GATE IN 2024: Instrumentation Engineering
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Instrumentation Engineering (IN)
General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each
Q.1 If ‘→’ denotes increasing order of intensity, then the meaning of the words
[drizzle → rain → downpour] is analogous to [ ______ → quarrel → feud].
Which one of the given options is appropriate to fill the blank?
(A) bicker
(B) bog
(C) dither
(D) dodge
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Q.2 Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.
Which of the above inferences can be logically deduced from statements 1 and 2?
(A) Only I and II
(B) Only II and III
(C) Only I and III
(D) Only III
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Q.3 A student was supposed to multiply a positive real number p with another positive
real number q. Instead, the student divided p by q. If the percentage error in the
student’s answer is 80%, the value of q is
(A) 5
(B) √2
(C) 2
(D) √5
Q.4 If the sum of the first 20 consecutive positive odd numbers is divided by 202 , the
result is
(A) 1
(B) 20
(C) 2
(D) 1/2
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Q.5 The ratio of the number of girls to boys in class VIII is the same as the ratio of the
number of boys to girls in class IX. The total number of students (boys and girls) in
classes VIII and IX is 450 and 360, respectively. If the number of girls in classes
VIII and IX is the same, then the number of girls in each class is
(A) 150
(B) 200
(C) 250
(D) 175
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Q.6 – Q.10 Carry TWO marks Each
Q.6 In the given text, the blanks are numbered (i)−(iv). Select the best match for
all the blanks.
Yoko Roi stands (i) as an author for standing (ii) as an honorary
fellow, after she stood (iii) her writings that stand (iv) the freedom of
speech.
(A) (i) out (ii) down (iii) in (iv) for
(B) (i) down (ii) out (iii) by (iv) in
(C) (i) down (ii) out (iii) for (iv) in
(D) (i) out (ii) down (iii) by (iv) for
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Q.7 Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container.
The figure below shows the arrangement of the chalk-sticks inside the cylinder.
The length of the container is equal to the length of the chalk-sticks. The ratio of
the occupied space to the empty space of the container is
(A) 5/2
(B) 7/2
(C) 9/2
(D) 3
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Q.8 The plot below shows the relationship between the mortality risk of cardiovascula r
disease and the number of steps a person walks per day. Based on the data, which
one of the following options is true?
1
Mortality Risk of Cardiovascular Disease
0.8
0.6
0.4
0.2
0
0 5000 10000 15000 20000
Steps/Day
(A) The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk
reduction on increasing the steps/day from 10000 to 20000.
(B) The risk reduction on increasing the steps/day from 0 to 5000 is less than the risk
reduction on increasing the steps/day from 15000 to 20000.
(C) For any 5000 increment in steps/day the largest risk reduction occurs on going from
0 to 5000.
(D) For any 5000 increment in steps/day the largest risk reduction occurs on going from
15000 to 20000.
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Q.9 Five cubes of identical size and another smaller cube are assembled as shown in
Figure A. If viewed from direction X, the planar image of the assembly appears as
Figure B.
Figure A Figure B
If viewed from direction Y, the planar image of the assembly (Figure A) will
appear as
(A)
(B)
(C)
(D)
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Q.10 Visualize a cube that is held with one of the four body diagonals aligned to the
vertical axis. Rotate the cube about this axis such that its view remains unchanged.
The magnitude of the minimum angle of rotation is
(A) 120°
(B) 60°
(C) 90°
(D) 180°
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Q.11 – Q.35 Carry ONE mark Each
Q.11 Let z = x + iy be a complex variable and z̅ be its complex conjugate. The equation
z̅2 + z2 = 2 represents a
(A) parabola
(B) hyperbola
(C) ellipse
(D) circle
Q.12 The pressure drop across a control valve is constant. The control valve with inherent
characteristic has decreasing sensitivity. If x represents the fraction of maximum
stem position of the control valve, then the function f(x) representing the fraction
of maximum flow is
(A) αx −1 , where α is constant
(B) √x
(C) x
(D) x2
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Q.13 A discrete-time sequence is given by x [n] = [1, 2, 3, 4] for 0 ≤ n ≤ 3. The zero
lag auto-correlation value of x [n] is
(A) 1
(B) 10
(C) 20
(D) 30
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Q.14 Match the following measuring devices with their principle of measurement.
Measuring Device Principle of Measurement
(P) Optical pyrometer (I) Variation in mutual inductance
(Q) Thermocouple (II) Change in resistance
(R) Strain gauge (III) Wavelength of radiated energy
(S) Linear variable (IV) Electromotive force generated by two
differential transformer dissimilar metals
(A) (P) − (III), (Q) − (IV), (R) − (II), (S) − (I)
(B) (P) − (IV), (Q) − (III), (R) − (II), (S) − (I)
(C) (P) − (III), (Q) − (I), (R) − (IV), (S) − (II)
(D) (P) − (II), (Q) − (IV), (R) − (I), (S) − (III)
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Q.15 The capacitor shown in the figure has parallel plates, with each plate having an
area A. The thickness of the dielectric materials are d1 and d2 and their relative
permittivities are ε1 and ε2 , respectively. Assume that the fringing field effects are
negligible and ε0 is the permittivity of free space.
If d1 is decreased by δd1 , the resultant capacitance becomes
(A) ε0 A
d
d1 − δd1 + ε 2
2
(B) ε0 A
d
d2 + ε 1
2
(C) ε0 A
d1
d2 − δd2 +
ε2
(D) ε0 A
d
d1 +δd1 + ε 2
2
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Q.16 Among the given options, the simplified form of the Boolean functio n
F = (A + A̅. B ) + A̅ . (A + B̅ ). C is
(A) A+B +C
(B) A. B. C
(C) B + A̅. C
(D) A̅ + B. C
Q.17 Consider the state-space representation of a system
ẋ = Ax + Bu
where x is the state vector, u is the input, A is the system matrix and B is the input
matrix. Choose the matrix A from the following options such that the system has a
pole at the origin.
(A) 0 1
[ ]
−2 −3
(B) 1 −1.5
[ ]
−2 3
(C) 1 1.5
[ ]
2 −3
(D) 0 1
[ ]
−2 3
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Q.18 The sinusoidal transfer function corresponding to the polar plot shown in the figur e,
for T > 0, is
(A) 1 − jωT
(B) 1 − jωT
1 + jωT
(C) 1 + jωT
(D) 1
1 + jωT
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Q.19 A matrix M is constructed by stacking three column vectors v1 , v2 , v3 as
M = [v1 v2 v3 ].
Choose the set of vectors from the following options such that rank(M) = 3.
(A) 1 0 1
v1 = [0] , v2 = [−1 ] , v3 = [ −1]
1 0 1
(B) 1 −1 0
v1 = [1] , v2 = [ 0] , v3 = [ 0]
1 1 0
(C) 1 −1 1
v1 = [0] , v2 = [ 0] , v3 = [ −1]
1 1 1
(D) 1 −1 0
v1 = [1] , v2 = [ 1] , v3 = [ −1]
1 −1 0
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Q.20 The capacitance formed between two concentric spherical metal shells having radii
x and y with y > x is
Note: ε is the permittivity of the medium between the shells.
(A) xy
4πε ( )
y −x
(B) x2
4πε ( )
y −x
(C) y2
4πε ( )
y −x
(D) y 2 − xy
4πε ( )
x
Q.21 A linear transducer is calibrated for the ranges shown in the figure. The gain of the
transducer is _______ mA/℃ (rounded off to two decimal places).
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Q.22 Consider a filter defined by the difference equation
y[n] − 0.5 y[n − 2] = a x[n − 4]
where x[n] and y[n] represent the input and output, respectively. If the magnitude
π π
response of the filter at ω = 2 is |H (2 )| = 0.5, the value of a is __________
(rounded off to two decimal places).
Q.23 Consider the circuit shown in the figure.
The CMOS digital logic circuit has infinite input impedance. Assume the opamp
is ideal. A 1.8 V Zener diode with a minimum Zener current of 2 mA is used. The
corresponding maximum value of resistance RZ is ________ kΩ.
(rounded off to one decimal place).
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Q.24 Figure shows an amplifier using an NMOS transistor. Assume that the transistor is
in saturation with device parameters, µn Cox = 250 µA/V2 , threshold voltage
VT = 0.65 V and W/L = 4. Ignore the channel length modulation effect. The drain
current of the transistor at the operating point is _________ µA (rounded off to
nearest integer).
Q.25 The number of complex multiplications required for computing a 16-point DFT
using the decimation- in-time radix-2 FFT is __________ (in integer).
Q.26 1
A 3 × 3 matrix P with all real elements has eigenvalues , 1, and −2. The value
4
−1
of |P | is _________ (rounded off to nearest integer).
Q.27 The Nyquist sampling frequency for x (t) = 10 sin2 (200πt) is __________ Hz
(rounded off to nearest integer).
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Q.28 The resistance of a 20 kΩ resistor is measured six consecutive times using an LCR
meter. The first five readings are 19 kΩ, 18 kΩ, 23 kΩ, 21 kΩ and 17 kΩ.
If the mean of the measurements and the true value are equal, the last reading
is ________ kΩ (rounded off to nearest integer).
Q.29 Consider the readout circuit of a piezoelectric sensor shown in the figure.
When the piezoelectric sensor generates a charge qp, the resulting change in voltage
Vx is −2 V. Then the corresponding change in the voltage Vout is _____V (rounde d
off to nearest integer).
Note: Assume all components are ideal.
Q.30 The voltage applied and the current drawn by a circuit are
v(t) = 95 + 200 cos(120πt) + 90 cos(360πt − 60°) V
i (t) = 4 cos(120πt − 60°) + 1.5 cos(240πt − 75°) A
The average power absorbed by the circuit is __________W (rounded off to
nearest integer).
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Q.31 The current i(t) drawn by a circuit is given as
i (t) = 4 + 30 cos(t) − 20 sin(t) + 15 cos(3t) − 10 sin(3t) A
The root-mean-square value of i(t) is ________ A (rounded off to one decimal
place).
Q.32 A linear potentiometer (0 − 10 kΩ) is used to measure the water level as shown in
the figure. The resistance between A and C varies linearly from 0 to 10 kΩ for a
change in water level from 0 to 20 cm. The sensor is excited using a DC voltage
source, VS = 10 V with an internal resistance, RS = 200 Ω. If Vout = 5 V, the water
level is ______ cm (rounded off to one decimal place).
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Q.33 The switch in the following figure has been closed for a long time (t < 0). It is
opened at t = 0 seconds. The value of dv c/dt at t = 0+ is __________ V/s
(rounded off to nearest integer).
Q.34 Consider a system given by the following first order differential equation:
dy
= y + 2t − t 2
dt
where, y(0) = 1 and 0 ≤ t < ∞. Using a step size ℎ = 0.1 for the improved Euler
method, the value of y(t) at t = 0.1 is _________ (rounded off to two decimal
places).
Q.35 Indian Premier League has divided the sixteen cricket teams into two equal pools:
Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four
have red logo jerseys. Five teams of Pool-B have blue logo jerseys while the rest
three have red logo jerseys.
If one team from each pool reaches the final, the probability that one team has a
blue logo jersey and another has a red logo jersey is ________ (rounded off to one
decimal place).
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Q.36 – Q.65 Carry TWO marks Each
Q.36 A wire of circular cross section with radius a is shown in the figure. The current
density is given by J = ks 2 , where k is a constant, s is the radial distance from the
axis and 0 ≤ s ≤ a. The total current I in the wire is
(A) πka4
2
(B) 2πka3
3
(C) πka3
2
(D) πka4
4
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Q.37 The measured values from a flow instrument, whose range is between 0 and 2 flow
units, are shown in the histogram. The systematic error (bias) and the maximum
error (in flow units), respectively are
(A) 0.12 and 0.14
(B) 0.01 and 0.10
(C) 0.10 and 0.14
(D) 0.04 and 0.12
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Q.38 Consider a discrete-time sequence
(0.2)n , 0≤n≤7
x[n] = {
0, otherwise
The region of convergence of X (z), the z-transform of x [n], consists of
(A) all values of z except z = 0.2
(B) all values of z
(C) all values of z except z = 0
(D) all values of z except z = ∞
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Q.39 In the bridge circuit shown in the figure, under balanced condition, the values of R
and C respectively, are
(A) 1.010 Ω and 19.802 µF
(B) 9.901 Ω and 0.505 µF
(C) 19.802 Ω and 1.01 µF
(D) 39.604 Ω and 2.02 µF
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Q.40 Laplace transform of a signal x(t) is
1
X(s) =
s 2 + 13s + 42
Let u(t) be the unit step function. Choose the signal x(t) from the following options
if the region of convergence is −7 < Re{s} < −6.
(A) −e −6t u(t) − e −7t u(−t)
(B) −e −6t u(−t) − e −7t u(t)
(C) e −6t u(t) − e −7t u(−t)
(D) −e −6t u(−t) − e −7t u(−t)
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Q.42 In the figure shown, the positive edge triggered D flip-flops are initially reset
to Q = 0. The logic gates and the multiplexers have no propagation delay. After
reset, a train of clock pulses (CLK) are applied. The logic-states of the inputs DIN,
S and the clock pulses are also shown in the figure. Assuming no timing violatio ns,
the sequence of output Y from the 3 rd clock to the 5th clock, Y3 Y4 Y5 is
(A) 001
(B) 010
(C) 000
(D) 011
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Q.43 In the figure shown, R = 1 kΩ and C = 0.1 µF. For a dc gain of −10, the 3 dB
cut-off frequency (rounded off to one decimal place) is
Assume the opamp is ideal.
(A) 159.1 Hz
(B) 1591.5 Hz
(C) 1750.7 Hz
(D) 175.0 Hz
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Q.44 Consider the feedback control system shown in the figure. The steady-state error
ess = lim (r(t) − y(t)) due to unit step reference r(t) is
t→∞
(A) K−1
K
(B) 1
2
(C) 0
(D) 1− K
K
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Q.45 The transfer function of a system is
ωn2
G (s) =
s 2 + 2ξωn s + ωn2
Choose the range of ξ and ωn (in rad/s) from the following options such that the
poles lie on the shaded region of the s-plane as shown in the figure.
(A) 1
ξ≥ and ωn ≥ 2
2
(B) 1
ξ≥ and ωn ≥ 2
4
(C) 1
ξ≥ and ωn ≥ √3
2
(D) 1
ξ≥ and ωn ≥ √3
4
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Q.46 Let C be the closed curve in the xy-plane, traversed in the counterclockwis e
direction along the boundary of the rectangle with vertices at
(0,0), (2,0), (2,1), (0,1). The value of the line integral
∮ (−e y dx + e x dy)
C
is
(A) e 2 + 2e − 3
(B) e 2 − 2e − 3
(C) e2 + e − 1
(D) e2 + e + 1
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Q.47 In the figure shown, assume
• α is the phase angle between the load current and the load voltage
• β is the phase angle by which pressure coil current lags the pressure coil
voltage of the wattmeter
• γ is the phase angle between currents in the pressure coil and the current
coil of the wattmeter
• δ is the phase angle of the voltage transformer
• is the phase angle of the current transformer
When the load has a lagging phase angle of α, which one of the following options
is correct?
(A) α = −γ ± δ ± θ − β
(B) α = −γ ± δ ± θ + β
(C) α = γ± δ ±θ+ β
(D) α = γ± δ ±θ− β
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Q.48 Consider an ultrasonic measurement system shown in the figure. The ultrasonic
transmitter (T) sends a continuous wave signal x(t) = cos(2πf1 t) volts towards an
object whose vibration is modeled as m(t) = 0.5 sin(2πf2 t) volts. Neglecting the
phase shift due to any other effect, the received signal at the receiver (R) is
y(t) = cos(2πf1 t+β cos(2πf2 t)) volts.
Assuming the frequency sensitivity factor as 500 Hz/volt, f1 = 40 kHz, f2 = 1 kHz,
the modulation index (β) and the frequency deviation in y(t), respectively, are
(A) 0.25 and 250 Hz
(B) 0.5 and 500 Hz
(C) 1 and 1000 Hz
(D) 0.75 and 1000 Hz
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Q.49 The complex functions f(z) = u(x, y) + i v(x, y) and ̅̅̅̅̅̅
f(z) = u (x, y) − i v(x, y)
are both analytic in a given domain. Choose the correct option(s) from the
following.
(A) ∂u ∂v
= =0
∂x ∂y
(B) ∂u ∂v
=− ≠0
∂y ∂x
(C) df(z)
=0
dz
(D) df(z)
≠0
dz
Q.50 The readings recorded from a 20-psig pressure gauge are given in the Table. The
regression line obtained for the data is y = 0.04 x + 10.32. The regression
coefficient of determination, R 2 = _________ (rounded off to three decimal
places).
x 1 2 3 4 5
y (psig) 10.3 10.5 10.4 10.5 10.5
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Q.51 In the figure shown, R = 4.5 kΩ, ΔR = 1.5 kΩ, and INA is assumed to be ideal.
The equivalent resistance between A and B is ____ kΩ (rounded off to nearest
integer).
Q.52 Consider the capacitive sensor circuit and its output voltage shown in the figur e.
The circuit is switched ON at t = 0. Assuming the opamp to be ideal, the frequency
of the output voltage Vo is __________ kHz (rounded off to two decimal places).
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Q.53 The 4-point DFTs of two sequences x[n] and y[n] are X [k] = [1, −j, 1, j] and
Y[k] = [1, 3j, 1, −3j], respectively. Assuming z[n] represents the 4-point circular
convolution of x[n] and y[n], the value of z[0] is __________ (rounded off to
nearest integer).
Note: The DFT of a N-point sequence x[n] is defined as
N−1
−j2πnk
X [k] = ∑ x[n]e N
n=0
Q.54 Consider the figure shown. For zero deflection in the galvanometer, the required
value of resistor Rx is ____ Ω (rounded off to nearest integer).
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Q.55 Consider a unity negative feedback system with its open-loop pole-zero map as
shown in the figure. If the point s = jα, α > 0, lies on the root locus, the value of
α is ________ (rounded off to nearest integer).
Note: The poles are marked with ⨯ in the figure.
Q.56 A shielded cable with Cstray = 20 pF and Rwire = 10 Ω is used to connect the inductive
sensors as shown in the figure. The RMS value of Vout is ____V (rounded off to
two decimal places).
Note: Assume all components are ideal, and sensors are not magnetically coupled.
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α VD
Q.57 In the figure shown, the diode current is given by ID = IS e T . VD is the diode
voltage in volts, T is the absolute temperature in Kelvin, α = 1.16 × 104 K/V, and
IS = 10−15 A is the saturation current. The dc current source, opamp and the
resistors are ideal, and are assumed to be temperature independent. The change in
the output voltage (Vout ) per Kelvin change in temperature is ________ mV
(rounded off to one decimal place).
Q.58 An ADC has a full scale voltage of 1.4 V, resolution of 200 mV, and produces
binary output data. The input signal of the ADC has a bandwidth of 500 MHz, and
it samples the data at the Nyquist rate. The parallel data output is converted to a
serial bit stream using a parallel-to-serial converter. The data rate at the output of
the parallel-to-serial converter is _____ Gbps (rounded off to nearest integer).
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Q.59 In the circuit shown, assume the opamp is ideal and the initial charge on the
capacitor is zero. The output voltage at time t = 2 ms is _____ V (rounded off to
one decimal place).
Q.60 In the figure shown, SW is a switch whose position changes from 1 to 0 when VC
changes from logic HIGH to LOW and vice versa. The bandwidth of the permanent
magnet moving coil (PMMC) type voltmeter is 1 Hz. If Vsense = 2 sin(4000πt) V and
Vref = 4 sin(2000πt) V, the voltmeter reading is ______V (rounded off to nearest
integer).
Note: Assume all components are ideal.
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Q.61 A 50 kVA transformer has an efficiency of 95% at full load and unity power factor.
Assume the core losses are negligible. The efficiency of the transformer at 75% of
the full load and 0.8 power factor is ________% (rounded off to one decimal
place).
Q.62 A three-phase squirrel-cage induction motor has a starting torque of 100% of the
full load torque and a maximum torque of 300% of the full load torque. Neglecting
the stator impedance, the slip at the maximum torque is ________% (rounded off
to two decimal places).
Q.63 Two magnetically coupled coils, when connected in series-aiding configuratio n,
have a total inductance of 500 mH. When connected in series-opposing
configuration, the coils have a total inductance of 300 mH. If the self-inductance of
both the coils are equal, then the coupling coefficient is ________ (rounded off to
two decimal places).
Q.64 The solution of an ordinary differential equation y ′′′ + 3y ′′ + 3y ′ + y = 30e −t is
y (t) = (c0 + c1 t − c2 t 2 + c3 t 3 )e −t
Given y(0) = 3, y ′ (0) = −3 and y ′′ (0) = −47, the value of (c0 + c1 + c2 + c3 )
is __________(rounded off to nearest integer).
Note: y ′′′ = d 3 y/dt 3 , y ′′ = d 2 y/dt 2 , y ′ = dy/dt and c0 , c1 , c2 , c3 are constants.
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Q.65 A random variable X has a probability density function
e −x , x≥0
fX (x ) = {
0, otherwise
The probability of X > 2 is ___________ (rounded off to three decimal places).
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Instrumentation Engineering (IN)
Final Answer Key
Question
Q. No. Session Section Key/Range Mark
Type
1 4 MCQ GA A 1
2 4 MCQ GA B 1
3 4 MCQ GA D 1
4 4 MCQ GA A 1
5 4 MCQ GA B 1
6 4 MCQ GA D 2
7 4 MCQ GA B 2
8 4 MCQ GA C 2
9 4 MCQ GA A 2
10 4 MCQ GA A 2
11 4 MCQ IN B 1
12 4 MCQ IN B 1
13 4 MCQ IN D 1
14 4 MCQ IN A 1
15 4 MCQ IN A 1
16 4 MCQ IN A 1
17 4 MCQ IN B 1
18 4 MCQ IN A 1
19 4 MCQ IN C 1
20 4 MCQ IN A 1
21 4 NAT IN 0.15 to 0.17 1
22 4 NAT IN 0.70 to 0.80 1
23 4 NAT IN 1.6 to 1.6 1
24 4 NAT IN 498 to 502 1
25 4 NAT IN 32 to 32 1
26 4 NAT IN -2 to -2 1
27 4 NAT IN 400 to 400 1
28 4 NAT IN 22 to 22 1
29 4 NAT IN -3 to -3 1
30 4 NAT IN 200 to 200 1
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31 4 NAT IN 27.0 to 30.0 1
32 4 NAT IN 10.1 to 10.3 1
33 4 NAT IN 15 to 15 1
34 4 NAT IN 1.10 to 1.12 1
35 4 NAT IN 0.5 to 0.5 1
36 4 MCQ IN A 2
37 4 MCQ IN A 2
38 4 MCQ IN C 2
39 4 MCQ IN C 2
40 4 MCQ IN B 2
41 4 MCQ IN A 2
42 4 MCQ IN A 2
43 4 MCQ IN A 2
44 4 MCQ IN A 2
45 4 MCQ IN A 2
46 4 MCQ IN A 2
47 4 MCQ IN C 2
48 4 MCQ IN A 2
49 4 MSQ IN A;C 2
50 4 NAT IN 0.450 to 0.550 2
51 4 NAT IN 4 to 4 2
52 4 NAT IN 6.00 to 6.30 2
53 4 NAT IN 2 to 2 2
54 4 NAT IN 58 to 62 2
55 4 NAT IN 2 to 2 2
56 4 NAT IN 2.81 to 2.85 2
57 4 NAT IN 9.5 to 10.5 2
58 4 NAT IN 3 to 3 2
59 4 NAT IN -2.6 to -2.4 2
60 4 NAT IN 0 to 0 2
61 4 NAT IN 95.2 to 95.4 2
62 4 NAT IN 17.00 to 17.30 2
63 4 NAT IN 0.25 to 0.25 2
64 4 NAT IN 33 to 33 2
65 4 NAT IN 0.130 to 0.140 2
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Source: GATE. Question paper published by GATE.