51 B IN 7 C IN 52 A IN 8 D IN 53 A IN 9 A IN 54 A IN 10 D IN 55 B IN 11 C IN 56 A IN 12 B IN 57 D IN 13 A IN 58 B IN 14 A IN 59 B IN 15 C IN 60 D IN 16 B IN 61 A IN 17 D IN 62 A IN 18 C IN 63 C IN 19 A IN 64 D IN 20 B IN 65 A IN 21 B IN 22 D IN 23 A IN 24 C IN 25 A IN 26 C IN 27 B IN 28 A IN 29 C IN 30 D IN 31 A IN 32 A IN 33 D IN 34 D IN 35 D IN 36 C IN 37 A IN 38 A IN 39 B IN 40 D IN 41 Marks to All IN 42 Marks to All IN 43 C IN 44 Marks to All IN 45 D
Official key not published for this paper.
Page 1 of 15
Source: GATE. Question paper published by GATE.