GATE IN 2023: Instrumentation Engineering
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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each
Q.1 The village was nestled in a green spot, _______ the ocean and the hills.
(A) through
(B) in
(C) at
(D) between
Q.2 Disagree : Protest : : Agree : _______
(By word meaning)
(A) Refuse
(B) Pretext
(C) Recommend
(D) Refute
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Q.3 A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two
adjacent digits being the same. For example, 137 is a frabjous number, while 133 is
not. How many such frabjous numbers exist?
(A) 125
(B) 720
(C) 60
(D) 80
Q.4 Which one among the following statements must be TRUE about the mean and the
median of the scores of all candidates appearing for GATE 2023?
(A) The median is at least as large as the mean.
(B) The mean is at least as large as the median.
(C) At most half the candidates have a score that is larger than the median.
(D) At most half the candidates have a score that is larger than the mean.
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Q.5 In the given diagram, ovals are marked at different heights (h) of a hill. Which one
of the following options P, Q, R, and S depicts the top view of the hill?
(A) P
(B) Q
(C) R
(D) S
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Q.6 – Q.10 Carry TWO marks Each
Q.6 Residency is a famous housing complex with many well-established individuals
among its residents. A recent survey conducted among the residents of the complex
revealed that all of those residents who are well established in their respective fields
happen to be academicians. The survey also revealed that most of these
academicians are authors of some best-selling books.
Based only on the information provided above, which one of the following
statements can be logically inferred with certainty?
(A) Some residents of the complex who are well established in their fields are also
authors of some best-selling books.
(B) All academicians residing in the complex are well established in their fields.
(C) Some authors of best-selling books are residents of the complex who are well
established in their fields.
(D) Some academicians residing in the complex are well established in their fields.
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Q.7 Ankita has to climb 5 stairs starting at the ground, while respecting the following
rules:
1. At any stage, Ankita can move either one or two stairs up.
2. At any stage, Ankita cannot move to a lower step.
Let F(N) denote the number of possible ways in which Ankita can reach the N tℎ
stair. For example, F(1) = 1, F(2) = 2, F(3) = 3.
The value of F(5) is _______.
(A) 8
(B) 7
(C) 6
(D) 5
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Q.8 The information contained in DNA is used to synthesize proteins that are necessary
for the functioning of life. DNA is composed of four nucleotides: Adenine (A),
Thymine (T), Cytosine (C), and Guanine (G). The information contained in DNA
can then be thought of as a sequence of these four nucleotides: A, T, C, and G. DNA
has coding and non-coding regions. Coding regions—where the sequence of these
nucleotides are read in groups of three to produce individual amino
acids—constitute only about 2% of human DNA. For example, the triplet of
nucleotides CCG codes for the amino acid glycine, while the triplet GGA codes for
the amino acid proline. Multiple amino acids are then assembled to form a protein.
Based only on the information provided above, which of the following statements
can be logically inferred with certainty?
(i) The majority of human DNA has no role in the synthesis of proteins.
(ii) The function of about 98% of human DNA is not understood.
(A) only (i)
(B) only (ii)
(C) both (i) and (ii)
(D) neither (i) nor (ii)
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Q.9 Which one of the given figures P, Q, R and S represents the graph of the following
function?
f(x) = | |x + 2| − |x − 1| |
(A) P
(B) Q
(C) R
(D) S
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Q.10 An opaque cylinder (shown below) is suspended in the path of a parallel beam of
light, such that its shadow is cast on a screen oriented perpendicular to the direction
of the light beam. The cylinder can be reoriented in any direction within the light
beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT
possible?
(A) P
(B) Q
(C) R
(D) S
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Q.11 – Q.35 Carry ONE mark Each
Q.11 Choose solution set S corresponding to the systems of two equations
x − 2y + z = 0
x−z=0
Note: denotes the set of real numbers
1 ∣
(A)
S = { α (1) ∣∣ α ∈ }
1 ∣
1 1 ∣
(B)
S = { α (1) + β (0) ∣∣ α, β ∈ }
1 1 ∣
1 2 ∣
(C)
S = { α (1) + β (1) ∣∣ α, β ∈ }
1 2 ∣
1 ∣
(D)
S = { α (0) ∣∣ α ∈ }
1 ∣
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Q.12 Inductance of a coil is measured as 10 mH, using an LCR meter, when no other
objects are present near the coil. The LCR meter uses a sinusoidal excitation at
10 kHz. If a pure copper sheet is brought near the coil, the same LCR meter will
read____________.
(A) less than 10 mH
(B) 10 mH
(C) more than 10 mH
(D) less than 10 mH initially and then stabilizes to more than 10 mH
Q.13 Which of the following flow meters offers the lowest resistance to the flow?
(A) Turbine flow meter
(B) Orifice flow meter*
(C) Venturi meter
(D) Electromagnetic flow meter
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Q.14 Pair the quantities (p) to (s) with the measuring devices (i) to (iv).
(i) Linear Variable Differential (p) Torque
Transformer (LVDT)
(ii) Thermistor (q) Pressure
(iii) Strain gauge (r) Linear position
(iv) Diaphragm (s) Temperature
(A) (i) - (r), (ii) - (s), (iii) - (q), (iv) - (p)
(B) (i) - (p), (ii) - (s), (iii) - (r), (iv) - (q)
(C) (i) - (r), (ii) - (s), (iii) - (p), (iv) - (q)
(D) (i) - (q), (ii) - (s), (iii) - (p), (iv) - (r)
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Q.15 ε ε A
Capacitance ‘C’ of a parallel plate structure is calculated as 20 pF using C = od r ,
where εo is the permittivity of free space, εr is the relative permittivity of the
dielectric, A is the overlapping area of the electrodes and d is the distance between
them. The value of C is then measured using an LCR meter. If the meter is assumed
to be ideal and it introduces no error due to cable capacitance, which one of the
following readings is likely to be correct?
(A) 20.5 pF
(B) 20 pF
(C) 19.5 pF
(D) 10 pF
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Q.16 The table shows the present state Q(t), next state Q(t+1), and the control input in a
flip-flop. Identify the flip-flop.
Q (t) Q (t+1) Input
0 0 0
0 1 1
1 0 1
1 1 0
(A) T flip-flop
(B) D flip-flop
(C) SR flip-flop
(D) JK flip-flop
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Q.17 Match the Exclusive-OR (XOR) operations (i) to (iv) with the results (p) to (s),
where X is a Boolean input.
(i) X X (p) 1
(ii) X X̅ (q) 0
(iii) X 0 (r) X̅
(iv) X 1 (s) X
(A) (i) - (q), (ii) - (r), (iii) - (s), (iv) - (p)
(B) (i) - (q), (ii) - (r), (iii) - (p), (iv) - (s)
(C) (i) - (p), (ii) - (s), (iii) - (q), (iv) - (r)
(D) (i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)
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Q.18 A light emitting diode (LED) emits light when it is _____biased. A photodiode
provides maximum sensitivity to light when it is_____ biased.
(A) forward, forward
(B) forward, reverse
(C) reverse, reverse
(D) reverse, forward
Q.19 1
F(z) = 1−z, when expanded as a power series around z = 2, would result in
F(z) = ∑∞ k
k=0 ak (z − 2) , with the region of convergence (ROC) |z − 2| < 1.
The coefficients ak , k ≥ 0, are given by the expression__________.
(A) (−1)k
(B) (−1)k+1
1 k
(C) ( )
2
−1 k+1
(D) ( )
2
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Q.20 The solution x(t), t ≥ 0, to the differential equation
ẍ = −kẋ , k > 0 with initial conditions x(0) = 1 and ẋ (0) = 0 is
(A) x(t) = 2e −kt + 2kt − 1
(B) x(t) = 2e −kt − 1
(C) x(t) = 1
(D) x(t) = 2e −kt − kt − 1
Q.21 A system has the transfer-function
Y(s) s−π
= s+π
X(s)
Let u(t) be the unit-step function. The input x(t) that results in a steady-state output
y(t) = sin πt is ______.
(A) x(t) = sin(πt) u(t)
π
(B) x(t) = sin (πt + ) u(t)
2
π
(C) x(t) = sin (πt − ) u(t)
2
π
(D) x(t) = cos (πt + ) u(t)
4
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Q.22 Choose the fastest logic family among the following:
(A) Transistor-Transistor Logic
(B) Emitter-Coupled Logic
(C) CMOS Logic
(D) Resistor-Transistor Logic
Q.23 1
What is lim f(x), where f(x) = x sin x ?
x→0
(A) 0
(B) 1
(C) ∞
(D) Limit does not exist
Q.24 The number of zeros of the polynomial P(s) = s 3 + 2s 2 + 5s + 80 in the right-
half plane is ______.
Q.25 1 (s−1)(s−2)
The number of times the Nyquist plot of G(s)H(s) = 2 (s+1)(s+2) encircles the
origin is ____.
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Q.26 The opamp in the circuit shown is ideal, except that it has an input bias current of
1 nA and an input offset voltage of 10 µV. The resulting worst-case output voltage
will be ±_____ µV (rounded off to the nearest integer).
Q.27 The force per unit length between two infinitely long parallel conductors, with a
gap of 2 cm between them is 10 µN/m. When the gap is doubled, the force per unit
length will be __________ µN/m (rounded off to one decimal place).
Q.28 Consider the discrete-time signal x[n] = u[−n + 5] − u[n + 3],
1; n ≥ 0
where u[n] = { .
0; n < 0
The smallest n for which x[n] = 0 is _______.
Q.29 Let y(t) = x(4t), where x(t) is a continuous-time periodic signal with
fundamental period of 100 s. The fundamental period of y(t) is ______ s (rounded
off to the nearest integer).
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Q.30 When the bridge given below is balanced, the current through the resistor Ra is
_____mA (rounded off to two decimal places).
Q.31 In the circuit given, the Thevenin equivalent resistance Rth across the terminals ‘a’
and ‘b’ is ___________Ω (rounded off to one decimal place).
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Q.32 X is a discrete random variable which takes values 0, 1 and 2. The probabilities are
P(X = 0) = 0.25 and P(X = 1) = 0.5. With E[ . ] denoting the expectation
operator, the value of E[X] − E[X 2 ] is _______(rounded off to one decimal
place).
Q.33 The diode in the circuit is ideal. The current source is (t) = π sin (3000π t) mA.
The magnitude of the average current flowing through the resistor R is ______mA
(rounded off to two decimal places).
Q.34 The full-scale range of the wattmeter shown in the circuit is 100 W. The turns ratio
of the individual transformers are indicated in the figure. The RMS value of the ac
source voltage Vs is 200 V. The wattmeter reading will be __________W (rounded
off to the nearest integer).
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Q.35 The no-load steady-state output voltage of a DC shunt generator is 200 V when it
is driven in the clockwise direction at its rated speed. If the same machine is driven
at the rated speed but in the opposite direction, the steady-state output voltage will
be ________V (rounded off to the nearest integer).
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Q.36 – Q.65 Carry TWO marks Each
Q.36 The impulse response of an LTI system is ℎ(t) = δ(t) + 0.5 δ(t − 4) , where δ(t)
7π
is the continuous-time unit impulse signal. If the input signal x(t) = cos ( 4 t), the
output is ______.
(A) 7π
0.5 cos ( t)
4
(B) 7π
1.5 cos ( t)
4
(C) 7π
0.5 sin ( t)
4
(D) 7π
1.5 sin ( t)
4
Q.37 The Laplace transform of the continuous-time signal x(t) = e −3t u(t − 5) is
______, where u(t) denotes the continuous-time unit step signal.
(A) e −5s
, Real{s} > −3
s+3
(B) e −5(s−3)
, Real{s} > 3
s−3
(C) e −5(s+3)
, Real{s} > −3
s+3
(D) e −5(s−3)
, Real{s} > −3
s+3
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Q.38 In a p-i-n photodiode, a pulse of light containing 8 × 1012 incident photons at
wavelength λ0 = 1.55 µm gives rise to an average 4 × 1012 electrons collected at the
terminals of the device. The quantum efficiency of the photodiode at this wavelength
is _______%.
(A) 50
(B) 54.2
(C) 62.5
(D) 80
Q.39 1−z
Let f(z) = j 1+z , where z denotes a complex number and j denotes √−1. The
inverse function f −1 (z) maps the real axis to the_________.
(A) unit circle with centre at the origin
(B) unit circle with centre not at the origin
(C) imaginary axis
(D) real axis
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Q.40 The simplified form of the Boolean function F (W, X, Y, Z) = Σ (4, 5, 10, 11, 12, 13,
14, 15) with the minimum number of terms and smallest number of literals in each
term is_________.
(A) ̅ XY̅ + WX̅Y
WX + W
(B) WX + WY + XY̅
(C) XY̅ + WY
(D) X̅Y + W
̅ Y̅
Q.41 For the given digital circuit, A = B = 1. Assume that AND, OR, and NOT gates have
propagation delays of 10 ns, 10 ns, and 5 ns respectively. All lines have zero
propagation delay. Given that C = 1 when the circuit is turned on, the frequency of
steady-state oscillation of the output Y is ______.
(A) 20 MHz
(B) 15 MHz
(C) 40 MHz
(D) 50 MHz
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Q.42 In the circuit shown, the initial binary content of shift register A is 1101 and that of
shift register B is 1010. The shift registers are positive-edge triggered, and the gates
have no delay.
When the shift control is high, what will be the binary content of the shift registers
A and B after four clock pulses?
(A) A = 1101, B = 1101
(B) A = 1110, B = 1001
(C) A = 0101, B = 1101
(D) A = 1010, B = 1111
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Q.43 The magnitude and phase plots shown in the figure match with the transfer-
function_______.
(A) 10000
s 2 + 2s + 10000
10000
(B) e −0.05s
s 2 + 2s + 10000
10000 −12
(C) 2
e −0.5×10 s
s + 2s + 10000
100
(D) s 2 + 2s + 100
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Q.44 A continuous real-valued signal x(t) has finite positive energy and
x(t) = 0, ∀ t < 0. From the list given below, select ALL the signals whose
continuous-time Fourier transform is purely imaginary.
(A) x(t) + x(−t)
(B) x(t) − x(−t)
(C) j(x(t) + x(−t))
(D) j(x(t) − x(−t))
Q.45 A silica-glass fiber has a core refractive index of 1.47 and a cladding refractive index
of 1.44. If the cladding is completely stripped out and the core is dipped in water
having a refractive index of 1.33, the numerical aperture of the modified fiber
is_______ (rounded off to three decimal places).
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Q.46 In the circuit shown, = 100π rad/s, R1 = R2 = 2.2 Ω and L = 7 mH. The capacitance
C for which Yin is purely real is _______________mF (rounded off to two decimal
places).
Q.47 The R-L circuit with R = 10 kΩ and L = 1 mH is excited by a step current I0u(t). At
t = 0− , there is a current IL = I0/5 flowing through the inductor. The minimum time
taken for the current through the inductor to reach 99% of its final value is _____µs
(rounded off to two decimal places).
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Q.48 1
Consider a standard negative feedback configuration with G(s) = (s−2)(s−3) and
K
the controller C(s) = KP + sI + KD s . The root-locus of G(s)C(s) is presented in
the figure below. The gain C(jω) = 2 at ω = 1 rad/s. The value of KD is _______
(rounded off to one decimal place).
Q.49 How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with
exactly one digit appearing twice?
Q.50 2 (1 − s)
The phase margin of the transfer function G(s) = (1 + s)2 is __________degrees.
(rounded off to the nearest integer).
Q.51 A wire-wound ‘resistive potentiometer type' angle sensor with 72 turns is used in an
application. The first turn of the potentiometer is connected to ground while its last
turn is connected to 3.6 V. The width of the wiper covers two turns ensuring make-
before-break. The output (wiper) voltage when the wiper is on top of both the turns
35 and 36 is _______V (rounded off to two decimal places).
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Q.52 The two secondaries of a linear variable differential transformer (LVDT) showed a
magnitude of 2 V (RMS) for zero displacement position of the core. It is noted that
the phase of one of the secondaries has a deviation of one degree from the expected
phase. Other than this deviation, the LVDT is ideal.
If the differential output sensitivity of the LVDT is 1 mV (RMS)/1 µm, the output
for zero displacement is __________ µm (rounded off to one decimal place).
Q.53 Five measurements are made using a weighing machine, and the readings are 80 kg,
79 kg, 81 kg, 79 kg and 81 kg. The sample standard deviation of the measurement
is ______________ kg (rounded off to two decimal places).
Q.54 Four strain gauges RA, RB, RC and RD, each with nominal resistance R, are connected
in a bridge configuration. When a force is applied, RA and RD increase by ∆R and
RB and RC decrease by ∆R as shown. A potentiometer with total resistance Rv is
connected as shown. If R = 100 Ω, and ∆R = 1 Ω, the minimum value of resistance
Rv required to balance the bridge is ______Ω (rounded off to two decimal places).
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Q.55 A sinusoidal current of i1 (t) = 1 sin(200πt) mA is flowing through a 4 H inductor
which is mutually coupled to another 5 H inductor carrying
i2 (t) = 2 sin(200πt) mA
as shown in the figure. The coupling coefficient between the inductors is 0.6. The
peak energy stored in the circuit is _______µJ (rounded off to two decimal places).
Q.56 The figure below shows a feedback amplifier constructed using an nMOS transistor.
Assume that µnCox = 1 mA/V2, threshold voltage VT = 1V and W/L = 2. The bias
voltage at the drain terminal is 4 V. The capacitors C∞ offer zero impedance at the
signal frequency. The ratio Vout/Vin is _____________(rounded off to two decimal
places).
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Q.57 Consider the real-valued function g(x) = max{(x − 2)2 , −2x + 7},
where x ∈ (−∞, ∞). The minimum value attained by g(x) is _______ (rounded
off to one decimal place).
Q.58 A short-circuit test is conducted on a single-phase transformer by shorting its
secondary. The frequency of input voltage is 1 kHz. The corresponding wattmeter
reading, primary current and primary voltage are 8 W, 2 A and 6 V respectively.
Assume that the no-load losses and the no-load currents are negligible, and the core
has linear magnetic characteristics. Keeping the secondary shorted, the primary is
1
connected to a 2 V (RMS), 1 kHz sinusoidal source in series with a 2π√5 mF
capacitor. The primary current (RMS) will be _____ A (rounded off to two decimal
places).
Q.59 The opamps in the circuit are ideal. The input signals are
VS1 = 3 + 0.10 sin(300t) V and VS2 = −2 + 0.11 sin(300t) V.
The average value of the voltage V0 is ______V (rounded off to two decimal
places).
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Q.60 In the circuit shown, the input voltage Vin = 100 mV. The switch and the opamp are
ideal. At time t = 0, the initial charge stored in the 10 nF capacitor is 1 nC, with the
polarity as indicated in the figure. The switch S is controlled using a 1 kHz square-
wave voltage signal Vs as shown. Whenever Vs is ‘High’, S is in position ‘1’ and
when Vs is ‘Low’, S is in position ‘2’.
At t = 20 ms, the magnitude of the voltage Vo will be _______ mV (rounded off
to the nearest integer).
Q.61 In the diagram shown, the frequency of the sinusoidal source voltage VS is 50 Hz.
230 230
The load voltage is 230 V (RMS), and the load impedance is +j Ω. The
√2 √2
1 Vx Vy
value of attenuator A1 = . The multiplier output voltage Vo = , where Vx
50√2 1V
and Vy are the inputs. The magnitude of the average value of the multiplier output
Vo is ____________V (rounded off to one decimal place).
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Q.62 In the circuit shown, assuming an ideal opamp, the value of the output voltage
Vo = ____ V (rounded off to one decimal place).
α
Q.63 The rank of the matrix A given below is one. The ratio β is _______ (rounded off
to the nearest integer).
1 4
A = [−3 α ]
β 6
Q.64 A 1.999 V True RMS 3-1/2 digit multimeter has an accuracy of
±0.1 % of reading ±2 digits.
It is used to measure 100 A (RMS) current flowing through a line using a 100:5
ratio, Class-1 current transformer with a burden of 0.1 Ω ±0.5 %.
The worst-case absolute error in the multimeter output is _________ V (rounded
off to three decimal places).
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Q.65 The voltage source Vs = 10√2 sin(20000πt) V has an internal resistance of
50 Ω. The RMS value of the current through R is_______mA (rounded off to one
decimal place).
*This option did not appear in GATE 2023 Examination. It appeared as “Turbine flow meter”,
that is, “Turbine flow meter” option was repeated.
END OF QUESTION PAPER
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GATE 2023 Instrumentation Engineering (IN)
Question Type (QT)
Q. No. Session Subject Name (SN) Key/Range (KY) Mark (MK)
MCQ/MSQ/NAT
1 5 MCQ GA D 1
2 5 MCQ GA C 1
3 5 MCQ GA D 1
4 5 MCQ GA C 1
5 5 MCQ GA B 1
6 5 MCQ GA MTA 2
7 5 MCQ GA A 2
8 5 MCQ GA D 2
9 5 MCQ GA A 2
10 5 MCQ GA D 2
11 5 MCQ IN A 1
12 5 MCQ IN A 1
13 5 MCQ IN D 1
14 5 MCQ IN C 1
15 5 MCQ IN A 1
16 5 MCQ IN A 1
17 5 MCQ IN D 1
18 5 MCQ IN B 1
19 5 MCQ IN B 1
20 5 MCQ IN C 1
21 5 MCQ IN C 1
22 5 MCQ IN B 1
23 5 MCQ IN A 1
24 5 NAT IN 2 to 2 1
25 5 NAT IN 2 to 2 1
26 5 NAT IN 1110 to 1110 1
27 5 NAT IN 4.9 to 5.1 1
28 5 NAT IN -3 to -3 1
29 5 NAT IN 25 to 25 1
30 5 NAT IN 0.99 to 1.01 1
31 5 NAT IN 1.0 to 1.0 1
32 5 NAT IN -0.5 to -0.5 1
33 5 NAT IN 0.95 to 1.05 1
34 5 NAT IN 0 to 0 1
35 5 NAT IN 0 to 0 1
36 5 MCQ IN A 2
37 5 MCQ IN C 2
38 5 MCQ IN A 2
39 5 MCQ IN A 2
40 5 MCQ IN C 2
41 5 MCQ IN A 2
42 5 MCQ IN C 2
43 5 MCQ IN B 2
44 5 MSQ IN B,C 2
45 5 NAT IN 0.620 to 0.640 2
Text of page 2
46 5 NAT IN 1.40 to 1.50 2
47 5 NAT IN 0.43 to 0.45 2
48 5 NAT IN 0.9 to 1.1 2
49 5 NAT IN 240 to 240 2
50 5 NAT IN -2 to 2 2
51 5 NAT IN 1.77 to 1.78 2
52 5 NAT IN 34.5 to 35.5 2
53 5 NAT IN 0.98 to 1.02 2
54 5 NAT IN 4.00 to 4.10 2
55 5 NAT IN 17.00 to 18.00 2
56 5 NAT IN 0.64 to 0.70 2
57 5 NAT IN 0.9 to 1.1 2
58 5 NAT IN 0.95 to 1.05 2
59 5 NAT IN 0.49 to 0.51 2
60 5 NAT IN 99 to 101 2
61 5 NAT IN 2.1 to 2.5 2
62 5 NAT IN 1.9 to 2.1 2
63 5 NAT IN -8 to -8 2
64 5 NAT IN 0.009 to 0.011 2
65 5 NAT IN 99.0 to 101.0 2
MTA = Marks to AllPage 1 of 35
Source: GATE. Question paper published by GATE.