GATE 2014 Question Paper for IN Instrumentation Engineering

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GATE 2014 Examination
IN: Instrumentation Engineering
Duration: 180 minutes Maximum Marks: 100

Read the following instructions carefully.

1. To login, enter your Registration Number and password provided to you. Kindly go through the various
symbols used in the test and understand their meaning before you start the examination.
2. Once you login and after the start of the examination, you can view all the questions in the question
paper, by clicking on the View All Questions button in the screen.
3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject
specific GATE paper for 85 marks. Both these sections are compulsory.
The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question
numbers 6 to 10 are of 2-mark each.
The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to
25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each.
4. Depending upon the GATE paper, there may be useful common data that may be required for
answering the questions. If the paper has such useful data, the same can be viewed by clicking on the
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GATE 2014 SET- 2 General Aptitude -GA

Q. 1 – Q. 5 carry one mark each.
Q.1 Choose the most appropriate word from the options given below to complete the following
sentence.

A person suffering from Alzheimer’s disease short-term memory loss.
(A) experienced (B) has experienced
(C) is experiencing (D) experiences

Q.2 Choose the most appropriate word from the options given below to complete the following
sentence.

____________ is the key to their happiness; they are satisfied with what they have.

)
14
(A) Contentment (B) Ambition (C) Perseverance (D) Hunger

Q.3 Which of the following options is the closest in meaning to the sentence below?

20
“As a woman, I have no country.”
(A) Women have no country.
(B) Women are not citizens of any country.
(C) Women’s solidarity knows no national boundaries.
(D) Women of all countries have equal legal rights.

Q.4
E
In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the
Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes
AT
is ____ years.

Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would
it take to double at this growth rate?
(G

(A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years
02

Q. 6 – Q. 10 carry two marks each.

Q.6 In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the
group. Which of the following statements is/are required to find the eldest child in the group?
A

Statements
1. Shiv is younger to Riaz.
G

2. Shiv is elder to Som.
(A) Statement 1by itself determines the eldest child.
(B) Statement 2 by itself determines the eldest child.
(C) Statements 1 and 2 are both required to determine the eldest child.
(D) Statements 1 and 2 are not sufficient to determine the eldest child.

GA 1/2

GATE 2014 SET- 2 General Aptitude -GA
Q.7 Moving into a world of big data will require us to change our thinking about the merits of
exactitude. To apply the conventional mindset of measurement to the digital, connected world of
the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with
exactness is an artefact of the information-deprived analog era. When data was sparse, every data
point was critical, and thus great care was taken to avoid letting any point bias the analysis.
From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier

The main point of the paragraph is:
(A) The twenty-first century is a digital world
(B) Big data is obsessed with exactness
(C) Exactitude is not critical in dealing with big data
(D) Sparse data leads to a bias in the analysis

)
Q.8 The total exports and revenues from the exports of a country are given in the two pie charts below.
The pie chart for exports shows the quantity of each item as a percentage of the total quantity of

14
exports. The pie chart for the revenues shows the percentage of the total revenue generated through
export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total
revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1
per kilogram to the revenue generated through export of Item 4 per kilogram?

20
Exports Revenues

Item 6
16%
Item 1
11%
E Item 6
19%
Item 1
12%
AT
Item 5 Item 2
12% 20% Item 2
Item 5 20%
20%
Item 3
Item 4 19%
Item 4 Item 3
22%
(G

6% 23%
02

(A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1

Q.9 X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is
1 km east of P. What is the distance between X and Q in km?
A

(A) 1 (B) √2 (C) √3 (D) 2

10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this
G

Q.10
kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A
particular patient is tested using this kit and is found to be positive. The probability that the
individual is actually positive is _______

END OF THE QUESTION PAPER

GA 2/2

GATE 2014 INSTRUMENTATION - IN

Q. 1 – Q. 25 carry one mark each.
Q.1 Given
𝜋𝜋
𝑥𝑥(𝑡𝑡) = 3 sin(1000 𝜋𝜋𝜋𝜋)and 𝑦𝑦(𝑡𝑡) = 5 cos �1000 𝜋𝜋𝜋𝜋 + 4 �

The x-yplot will be

(A) a circle (B)a multi-loop closed curve

(C)a hyperbola (D)an ellipse

)
Q.2 Given that x is a random variable in the range[0,∞]with a probability densityfunction
𝑥𝑥
−

14
𝑒𝑒 2
, the value of the constant K is___________.
𝐾𝐾

20
Q.3 The figure shows the plot of y as a function of x
E
AT
(G

The function shown is the solution of the differential equation (assuming all initial conditions to be
IN

zero) is :

(A)
d2y
=1 (B)
dy
=x (C) dy = − x (D)
dy
= x
dx 2 dx dx dx

Q.4 A vector is defined as
f = yˆi + xˆj + zkˆ
where ˆi , ˆj and kˆ are unit vectors in Cartesian (x,y,z) coordinate system.
The surface integral ∯ 𝐟𝐟. 𝐝𝐝𝐝𝐝 over the closed surface S of a cube with vertices having the following
coordinates: (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1) is
___________.

IN 1/15

GATE 2014 INSTRUMENTATION - IN

Q.5 The figure shows the schematic of a production process with machines A, B and C. An input job
needs to be pre-processed either by A or by B before it is fed to C, from which the final finished
product comes out. The probabilities of failure of the machines are given as:
PA=0.15, PB=0.05, PC=0.1.

A
Input job
C Finished
product

B
Assuming independence of failures of the machines, the probability that a given job is successfully

)
processed (up to the third decimal place) is ___________.

14
Q.6 The circuit shown in figure was at steady state for𝑡𝑡 < 0 with the switch at position ‘A’. The switch
is thrown to position ‘B’ at time 𝑡𝑡 = 0. The voltage 𝑉𝑉 (volts) across the 10 Ω resistor at time
𝑡𝑡 = 0+ is___________.

+ A
2Ω

B
20
E
10 Ω V t=0 5H
AT

_ 6V

Q.7 The average real power in watts delivered to a load impedance 𝑍𝑍𝐿𝐿 = (4 − 𝑗𝑗2)Ω by an ideal current
(G

source 𝑖𝑖(𝑡𝑡) = 4 sin(ω𝑡𝑡 + 20°)A is ___________.

Q.8 Time domain expressions for the voltage 𝑣𝑣1 (𝑡𝑡) and 𝑣𝑣2 (𝑡𝑡) are given as
𝑣𝑣1 (𝑡𝑡) = 𝑉𝑉𝑚𝑚 sin(10𝑡𝑡 − 130°)and𝑣𝑣2 (𝑡𝑡) = 𝑉𝑉𝑚𝑚 cos(10𝑡𝑡 + 10°).
Which one of the following statements is TRUE?
IN

(A)𝑣𝑣1 (𝑡𝑡)leads 𝑣𝑣2 (𝑡𝑡) by 130o (B)𝑣𝑣1 (𝑡𝑡) lags 𝑣𝑣2 (𝑡𝑡) by 130o

(C)𝑣𝑣1 (𝑡𝑡) lags 𝑣𝑣2 (𝑡𝑡) by −130o (D)𝑣𝑣1 (𝑡𝑡) leads𝑣𝑣2 (𝑡𝑡)by −130o

Q.9 A pHelectrode obeys Nernst equation and is being operated at 25°C. The change in the open
circuit voltage in millivolts across the electrode for a pH change from 6 to 8 is ___________.

IN 2/15

GATE 2014 INSTRUMENTATION - IN

Q.10 The pressure and velocity at the throat of a Venturi tube, measuring the flow of a liquid, are related
to the upstream pressure and velocity, respectively, as follows:
(A) pressure is lower but velocity is higher

(B) pressure is higher but velocity is lower

(C) both pressure and velocity are lower

(D) pressure and velocity are identical

Q.11 Semiconductor strain gages typically have much higher gage factors than those of metallic strain
gages, primarily due to :

)
(A) higher temperature sensitivity

14
(B) higher Poisson’s ratio

(C) higher piezoresitive coefficient

(D) higher magnetostrictive coefficient

Q.12
20
For a rotameter, which one of the following statements is TRUE?
(A) the weight of the float is balanced by the buoyancy and the drag force acting on the float

(B) the velocity of the fluid remains constant for all positions of the float
E
(C) the measurement of volume flow rate of gas is not possible
AT

(D) the volume flow rate is insensitive to changes in density of the fluid

Q.13 For the op-amp shown in the figure, the bias currents are Ib1= 450 nA and Ib2=350 nA. The values
of the input bias current (IB) and the input offset current (If) are:
(G
IN

(A) IB= 800 nA, If=50 nA (B) IB= 800 nA, If=100nA

(C) IB= 400 nA, If=50nA (D) IB= 400 nA, If=100nA

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GATE 2014 INSTRUMENTATION - IN

Q.14 The amplifier in the figure has gain of −10 and input resistance of 50 kΩ. The values of Ri and
Rfare:
Rf

Ri

V0
Vin +

(A) Ri= 500 kΩ, Rf = 50 kΩ (B) Ri= 50 kΩ, Rf = 500 kΩ

)
14
(C) Ri= 5 kΩ, Rf = 10 kΩ (D) Ri= 50 kΩ, Rf = 200 kΩ

Q.15 For the circuit shown in the figure assume ideal diodes with zero forward resistance and zero

20
forward voltage drop. The current through the diode D2 in mAis ___________.
E
AT
(G

Q.16 The system function of an LTI system is given by
1 − 13𝑧𝑧−1
𝐻𝐻(𝑧𝑧) =
1 − 14𝑧𝑧−1
IN

The above system can have stable inverse if the region of convergence of H(z)is defined as
1 1 1 1
(A) |𝑧𝑧| < 4 (B) |𝑧𝑧| < 12 (C) |𝑧𝑧| > 4 (D) |𝑧𝑧| < 3

IN 4/15

GATE 2014 INSTRUMENTATION - IN

Q.17 The figure is a logic circuit with inputs A and B and output Y.Vss = + 5 V. The circuit is of type

)
14
(A) NOR (B) AND 20(C) OR (D) NAND
E
Q.18 The impulse response of an LTI system is given as :
 ωc
 π n=0
AT

h [ n] = 
 sin ωc n n ≠ 0
 π n
It represents an ideal
(A)non-causal, low-pass filter (B) causal, low-pass filter
(G

(C) non-causal, high-pass filter (D) causal, high-pass filter

Q.19 A discrete-time signal 𝑥𝑥[𝑛𝑛] is obtained by sampling an analog signal at 10 kHz. The signal 𝑥𝑥[𝑛𝑛]is
filtered by a system with impulse response ℎ[𝑛𝑛] = 0.5{𝛿𝛿[𝑛𝑛] + 𝛿𝛿[𝑛𝑛 − 1]}. The 3dB cutoff
IN

frequency of the filter is:
(A) 1.25 kHz (B) 2.50 kHz (C) 4 .00 kHz (D) 5.00 kHz

Q.20 A full duplex binary FSK transmission is made through a channel of bandwidth 10 kHz. In each
direction of transmission the two carriers used for the two states are separated by 2 kHz. The
maximum baud rate for this transmission is:
(A) 2000 bps (B) 3000 bps (C) 5000 bps (D) 10000 bps

IN 5/15

GATE 2014 INSTRUMENTATION - IN

Q.21 A loop transfer function is given by :
𝐾𝐾(𝑠𝑠 + 2)
𝐺𝐺(𝑠𝑠)𝐻𝐻(𝑠𝑠) =
𝑠𝑠 2 (𝑠𝑠 + 10)
The point of intersection of the asymptotes of 𝐺𝐺(𝑠𝑠)𝐻𝐻(𝑠𝑠)on the real axis in the 𝑠𝑠-plane is at
___________.

Q.22 The resistance and inductance of an inductive coil are measured using an AC bridge as shown in
the figure. The bridge is to be balanced by varying the impedance Z2.

)
14
(B) R and L 20
For obtaining balance, Z2 should consist of element(s):
(A) R and C (C) L and C (D) Only C
E
Q.23 A plant has an open-loop transfer function,
20
Gp ( s ) = .
( s + 0.1)( s + 2 )( s + 100 )
AT

The approximate model obtained by retaining only one of the above poles, which is closest to the
frequency response of the original transfer function at low frequency is

0.1 2 100 20
(G

(A) (B) (C) (D)
s + 0.1 s+2 s + 100 s + 0.1

Q.24 In order to remove respiration related motion artifacts from an ECG signal, the following filter
should be used:
IN

(A) low-pass filter with fc = 0.5 Hz

(B) high-pass filter with fc = 0.5 Hz

(C)high-pass filter with fc = 49.5 Hz

(D)band-pass filter with passband between 0.1 Hz and 0.5 Hz

Q.25 In a time-of-flight mass spectrometerif𝑞𝑞 is the charge and 𝑚𝑚 the mass of the ionized species,then
the time of flight is proportional to

√𝑚𝑚 √𝑞𝑞 𝑚𝑚 𝑞𝑞
(B) (C) (D)
(A)
√𝑞𝑞 √𝑚𝑚 √𝑞𝑞 √𝑚𝑚

IN 6/15

GATE 2014 INSTRUMENTATION - IN

Q. 31 – Q. 55 carry two marks each.

Q.26 A scalar valued function is defined as f ( x ) = xT Ax + bT x + c , where A is a symmetric positive
definite matrix with dimension n× n ; b and x are vectors of dimension n×1. The minimum value
of f ( x ) will occur when x equals

( ) b ( ) b
−1 −1
(A) AT A (B) − AT A

-1
A b A-1 b
(C)− � � (D)
2 2

)
14
Q.27 The iteration step in order to solvefor the cube roots of a given number Nusing the Newton-
Raphson’s method is

1 N
( N − xk3 )

20
1
(A) xk +1 =xk + =
3
(B) xk +1  2 xk + 2 
3 xk 

1 N
(C) xk +1 =xk −
1
3
( N − xk3 ) =
(D) xk +1  2 xk − 2 
3 xk 
E
Q.28 For the matrix A satisfying the equation given below, the eigenvaluesare
AT

1 2 3 1 2 3
[ A ] 7 8 9  =  4 5 6
 4 5 6  7 8 9 

(A)(1, −𝑗𝑗, 𝑗𝑗) (B)(1, 1, 0)
(G

(C)(1, 1, −1) (D)(1, 0, 0)

Q.29 In the circuit shown in the figure, initially the capacitor is uncharged. The switch ‘S’ is closed at
𝑡𝑡 = 0. Two milliseconds after the switch is closed, the current through the capacitor (in mA) is
IN

___________.

2 kΩ S
ic (t)
t= 0
5V 4 µF
2 kΩ

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GATE 2014 INSTRUMENTATION - IN

Q.30 A capacitor ‘C’ is to be connected across the terminals ‘A’ and ‘B’ as shown in the figure so that
the power factor of the parallel combination becomes unity. The value of the capacitance required
in µF is___________.

A

4Ω

60 V
50 Hz
j1Ω

)
14
B

Q.31 The resistance of a wire is given by the expression

20
4ρ𝐿𝐿
𝑅𝑅 = ,
𝜋𝜋𝜋𝜋 2
where, ρis the resistivity (Ω-meter),L is the length (meter) and D (meter) is the diameter of the
wire. The error in measurement of each of the parameters ρ, L, and D is ±1.0% . Assuming that
the errors are independent random variables, the percent error in measurement of R is
___________.
E
Q.32 The circuit shown in the figure contains a dependent current source between A and B terminals.
AT

The Thevenin’s equivalent resistance in kΩbetween the terminals C and D is ___________.
5 kΩ A 5 kΩ
C

+
10−4 Vx
(G

10 V vx
_
B D
IN

Q.33 A thermistor has a resistance of 1 kΩ at temperature 298 Kand 465 Ω at temperature 316 K. The
temperature sensitivity in K-1[i.e. (1/R)(dR/dT), where R is the resistance at the temperature T(in
K)], of this thermistor at 316 K is ___________.

Q.34 A barium titanate piezoelectric crystal with d33=150 pC/N, Ccrystal = 25 pF and Rcrystal = 1010 Ω is
used to measure the amplitude of a step force. The voltage output is measured using a digital
voltmeter with input impedance 1013 Ω connected across the crystal. All other capacitances and
resistances may be neglected. A step force of 2 N is applied from direction “3” on the crystal. The
time in milliseconds within which the voltmeter should sample the crystal output voltage so that the
drop from the peak value is no more than 0.12V is ___________.

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GATE 2014 INSTRUMENTATION - IN

Q.35 A thermopile is constructed using 10 junctions of Chromel-Constantan (sensitivity 60µV/°C for
each junction) connected in series. The output is fed to an amplifier having an infinite input
impedance and a gain of 10. The output from the amplifier is acquired using a 10-bit ADC, with
reference voltage of 5 V. The resolution of this system in units of °C is ___________.

Q.36 A transit time ultrasonic flowmeter uses a pair of ultrasonic transducers placed at 45° angle, as
shown in the figure.

)
14
20
The inner diameter of the pipe is 0.5 m. The differential transit time is directly measured using a
clock of frequency 5 MHz. The velocity of the fluid is small compared to the velocity of sound in
the static fluid, which is 1500 m/s and the size of the crystals is negligible compared to the diameter
of the pipe. The minimum change in fluid velocity (m/s) that can be measured using this system is
___________.
E
Q.37 Assuming an ideal op-amp in linear range of operation, the magnitude of the transfer impedance
𝑣𝑣0
AT

in MΩ of the current to voltage converter shown in the figure is ___________.
𝑖𝑖
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Q.38 For the circuit shown in the figure, the transistor has β = 40, 𝑉𝑉𝐵𝐵𝐵𝐵 = 0.7 V, and the voltage across
the Zener diode is 15 V.The current (in mA) through the Zener diode is ___________.

+30 V

330 Ω 100 Ω

)
Q.39 In the figure, transistors T1 and T2 have identical characteristics. 𝑉𝑉𝐶𝐶𝐶𝐶(𝑠𝑠𝑠𝑠𝑠𝑠 ) of transistor T3 is 0.1 V.

14
The voltage 𝑉𝑉1 is high enough to put T3 in saturation. Voltage 𝑉𝑉𝐵𝐵𝐵𝐵 of transistors T1, T2 and T3is 0.7
V. The value of (𝑉𝑉1 − 𝑉𝑉2 ) in Vis ___________.

9V

5 kΩ
V1 T3 20
E
3 kΩ
V2
AT

T1 T2
(G

Q.40 The figures show an oscillator circuit having an ideal Schmitt trigger and its input-output
()
characteristics. The time period (in ms) of vo t is___________.
IN

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GATE 2014 INSTRUMENTATION - IN

Q.41 An N-bit ADC has an analog reference voltage V. Assuming zero mean and uniform distribution of
the quantization error, the quantization noise power will be:

𝑉𝑉 2 𝑉𝑉 2
(A) (B)
12(2𝑁𝑁 −1)2 12(2𝑁𝑁 −1)

𝑉𝑉 𝑉𝑉 2
(C) (D)
12(2𝑁𝑁 −1) √12

Q.42 A microprocessor accepts external interrupts (Ext INT) through a Programmable Interrupt

)
Controller as shown in the figure.

14
20
Assuming vectored interrupt, a correct sequence of operations when a single external interrupt (Ext
INT1) is received will be :
E
(A) Ext INT1→ INTA→Data Read→INT

(B) Ext INT1→ INT→INTA→Data Read
AT

(C) Ext INT1→ INT→INTA→Address Write

(D) Ext INT1→ INT→ Data Read→Address Write
(G
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GATE 2014 INSTRUMENTATION - IN

Q.43 The circuit in the figure represents a counter-based unipolar ADC. When SOC is asserted the
counter is reset and clock is enabled so that the counter counts up and the DAC output grows.
When the DAC output exceeds the input sample value, the comparator switches from logic 0 to
logic 1, disabling the clock and enabling the output buffer by asserting EOC. Assuming all
components to be ideal, 𝑉𝑉ref , DAC output and input to be positive, the maximum error in
conversion of the analog sample value is:

)
14
(A)directly proportional to𝑉𝑉ref
20 (B) inversely proportional to 𝑉𝑉ref
E
(C)independent of𝑉𝑉ref (D)directly proportional to clock frequency
AT

Q.44 𝑋𝑋(𝑘𝑘)is the Discrete Fourier Transform of a 6-point real sequence 𝑥𝑥(𝑛𝑛).

If 𝑋𝑋(0) = 9 + 𝑗𝑗0, 𝑋𝑋(2) = 2 + 𝑗𝑗2, 𝑋𝑋(3) = 3 – 𝑗𝑗0, 𝑋𝑋(5) = 1 – 𝑗𝑗1, 𝑥𝑥(0) is
(A) 3 (B) 9 (C) 15 (D) 18
(G

Q.45 The transfer function of a digital system is given by:

𝑏𝑏0
−1 −2
; where𝑎𝑎2 is real.
1− 𝑧𝑧 + 𝑎𝑎 2 𝑧𝑧

The transfer function is BIBO stable if the value of 𝑎𝑎2 is:
IN

(A) −1.5 (B) −0.75 (C) 0.5 (D) 1.5

Q.46 The transfer function of a system is given by
−𝑠𝑠
𝑒𝑒 �500
𝐺𝐺(𝑠𝑠) =
𝑠𝑠 + 500
The input to the system is 𝑥𝑥(𝑡𝑡) = sin 100𝜋𝜋𝜋𝜋. In periodic steady state the output of the system is
found to be 𝑦𝑦(𝑡𝑡) = 𝐴𝐴sin(100𝜋𝜋𝜋𝜋 − 𝜙𝜙). The phase angle (𝜙𝜙) in degree is ___________.

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GATE 2014 INSTRUMENTATION - IN

Q.47 In the microprocessor controlled measurement scheme shown in the figure, Rx is the unknown
resistance to be measured, while Rref and Cref are known. Cref is charged from voltage VL to VH (by
a constant DC voltage source VS), once through Rref in Tref seconds and then discharged to VL . It
isagain charged from voltage VL to VH throughRxin Tx seconds.

)
If Tx = kTref then

14
 VL   VH 
=
(A) Rx kRref 1 −  (B) Rx = kRref ln  
 VH   VL 

20
(C) Rx = kRref (D) Rx = Rref ln k

Q.48 Frequency of an analog periodic signal in the range of 5kHz - 10kHz is to be measured with a
E
resolution of 100Hz by measuring its period with a counter. Assuming negligible signal and
transition delays the minimum clock frequency and minimum number of bits in the counter
needed, respectively, are:
AT

(A) 1 MHz, 10-bits (B) 10 MHz, 10-bits

(C) 1 MHz, 8-bits (D) 10MHz, 8-bits
(G

Q.49 The loop transfer function of a feedback control system is given by
1
G (s) H (s) =
s ( s + 1)( 9 s + 1)
Its phase crossover frequency (in rad/s), approximated to two decimal places, is ___________.
IN

Q.50 Consider a transport lag process with a transfer function
𝐺𝐺𝑝𝑝 (𝑠𝑠) = 𝑒𝑒 −𝑠𝑠 .
The process is controlled by a purely integral controller with transfer function
𝐾𝐾𝑖𝑖
𝐺𝐺𝑐𝑐 (𝑠𝑠) =
𝑠𝑠
in a unity feedback configuration. The value of𝐾𝐾𝑖𝑖 for which the closed loop plant has a pole
at𝑠𝑠 = −1, is ___________.

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Q.51 Consider the control system shown in figurewith feedforwardaction for rejection of a measurable
disturbance d ( t ) . The value of K, for whichthe disturbance response at the output 𝑦𝑦(𝑡𝑡) is zero
mean, is:

)
(A) 1 (B)−1 (C) 2 (D) −2

14
Q.52 A mixture contains two mutually inert solutions ‘X’ and ‘Y’ in equal volumes. The mixture is
examined in a spectrophotometer using a cuvette. It is observed that the transmittance is 0.40. With
only the solution ‘X’ in the same cuvette, the transmittance is 0.20. With only solution ‘Y’ in the
cuvette the transmittance is___________.

Q.53

20
Monochromatic light from a step index (n1 = 1.500; n2 = 1.485), multimode optical fiber of core
diameter 100 µm is incident through air (n = 1.000) onto a linear photo-detector array placed at 1
mm distance from the tip of the fiber. The tip of the fiber is polished and its exit plane is
perpendicular to the axis of the fiber. The detector array is oriented parallel to the exit plane of the
tip. The array consists of photo-detector elements each of 5 µm diameter. The distance between the
edges of two adjacent elements can be assumed to be zero. The number of elements illuminated by
E
the light coming out of the fiber is___________.
AT

Q.54 An image of the chest of a patient is taken with an X-ray machine on a photographic film. The
Hurter-Driffield (HD) curve of the film is shown in the figure. The highly absorbing parts of the
body (e.g. bones), show up as low exposure regions(mapped near A) and the less absorbing parts
(e.g. muscles) show up as high exposure regions(mapped near B).
(G
IN

If the exposure time is increased 10 times, while keeping the voltages and currents in the X-ray
machine constant, in the image,
(A)contrast decreases since B moves into the shoulder region

(B)contrast decreases since both A and B move into the shoulder region

(C)contrast increases sinceA moves into the toe region

(D)contrast decreases since both A and B move into the toe region
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GATE 2014 INSTRUMENTATION - IN

Q.55

)
14
For the given low-pass circuit shown in the figure, the cutoff frequency in Hz will be ___________.

20
END OF THE QUESTION PAPER
E
AT
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