GATE 2021 Question Paper IN Instrumentation Engineering

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 Getting to the top is ________________ than staying on top.

(A) more easy

(B) much easy

(C) easiest

(D) easier

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Q.2

The mirror image of the above text about the x-axis is

(A)

(B)

(C)

(D)

Q.3 In a company, 35% of the employees drink coffee, 40% of the employees
drink tea and 10% of the employees drink both tea and coffee. What % of
employees drink neither tea nor coffee?

(A) 15

(B) 25

(C) 35

(D) 40

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Q.4  and ⊙ are two operators on numbers p and q such that
p2 + q2 𝒑𝟐
pq = and 𝒑 ⊙ 𝒒 = 𝒒 ;
pq
If 𝒙 ⊕ 𝒚 = 𝟐 ⊙ 𝟐, then x =

(A) y
2

(B) y

(C) 3y
2

(D) 2 y

Q.5 Four persons P, Q, R and S are to be seated in a row, all facing the same
direction, but not necessarily in the same order. P and R cannot sit adjacent
to each other. S should be seated to the right of Q. The number of distinct
seating arrangements possible is:

(A) 2

(B) 4

(C) 6

(D) 8

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Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q.6 Statement: Either P marries Q or X marries Y
Among the options below, the logical NEGATION of the above statement is:

(A) P does not marry Q and X marries Y.

(B) Neither P marries Q nor X marries Y.

(C) X does not marry Y and P marries Q.

(D) P marries Q and X marries Y.

Q.7 Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4
cm each.
Folding operation 1: The sheet is folded into half by joining the short edges of
the current shape.
Folding operation 2: The sheet is folded into half by joining the long edges of
the current shape.
Folding operation 1 is carried out on Sheet M three times.
Folding operation 2 is carried out on Sheet N three times.
The ratio of perimeters of the final folded shape of Sheet N to the final folded
shape of Sheet M is ______.

(A) 13 : 7

(B) 3 : 2

(C) 7 : 5

(D) 5 : 13

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Q.8 P

θ
T Q

S R

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to
form a star as shown in the figure above.
The value of , in degrees, is ______

(A) 36

(B) 45

(C) 72

(D) 108

Q.9 A function, , is defined by
 p − q ) , if p  q,
 ( p,q ) =  (
2

 p + q, if p  q.

 ( − ( −3 + 2 ) ,( −2 + 3) )
The value of the expression is:
( − ( −2 + 1) )
(A) −1

(B) 0

(C) 16
3
(D) 16

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Q.10 Humans have the ability to construct worlds entirely in their minds, which
don’t exist in the physical world. So far as we know, no other species possesses
this ability. This skill is so important that we have different words to refer to
its different flavors, such as imagination, invention and innovation.
Based on the above passage, which one of the following is TRUE?

(A) No species possess the ability to construct worlds in their minds.

(B) The terms imagination, invention and innovation refer to unrelated skills.

(C) We do not know of any species other than humans who possess the ability to
construct mental worlds.

(D) Imagination, invention and innovation are unrelated to the ability to construct
mental worlds.

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Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 Consider the row vectors 𝒗 = (𝟏, 𝟎) and 𝒘 = (𝟐, 𝟎). The rank of the matrix
𝑴 = 𝟐𝒗𝑻 𝒗 + 𝟑𝒘𝑻 𝒘, where the superscript T denotes the transpose, is

(A) 1

(B) 2

(C) 3

(D) 4

Q.2 Consider the sequence 𝒙𝒏 = 𝟎. 𝟓𝒙𝒏−𝟏 + 𝟏, 𝒏 = 𝟏, 𝟐, … … with 𝒙𝟎 = 𝟎. Then
𝐥𝐢𝐦 𝒙𝒏 is
𝒏→∞

(A) 0

(B) 1

(C) 2

(D) ∞

Q.3 An infinitely long line, with uniform positive charge density, lies along the z-
axis. In cylindrical coordinates (𝒓, ∅, 𝐳), at any point ⃗𝑷
⃗ not on the z-axis, the
direction of the electric field is

(A) 𝑟̂

̂
(B) ∅

(C) 𝑧̂

(D) (𝑟̂ +𝑧̂ )
√2

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Q.4 The input-output relationship of an LTI system is given below.

For an input x[n] shown below

the peak value of the output when x[n] passes through h is ____.

(A) 2

(B) 4

(C) 5

(D) 6

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Q.5 In an ac main, the rms voltage Vac, rms current Iac and power Wac are
measured as: Vac = 100 V ± 1%, Iac = 1 A ± 1% and Wac = 50 W ± 2% (errors
are with respect to readings). The percentage error in calculating the power
factor using these readings is

(A) 1%

(B) 2%

(C) 3%

(D) 4%

Q.6 Let 𝒖(𝒕) denote the unit step function. The bilateral Laplace transform of
the function 𝒇(𝒕) = 𝒆𝒕 𝒖(−𝒕) is ____.

(A) 1
with real part of s < 1
𝑠−1

(B) 1
with real part of s > 1
𝑠−1

(C) −1
with real part of s < 1
𝑠−1

(D) −1
with real part of s > 1
𝑠−1

Q.7 Input-output characteristic of a temperature sensor is exponential for a

(A) Thermistor

(B) Thermocouple

(C) Resistive Temperature Device (RTD)

(D) Mercury thermometer

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Q.8 The signal 𝐬𝐢𝐧(√𝟐𝝅𝒕) is

(A) periodic with period T = √2𝜋

(B) not periodic

(C) periodic with period T = 2𝜋

(D) periodic with period T = 4𝜋 2

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Q.9 – Q.11 Multiple Select Question (MSQ), carry ONE mark each (no negative
marks).

Q.9 The step response of a circuit is seen to have an oscillatory behaviour at the
output with oscillations dying down after some time. The correct inference(s)
regarding the transfer function from input to output is/are

(A) that it is of at least second order.

(B) that it has at least one pole-pair that is underdamped.

(C) that it does not have a real pole.

(D) that it is a first order system.

Q.10 For a 4-bit Flash type Analog to Digital Convertor (ADC) with full scale
input voltage range “V”, which of the following statement(s) is/are true?

(A) The ADC requires 15 comparators.

(B) The ADC requires one 4 to 2 priority encoder and 4 comparators.

(C) 𝑉
A change in the input voltage by will always flip MSB of the output.
16

(D) 𝑉
A change in the input voltage by will always flip the LSB of the output.
16

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Q.11 A 16-bit microprocessor has twenty address lines (A0 to A19) and 16 data
lines. The higher eight significant lines of the data bus of the processor are
tied to the 8-data lines of a 16 Kbyte memory that can store one byte in each
of its 16K address locations. The memory chip should map onto contiguous
memory locations and occupy only 16 Kbyte of memory space. Which of the
following statement(s) is/are correct with respect to the above design?

(A) If the 16 Kbyte of memory chip is mapped with a starting address of 80000H,
then the ending address will be 83FFFH.

(B) The active high chip-select needed to map the 16 Kbyte memory with a starting
address at F0000H is given by the logic expression (A19 · A18 · A17 · A16).

(C) The 16 Kbyte memory cannot be mapped with contiguous address locations with
a starting address as 0F000H using only A19 to A14 for generating chip select.

(D) The above chip cannot be interfaced as the width of the data bus of the processor
and the memory chip differs.

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Q.12 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative
marks).

Q.12 A single-phase transformer has a magnetizing inductance of 250 mH and a
core loss resistance of 300 Ω, referred to primary side. When excited with a
230 V, 50 Hz sinusoidal supply at the primary, the power factor of the input
current drawn, with secondary on open circuit, is ____ (rounded off to two
decimal places).

Q.13 Taking N as positive for clockwise encirclement, otherwise negative, the
𝟑
number of encirclements N of (−𝟏 , 𝟎) in the Nyquist plot of 𝑮(𝒔) = 𝒔−𝟏 is
____.

Q.14 The diode used in the circuit has a fixed voltage drop of 0.6 V when forward
biased. A signal vs is given to the ideal OpAmp as shown. When vs is at its
positive peak, the output (vOA) of the OpAmp in volts is _______.

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Q.15 The transistor Q1 has a current gain 1 = 99 and the transistor Q2 has a
current gain 2 = 49. The current IB2 in microampere is _______.

Q.16 A 300 V, 5 A, LPF wattmeter has a full scale of 300 W. The wattmeter can
be used for loads supplied by 300 V ac mains with a maximum power factor
of ___________ (rounded off to one decimal place).

Q.17 A 10-bit ADC has a full-scale of 10.230 V, when the digital output is
(11 1111 1111)2. The quantization error of the ADC in millivolt is _________.

Q.18 A strain gage having nominal resistance of 1000 Ω has a gage factor of 2.5.
If the strain applied to the gage is 100 µm/m, its resistance in ohm will change
to ____________ (rounded off to two decimal places).

Q.19 Given: Density of mercury is 13,600 kg/m3 and acceleration due to gravity is
9.81 m/s2. Atmospheric pressure is 101 kPa. In a mercury U-tube
manometer, the difference between the heights of the liquid in the U-tube is
1 cm. The differential pressure being measured in pascal is ______ (rounded
off to the nearest integer).

Q.20 A piezoresistive pressure sensor has a sensitivity of 1 (mV/V)/kPa. The
sensor is excited with a dc supply of 10 V and the output is read using a 3 ½
digit 200 mV full-scale digital multimeter. The resolution of the
measurement set-up, in pascal is ___.

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Q.21 An amplitude modulation (AM) scheme uses tone modulation, with
modulation index of 0.6. The power efficiency of the AM scheme is ____ %
(rounded off to one decimal place).

Q.22 When the movable arm of a Michelson interferometer in vacuum (𝒏 = 𝟏) is
moved by 𝟑𝟐𝟓 𝛍𝐦, the number of fringe crossings is 1000. The wavelength
of the laser used in nanometers is ____.

Q.23 Consider the function 𝒇(𝒙) = −𝒙𝟐 + 𝟏𝟎𝒙 + 𝟏𝟎𝟎. The minimum value of the
function in the interval [𝟓, 𝟏𝟎] is ___.

Q.24 𝟏
Let 𝒇(𝒛) = defined in the complex plane. The integral ∮𝒄 𝒇(𝒛)𝒅𝒛
𝒛𝟐 +𝟔𝒛+𝟗
over the contour of a circle c with center at the origin and unit radius is
____.

Q.25 The determinant of the matrix M shown below is ____.
1 2 0 0
3 4 0 0
M=[ ]
0 0 4 3
0 0 2 1

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Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong
answer: – 2/3).

Q.26 𝒇(𝒛) = (𝒛 − 𝟏)−𝟏 − 𝟏 + (𝒛 − 𝟏) − (𝒛 − 𝟏)𝟐 + ⋯ is the series
expansion of

(A) −1
for |𝑧 − 1| < 1
𝑧(𝑧 − 1)

(B) 1
for |𝑧 − 1| < 1
𝑧(𝑧 − 1)

(C) 1
for |𝑧 − 1| < 1
(𝑧 − 1)2

(D) −1
for |𝑧 − 1| < 1
(𝑧 − 1)

Q.27 A single-phase transformer has maximum efficiency of 98 %. The core losses
are 80 W and the equivalent winding resistance as seen from the primary
side is 0.5 Ω. The rated current on the primary side is 25 A. The percentage
of the rated input current at which the maximum efficiency occurs is

(A) 35.7%

(B) 50.6%

(C) 80.5%

(D) 100%

Q.28 A slip-ring induction motor is expected to be started by adding extra
resistance in the rotor circuit. The benefit that is derived by adding extra
resistance in the rotor circuit in comparison to the rotor being shorted is

(A) The starting torque would be higher.

(B) The power factor at start will be lower.

(C) The starting current is higher.

(D) The losses at starting would be lower.

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Q.29 Consider a unity feedback configuration with a plant and a PID controller
𝟏 (𝒔+𝟑−𝒋)(𝒔+𝟑+𝒋)
as shown in the figure. 𝑮(𝒔) = and 𝑪(𝒔) = 𝑲
(𝒔+𝟏)(𝒔+𝟑) 𝒔
with K being scalar. The closed loop is

C(s) G(s)
+_

(A) only stable for 𝐾 > 0

(B) only stable for 𝐾 between -1 and +1

(C) only stable for 𝐾 < 0

(D) stable for all values of 𝐾

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Q.30 The output Vo of the ideal OpAmp used in the circuit shown below is 5 V.
Then the value of resistor RL in kilo ohm (k) is

(A) 2.5

(B) 5

(C) 25

(D) 50

Q.31 A Boolean function F of three variables X, Y, and Z is given as
F (X, Y, Z) = (Xʹ + Y + Z)˖(X + Yʹ + Zʹ )˖(Xʹ + Y + Zʹ )˖( Xʹ Yʹ Zʹ + Xʹ Y Zʹ + X Y
Zʹ )
Which one of the following is true?

(A) F (X, Y, Z) = (X + Y + Zʹ)˖( Xʹ + Yʹ +Zʹ )

(B) F (X, Y, Z) = (Xʹ + Y)˖(X + Y ʹ+ Zʹ )

(C) F (X, Y, Z) = Xʹ Zʹ + Y Zʹ

(D) F (X, Y, Z) = Xʹ Yʹ Z + X Y Z

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Q.32 A 10½ digit Counter-timer is set in the ‘frequency mode’ of operation (with
Ts = 1 s). For a specific input, the reading obtained is 1000. Without
disconnecting this input, the Counter-timer is changed to operate in the
‘Period mode’ and the range selected is microseconds (µs, with fs = 1 MHz).
The counter will then display

(A) 0

(B) 10

(C) 100

(D) 1000

Q.33 A J-type thermocouple has an output voltage Vθ = (13650 + 50 θx) µV, where
θx is the junction temperature in Celsius (oC). The thermocouple is used with
reference junction compensation, as shown in the figure. The
Instrumentation amplifier used has a gain G = 20. If θRef is 1 oC, for an input
θx of 100 oC, the output Vo of the instrumentation amplifier in millivolt is

+ Instrumentation
θx amplifier
_ +
G = 20 Vo
_ _

θRef +

(A) 98 mV

(B) 99 mV

(C) 100 mV

(D) 101 mV

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Q.34 A laser pulse is sent from ground level to the bottom of a concrete water tank
at normal incidence. The tank is filled with water up to 2 m below the ground
level. The reflected pulse from the bottom of the tank travels back and hits
the detector. The round-trip time elapsed between sending the laser pulse,
the pulse hitting the bottom of the tank, reflecting back and sensed by the
detector is 100 ns. The depth of the tank from ground level marked as 𝒙 in
metre is ____.
(Refractive index of water 𝐧𝐰𝐚𝐭𝐞𝐫 = 𝟏. 𝟑 and velocity of light in air
𝐜𝐚𝐢𝐫 = 𝟑 × 𝟏𝟎𝟖 𝐦/𝐬)

(A) 9

(B) 10

(C) 11

(D) 12

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Q.35 A 4 × 1 multiplexer with two selector lines is used to realize a Boolean
function F having four Boolean variables X, Y, Z and W as shown below. S0
and S1 denote the least significant bit (LSB) and most significant bit (MSB)
of the selector lines of the multiplexer respectively. I0, I1, I2, I3 are the input
lines of the multiplexer.

Z Wˊ I3
ZW I
4 to 1
F
0 I
MUX
Zˊ+ W I
S S

X Y
The canonical sum of product representation of F is

(A) F (X, Y, Z, W) = Σ m( , ,3, 4, 5)

(B) F (X, Y, Z, W) = Σ m( , ,3,11,14)

(C) F (X, Y, Z, W) = Σ m( ,5,9, , 4)

(D) F (X, Y, Z, W) = Σ m(1,3,7,9,15)

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Q.36 Given below is the diagram of a synchronous sequential circuit with one
J-K flip-flop and one T flip-flop with their outputs denoted as A and B
respectively, with JA = (Aʹ + Bʹ), KA = (A + B), and TB = A.

Aʹ+Bʹ
JA A A TB B

A+B Bʹ
KA Aʹ

Clock
Starting from the initial state (AB = 00), the sequence of states (AB) visited
by the circuit is

(A) → → → → …

(B) → 10→ 01 → 1 → …

(C) → 0→ 1 → → …

(D) → → 1→ …

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Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative
marks).

Q.37 Consider that X and Y are independent continuous valued random variables
with uniform PDF given by X ~ U(2, 3) and Y ~ U(1, 4). Then P(Y ≤ X) is
equal to __________ (rounded off to two decimal places).

Q.38 𝟐 𝟓
Given A = ( ) . The value of the determinant │A4 -5A3 +6A2 +2 I│=
𝟎 𝟑
___.

Q.39 The figure below shows an electrically conductive bar of square cross-section
resting on a plane surface. The bar of mass of 1 kg has a depth of 0.5 m along
the y direction. The coefficient of friction between the bar and the surface is
0.1. Assume the acceleration due to gravity to be 10 m/s2. The system faces a
uniform flux density B = −𝟏 𝒛̂ T. At time t = 0, a current of 10 A is switched
onto the bar and is maintained.

z
y

x

When the bar has moved by 1 m, its speed in metre per second is ____
(rounded off to one decimal place).

Q.40 A toroid made of CRGO has an inner diameter of 10 cm and an outer
diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper
wire is wound on the core. µo = 4π×10-7 H/m and µR of CRGO is 3000. When
a current of 5 mA flows through the winding, the flux density in the core in
millitesla is ____.

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Q.41 An air cored coil having a winding resistance of 10 Ω is connected in series
with a variable capacitor Cx. The series circuit is excited by a 10 V sinusoidal
voltage source of angular frequency 1000 rad/s. As the value of the capacitor
is varied, a maximum voltage of 30 V was observed across it. Neglecting skin-
effect, the value of the inductance of the coil in millihenry is _____.

Q.42 A household fan consumes 60 W and draws a current of 0.3125 A (rms) when
connected to a 230 V (rms) ac, 50 Hz single phase mains. The reactive power
drawn by the fan in VAr is ____________ (rounded off to the nearest
integer).

Q.43 Given 𝒚(𝒕) = 𝒆−𝟑𝒕 𝒖(𝒕) ∗ 𝒖(𝒕 + 𝟑), where * denotes convolution operation.
The value of 𝒚(𝒕) 𝐚𝐬 𝒕 → ∞ is ____________ (rounded off to two decimal
places).

Q.44 The input signal shown below

3 3 3 3

is passed through the filter with the following taps

The number of non-zero output samples is ____.

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Q.45 A sinusoid (√𝟐 𝐬𝐢𝐧 𝒕) 𝝁(𝒕), where 𝝁(𝒕) is the step input, is applied to a system
𝟏
with transfer-function 𝑮(𝒔) = . The amplitude of the steady state
𝒔+𝟏
output is ____.

Q.46 𝟐
Consider a system with transfer-function 𝑮(𝒔) = . A unit step function
𝒔+𝟏
𝝁(𝒕) is applied to the system, which results in an output y(𝒕).
If 𝒆(𝒕) = 𝒚(𝒕) − 𝝁(𝒕), then 𝐥𝐢𝐦 𝒆(𝒕) is ____.
𝒕→∞

Q.47 The circuit shown below uses an ideal OpAmp. Output VO in volt is ________
(rounded off to one decimal place).

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Q.48 All the transistors used in the circuit are matched and have a current gain
 of 20. Neglecting the Early effect, the current IO4 in milliampere is _____.

Q.49 The power in a 400 V (rms, line-line) three-phase, three-wire RYB sequence
system is measured using the two wattmeters, as shown. The R-line current
is 5∠60⁰ A. Wattmeter W1 in the R-line will read (in watt) _________.
400 V (rms, line-line), 3-phase,

R

W1 Z
RYB sequence

W2 Z Z

Y

B

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Q.50 A 3½ digit, rectifier type digital meter is set to read in its 2000 V range. A
symmetrical square wave of frequency 50 Hz and amplitude ±100 V is
measured using the meter. The meter will read _____.

Q.51 A bar primary current transformer of rating 1000/1 A, 5VA, UPF has 995
secondary turns. It exhibits zero ratio error and phase error of 30 minutes
at 1000 A with rated burden. The watt loss component of the primary
excitation current in ampere is __________ (rounded off to one decimal
place).

Q.52 In the bridge circuit shown, the voltmeter V showed zero when the value of
the resistors are: R1 = 100 , R2 = 110 , and R3 = 90 . If (R1/R2) = (RA/RB),
the value of R4 in ohm is _____.

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Q.53 For the full bridge made of linear strain gages with gage factor 2 as shown
in the diagram, R1 = R2 = R3 = R4 = 100 Ω at 0 oC and strain is 0. The
temperature coefficient of resistance of the strain gages used is 0.005 per oC.
All strain gages are made of same material and exposed to same
temperature. While measuring a strain of 0.01 at a temperature of 50 oC, the
output VO in millivolt is _____ (rounded off to two decimal places).

Q.54 A signal having a bandwidth of 5 MHz is transmitted using the Pulse code
modulation (PCM) scheme as follows. The signal is sampled at a rate of 50%
above the Nyquist rate and quantized into 256 levels. The binary pulse rate
of the PCM signal in Mbits per second is ___.

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Q.55 In the figure shown, a large multimode fiber with 𝒏𝒄𝒐𝒓𝒆 = 𝟏. 𝟓 𝐚𝐧𝐝 𝒏𝒄𝒍𝒂𝒅 =
𝟏. 𝟐 is used for sensing. A portion with the cladding removed passes through
a liquid with refractive index 𝒏𝒍𝒊𝒒𝒖𝒊𝒅 . An LED is used to illuminate the fiber
from one end and a paper is placed on the other end, 1 cm from the end of
the fiber. The paper shows a spot with radius 1 cm. The refractive index
𝒏𝒍𝒊𝒒𝒖𝒊𝒅 of the liquid (rounded off to two decimal places) is ____________.

END OF THE QUESTION PAPER

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