GATE 2026 Question Paper Instrumentation Engineering (IN)

FOR GATE EXAM PREPARATION

GATE 2026
Question Paper ·
Instrumentation
Engineering (IN)
EXAM YEAR TYPE SUBJECT

GATE 2026 Question Paper Instrumentation Engineering (IN)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 Suresh said, “I did it yesterday.”

Which one of the following options is the correct form of this sentence in indirect
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speech?

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(A) a Suresh said that I did it yesterday.

(B) Suresh says I did it yesterday.

(C) Suresh says that he did it the day before.

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(D) Suresh said that he had done it the day before.

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Q.2 To continue the sequence of tiles shown, the tile indicated by the question mark
should be

(A)

(B)

(C)

(D)

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Q.3 Consider an art gallery whose walkways are shown as lines in the diagram. A
black dot represents a junction of two walkways. A guard may be placed at a
junction to watch over the walkways that join at that junction. The minimum
number of guards needed to watch all the walkways is ________.

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(A) 2
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(B) 3
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(C) 4 a
(D) 5

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Q.4 The 2nd of June is a Thursday in a certain year. Which day of the week is the
3rd of July in that year?

(A) Thursday

(B) Friday

(C) Saturday

(D) Sunday

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Q.5 A coin with heads facing up is shown as and a coin with tails facing up is
shown as .

Six coins are placed in the Starting Arrangement, as shown in the figure below.
A “step” is defined as interchanging a pair of adjacent coins without flipping
them. The minimum number of steps needed to go from the Starting Arrangement
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to the Final Arrangement, as shown in the figure, is ________.
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(A) 3

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(B) 6

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(C) 9
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(D) 12

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Q.6 – Q.10 Carry TWO marks Each

Q.6 Exacerbate : Mitigate :: ___________

Choose the option with the correct pair of words to fill the blank.

(A) Aggravate : Alleviate

(B) Alleviate : Precipitate

(C) Aggravate : Precipitate

(D) Emancipate : Exonerate

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Q.7 A paper shown in Panel I is folded along the dashed lines (- - -) to construct a
cube. The shaded regions shown in Panel I appear on the outer surface of the cube.
Referring to cubes shown in Panel II, which one of the options is correct?

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(A) Only (i) can correspond to the unfolded cube in Panel I.

(B) Only (ii) can correspond to the unfolded cube in Panel I.

(C) Both (i) and (ii) can correspond to the unfolded cube in Panel I.
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(D) Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

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Q.8 In a population, patients who have high cholesterol also have high blood-pressure
(BP). Some patients with high BP also have diabetes. There are no patients who
have both high cholesterol and diabetes. Furthermore,

1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.

Then the number of patients who have both diabetes and high BP is _______

(A) 0

(B) 15

(C) 20

(D) 10

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Q.9 Four people P, Q, R, and S, of different ages, make the following observations.

P – I am younger than S.

Q – I am neither the youngest nor the oldest.

R – P is older than me. m
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Based on these observations, the youngest person is ______.
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(A) P

(B) Q

(C) R
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(D) S
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Q.10 Circles 𝐶1 , 𝐶2 , and 𝐶3 , with centers 𝑂1, 𝑂2, and 𝑂3 , and radii 𝑟1 , 𝑟2 , and 𝑟3 ,
respectively, touch each other as shown in the following figure. Given 𝑟1 = 2 cm,
𝑟2 = 1 cm and the angle ∠𝑂1 𝑂3 𝑂2 is 90°, 𝑟3 = _____ cm.

(A) 1
(−3 + √17 )
2

(B) 1
(3 + √17 )
2

(C) 1
(−2 + √17 )
2

(D) 1
(−3 + 2√17 )
2

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Q.11 – Q.35 Carry ONE mark Each

Q.11 A matrix 𝑃 ∈ ℝ3×3 satisfies 𝑃3 − 4𝑃2 + 5𝑃 − 2𝐼 = 0 where 𝐼 is a 3 × 3 identity
matrix.

The set of all possible eigenvalues of matrix 𝑃 is ___. m
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(A) ag{1,2,3}

(B) {1}

(C) {1,2}

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(D) {2}

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Q.12
a
Which one among the following statements is true for the function 𝑓(𝑥) = 𝑥|𝑥| ?

(A) 𝑓(𝑥) is discontinuous but not differentiable at 𝑥 = 0.

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(B) 𝑓(𝑥) is discontinuous and differentiable at 𝑥 = 0.
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s e (C) 𝑓(𝑥) is continuous but not differentiable at 𝑥 = 0.
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a (D) 𝑓(𝑥) is continuous and differentiable at 𝑥 = 0.

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Q.13 Consider a function 𝑓(𝑧) = 𝑧 2 + 𝑧 + 1 where 𝑧 ∈ ℂ is a complex variable. A
simple closed contour 𝛾 in 𝑧-plane encloses the point 𝑧 = 1 + 0𝑗.

𝑓(𝑧)
The value of integral ∮𝛾 𝑑𝑧 = _______.
𝑧−1

(A) 6𝜋𝑗

(B) 3𝜋𝑗

(C) 12𝜋𝑗

(D) 𝜋𝑗

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Q.14 Consider a matrix

1 0 2
𝑨 = [−1 1 0]
0 1 2
1 𝑥1
m
Let 𝒃 = [3] and 𝒙 = [𝑥2 ]
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0 𝑥3

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The number of solutions to the linear system of equations 𝑨𝒙 = 𝒃 is _____.
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(A) 0

(B) 1

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(C) 6

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(D) infinitely many
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Q.15 An electric field has a potential of 𝑉(𝑥, 𝑦, 𝑧) = √𝑥 2 + 𝑦 2 + 𝑧 2 V.

A charge of 1 coulomb placed at (𝑖̂ + 𝑗̂ + 𝑘̂) experiences a force of

𝐹⃗ = (𝑎𝑖̂ + 𝑏𝑗̂ + 𝑐𝑘̂) N

The values of (𝑎, 𝑏, 𝑐) are ______.

(A) 1 1 1
𝑎= ,𝑏 = ,𝑐 =
√3 √3 √3

(B) 1 1 1
𝑎 = ,𝑏 = ,𝑐 =
3 3 3

(C) 1
𝑎 = 0, 𝑏 = 1, 𝑐 =
√3

(D) 1
𝑎 = 0, 𝑏 = 1, 𝑐 =
3

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Q.16 The RLC filter shown below acts as a ________.

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Vin Vout m
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(A) low pass filter

(B) high pass filter

(C) band pass filter
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(D) band stop filter
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Q.17 A single phase step-down transformer has a high voltage primary winding and a
low voltage secondary winding. The secondary winding is connected to a load
impedance Z2. The impedance Z2 when referred to the primary winding is denoted
by 𝑍2′ . Which of the following conditions is true?

(A) 𝑍2′ = 𝑍2

(B) 0.5 𝑍2 < 𝑍2′ < 𝑍2

(C) 𝑍2′ > 𝑍2

(D) 𝑍2′ ≤ 0.5 𝑍2

Q.18 A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter
with cut-off frequency of 21 kHz. The output signal is a _______.

(A) 20 kHz sine wave

(B) 20 kHz square wave

(C) 20 kHz triangular wave

(D) 20 kHz saw-tooth wave

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Q.19 Given 𝑥(𝑡) = 4 sin(15𝜋 𝑡) + 7 cos(4𝜋 𝑡), where t is in seconds.

The fundamental period of 𝑥(𝑡) is _____ seconds.

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(A)
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(B)
a 60

(C) 30

(D) 2

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Q.20 Among the following, the differential equation(s) not representative of a linear
dynamical system is/are ____.

𝑑2𝑥 𝑑𝑥
(i) + 2𝑡 + 𝑥(𝑡) = 𝑢(𝑡)
𝑑𝑡 2 𝑑𝑡

𝑑𝑥 2 𝑑𝑥
(ii) ( 𝑑𝑡 ) + 2 𝑑𝑡 + 𝑥(𝑡) = 𝑢(𝑡)

𝑑2𝑥 𝑑𝑥
(iii) +2 + 𝑥(𝑡) = 𝑢(𝑡)
𝑑𝑡 2 𝑑𝑡

(A) (i) and (ii) only

(B) (i) only

(C) (ii) only

(D) (ii) and (iii) only

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Q.21 A common gate amplifier represents a _____________.

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(A) voltage controlled voltage source
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current m
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(B)
s e controlled current source
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(C) agvoltage controlled current source

(D) current controlled voltage source

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Q.22 In the circuit shown, the BJT has a  of 100. The base-emitter junction voltage is
0.65 V. The quiescent collector current, IC is _______ mA.

5V
5 kW 5 kW
IC

5 kW 5 kW

(A) 0.365

(B) 0.435

(C) 0.625

(D) 0.862

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Q.23 The maximum signal to quantization noise ratio (SQNR) for a 16-bit analog-to-
digital converter is approximately _________ dB.

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(A) 48

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(B) a 68

(C) 88

(D) 98

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Q.24
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The Kelvin double bridge is used to measure ______ valued resistances and has
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______ resistors in its construction.

(A) low ; three-terminal

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(B) low ; four-terminal
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Q.25 Active strain gauges are connected in a half-bridge configuration to measure strain
in a cantilever element. When powered by a voltage source of 10 V, the voltage at
the output of the bridge is 1 mV. If the gauge factor is 2.5, the strain in the cantilever
element is ________ microstrain.

(A) 40

(B) 80

(C) 20

(D) 160

Q.26 A glass pH electrode behaves linearly with an output change of 60 mV per unit
change in pH. The measurement reference is set such that a solution of pH 6
produces an output of 60 mV. The pH of a solution that results in an output of
−90 mV is _______ .

(A) 3.5

(B) 3

(C) 8

(D) 8.5

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Q.27 An analog speech signal contains signals from 200 Hz to 2400 Hz. It is sampled at
6 kHz and quantized with 512 levels for pulse code modulation (PCM). The bit rate
will be _____ kbps.
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(A)
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(B) 48

(C) 19.2

(D) 54
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Q.28 a
The slope efficiency of a laser is 0.5 W/A, and the output optical power at a
current of 100 mA is 30 mW. Assuming piece-wise linear characteristics of the laser
diode, the threshold current of the laser is ________ mA.

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(A) 0

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(D) 60

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Q.29 In a linear element, the measured current is 100 mA ± 2.5% and the measured
voltage is 5 V ± 5%. Which of the following options show(s) the consumed power?

(A) (500 ± 37.5) mW

(B) (500 ± 12.5) mW

(C) 500 mW ± 7.5%

(D) 500 mW ± 2.5%

Q.30 Which of the following statements is/are correct for a thermocouple?

(A) It is based on the Seebeck Effect.

(B) The change in resistance is measured.

(C) The voltage difference between the two junctions is linearly proportional to the
temperature difference between the junctions.

(D) It is based on the concept of Joule Heating.

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Q.31 A data set is given to be [1, 2, 0, −1, −3, 1, 2, 0, 1].

The median of the data set is ____. (rounded off to the nearest integer)

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Q.32 The potential difference between nodes 𝐴 and 𝐵 in a circuit is 𝑣𝐴 − 𝑣𝐵 = 5 V. The

o m m
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work done in moving a charge of 1 coulomb from point 𝐵 to 𝐴 is ____ J. (answer
s e
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in integer)
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Q.33 a In a series 𝑅𝐿 circuit shown in the figure, the current through the resistor lags the
AC source voltage by 45°. Let 𝑅 = 100𝜋 Ω and 𝐿 = 2 H.

R

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The frequency of the source is ____ Hz. (rounded off to the nearest integer)

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Q.34 In the circuit below the maximum value of vout is ________ V. (rounded off to the

nearest integer)

4W

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Q.35 The minimum number of comparators required in a 6-bit flash analog-to-digital
converter is ________. (answer in integer)

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Q.36 – Q.65 Carry TWO marks Each

Q.36 A box contains three apples and two oranges. Two fruits are removed randomly in
succession. The probability that the first is an apple and the second is an orange
is _____ .

(A) 3
5

(B) 3
20

(C) 3
10

(D) 2
5

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Q.37 An electric field in free space is

𝐸⃗⃗ = (2𝑥 + 5𝑦 + 6𝑧)𝑖̂ + (5𝑥 + 4𝑦 + 10𝑧)𝑗̂ + (6𝑥 + 10𝑦 + 2𝑧)𝑘̂ V/m.

The charge density is ____ C/m3. (𝜖0 is the permittivity of free space)
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g l a ag
(A)
a 8𝜖 0

(B) 10𝜖0

(C) 6𝜖0

(D) 4𝜖0
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Q.38 A straight thin wire carrying a current of 𝐼 = 1 A in the direction

1 2 1
𝑛̂ = 𝑖̂ + 𝑗̂ + 𝑘̂ is placed inside a magnetic field of 𝐵⃗⃗ = (2𝑖̂ + 2𝑘̂) T.
√6 √6 √6
The force per unit length on the wire is _____ N/m.

(A) 2√6𝑖̂ − 2√6𝑘̂

(B)
3 3 3
√ 𝑖̂ − √ 𝑗̂ + √ 𝑘̂
2 4 4

(C) 4 4
𝑖̂ − 𝑘̂
√6 √6

(D)
3 3 3
√ 𝑖̂ + √ 𝑗̂ + √ 𝑘̂
2 4 4

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Q.39 A two-port network has z-parameters z11 = z22 = 10 W, and z12 = z21 = 5 W.

The value of RL such that maximum power is transferred to RL is _________ W.

5W m
5 V .com m .co
m z11 z12 s e
s e RL l a
g l a z21 z22 ag
a

(A) 5.67
m
(B) 8.33
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(C) 10.33
a
(D) 25.67

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Q.40 In the circuit shown below, the value of the output voltage 𝑉0 is _____ V.

1W 1W

2W 2W 2W 2W
V0
4V 4V

(A) 2

(B) 3

(C) 4

(D) 8

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Q.41 A signal x(t ) is shown below.

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The plot of y(t )  1  x(4  t ) is shown in ______.
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(A)

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(B)
g la
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(C)

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s e g l a
g la (D) a
a

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Q.42 In the table shown below, List-I are the system responses to input 𝑥(𝑡) and List-II
are the system properties. The correct matching is ____.

List-I List-II

(M) x 2 (t ) (I) Linear and Time-invariant

(N) x(t ) (II) Non-linear and Time-varying

(O) | x(3  t ) | (III) Linear and Time-varying

(P) x(t  3) (IV) Non-linear and Time-invariant

(A) M-IV, N-III, O-II, P-I

(B) M-II, N-I, O-IV, P-III

(C) M-III, N-IV, O-II, P-I

(D) M-I, N-IV, O-III, P-II

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Q.43 Given two signals: 𝑥(𝑡) = 𝑢(𝑡 − 2) − 𝑢(𝑡 − 3), and 𝑦(𝑡) = 𝑒 −4𝑡 𝑢(𝑡).

If 𝑧(𝑡) = 𝑥(𝑡) ∗ 𝑦(𝑡), then 𝑍(𝑠) is _______.

m
c o m m .co
𝑒 [𝑒 −.1] s e
e+m4)
−3𝑠 𝑠
(A)
s l a
la ag
𝑠(𝑠
g
a 𝑒 [𝑒 − 1]
(B) −𝑠 −3𝑠

(𝑠 + 3)(𝑠 + 4)

(C) 𝑒 −3𝑠 [1 − 𝑒 𝑠 ]
(𝑠 + 3)(𝑠 + 4)

m
(D) 𝑒 −3𝑠 [1 − 𝑒 𝑠 ]
m .co
𝑠(𝑠 + 4)
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.44 A linear time invariant (LTI) system is described by:

𝑥̇ 0 1 𝑥1 1
[ 1] = [ ][ ] + [ ]𝑢
𝑥̇ 2 −10 −7 𝑥2 1
𝑥1
𝑦 = [1 1] [𝑥 ]
2

The poles of the system are ____.

(A) −2, −5

(B) 2, 5

(C) −2, 5

(D) 2, − 5

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Q.45 In the circuit shown below, R is 1 kW and Rf is 10 kW. If Vin is 100 mV and the
op-amps have supply voltages of ±15 V, then Vout is _______ V.

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.co m
Rf
s e
Vsinem l a
ag
R Vout
g la
a Rf

m
(A) −15
m .co
s e
(B) 15
g la
a
(C) 2.1

(D) 1.1

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m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.46 In the following active filter circuit with ideal op-amps, R is 1 kW, C is 1 F, and
Vin has an amplitude of 1 V at 1000 rad/s.

The amplitude of Vout is __________ V.

R

R C R
R C R R
Vin
Vout

(A) 0.5

(B) 0.707

(C) 1.0

(D) 1.414

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Q.47 The initial state of Q3Q2Q1Q0 in the digital circuit shown below is 1011.

The new value of Q3Q2Q1Q0 after two rising edges of the clock (CLK) will be
_____.

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m .co s e m
s e l a
a ag
D3 Q3 D2 Q2 D1 Q1 D0 Q0
g l
a
CLK CLK CLK CLK

CLK

m
(A) 1101
m .co
s e
(B) 0101
g la
a
(C) 1010

(D) 1011

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m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.48 A closed Lissajous pattern observed on an oscilloscope in the 𝐗 − 𝐘 mode has three
horizontal tangencies and two vertical tangencies in steady state. If the signal-
frequency on channel-𝐗 is 600 Hz, then the signal-frequency on channel-𝐘
is ___________ Hz.

(A) 300

(B) 400

(C) 600

(D) 900

Q.49 If the definition of SI unit ‘X’ is required to define SI unit ‘Y’, the dependency is
indicated as X  Y. A valid order of dependencies, as per present convention,
is ___________.

(A) metre  second  kilogram  kelvin

(B) second  metre  kilogram  kelvin

(C) metre  second  kelvin  kilogram

(D) second  kilogram  kelvin  metre

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Q.50 A parallel plate capacitive displacement sensor has a plate area of 2 cm2. The air
gap between the plates is decreased by 0.1 mm from an initial value of 0.5 mm. The
percentage change in the capacitance value is ______ %.

(Assume permittivity as 𝜖0 = 8.854 × 10−12 𝐹/𝑚)
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m .co s e m
s e l a
l a
(A) ag10.0
ag

(B) 14.1

(C) 25.0

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.co
(D) 30.0

e m
las
ag

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m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
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Q.51 The emitted radiant energy from a piece of metal was measured using a pyrometer.
The temperature was calculated to be 1000 °C, assuming a surface emissivity of
0.8. It was later found that the true surface emissivity was 0.7.

The actual temperature of the object is nearest to ______ °C.

(A) 1043

(B) 958

(C) 1033

(D) 967

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Q.52 An amplitude modulated voltage signal 𝑥(𝑡) drives a load of 1 W.

𝑥(𝑡) = 𝐾 cos(300𝜋 𝑡) + 𝐿 cos(240𝜋 𝑡) + 𝐿 cos(360𝜋 𝑡).

If the efficiency is 60% and the carrier power is 50 W, the value of 𝐿 is ______ V.
m
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m .co s e m
s e l a
g l a ag
a
(A) 8.66

(B) 1.22

(C) 0.81

(D) 17.32
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s e
g la
Q.53 Given 𝑓(𝑥, 𝑦) = 𝑥 − 2𝑥𝑦a+ 𝑦
2 2

The complete contour of the equation 𝑓(𝑥, 𝑦) = 1 is described by the option(s) ___.

m
.co
(A) A line, 𝑥 − 𝑦 = 1
m
c. o(B) s e m
e m A circle with radius 1
l a
las ag
ag (C) An ellipse with length of major axis equal to 1

(D) A line, 𝑥 − 𝑦 = −1

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s em l a
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Q.54 𝑑2 𝑥
Given a differential equation + 𝑥 = 0 with 𝑥(0) ≠ 0.
𝑑𝑡 2

Which of the following statements is/are true?

(A) 𝑑𝑥(𝑡) 2
|𝑥(𝑡)|2 + | | = 0 for all 𝑡 ≥ 0
𝑑𝑡

(B) 𝑑𝑥(𝑡) 2
|𝑥(𝑡)|2 + | | = 𝑐 for all 𝑡 ≥ 0, for some real constant 𝑐 > 0
𝑑𝑡

(C) 𝑑𝑥(𝑡) 2
|𝑥(𝑡)|2 + | | = e𝑗𝑡 for all 𝑡 ≥ 0
𝑑𝑡

(D) 𝑑𝑥(𝑡) 2
|𝑥(𝑡)|2 + | | = sin 𝑡 for all 𝑡 ≥ 0
𝑑𝑡

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Q.55 Which of the following functions represent(s) the output of the CMOS logic-gate
shown in the circuit below?

VDD

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m C .co
A
m .fco B s e m
s e l a
g l a ag
a

(A) ̅+B
𝑓=A ̅ ⋅ C̅

m
(B) 𝑓 = ̅̅̅̅̅̅̅̅
A+BC
m .co
s e
̅ ⋅ (B
̅ + C̅) g la
(C) 𝑓= A
a
(D) 𝑓 = ̅̅̅̅̅̅̅̅̅̅̅̅̅̅
A ⋅ (B + C)

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m .co s e m
s e g l a
g la a
a

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s em l a
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Q.56 A 16-bit processor has 16-bit wide instructions and a few internal registers. Every
16-bit instruction is encoded in a fixed format with one operation code of 7 bits and
up to three operands. The operand can be an internal register and each operand is
encoded by 3 bits. All the internal registers can be specified in an instruction using
three bits.

The correct statement(s) for this processor is/are _____.

(A) The processor has 16 internal registers.

(B) The processor can support 128 unique operation codes (Opcodes).

(C) The processor has up to 8 internal registers.

(D) The processor can support 512 unique operation codes (Opcodes).

Q.57 1, 𝑡 ∈ [0,2]
Let 𝑓(𝑡) = {−𝑡 + 3, 𝑡 ∈ [2,3]
0, otherwise

Then

∞
∫−∞ 𝑓(𝜏)𝑑𝜏 =_____. (rounded off to one decimal place)

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Q.58 A single phase transformer has a rating of 10 kVA, 50 Hz, 1100 V/ 220 V. In an
open circuit test with the high voltage side open, the following are obtained:

 Voltage applied to the low voltage winding = 220 V

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Measured power = 363 W
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.co
 Measured current = 2.75 A
e m
s em reactance 𝑋 referred to the high voltage winding is __________Ω.glas
la off to the nearest integer)
Magnetizing
a
𝑚

ag(rounded

Q.59 A linear time invariant (LTI) system has a transfer function

10(𝑠 + 1)
𝐺(𝑠) =
𝑠(𝑠 2 + 2𝑠 + 5)

m
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The system is placed in unity negative feedback configuration.

e m
s
For a unit ramp reference, the steady state error is _______.
la
g
(rounded off to two decimalaplaces)

Q.60 𝐾
The system 𝐺 (𝑠) = has a gain margin of 20 dB. The value of K
(𝑠+1)4
is ______. (rounded off to two decimal places)

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Q.61 In the phase-locked-loop circuit shown below, the output of the VCO is a digital
e m
e m square wave.
l as
las g
g Loop a VCO
a Input ÷20 counter Phase
detector filter
Output

÷1024 counter

If the input is a square wave at 10 kHz, the steady state frequency of the output
is ________ kHz. (rounded off to the nearest integer)

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Q.62 A digital counter increments its count every 0.1 s. The counter is used in an
instrument to measure frequency. The counter is operated for one period of the input
signal to the instrument to measure its frequency. The input signal is approximately
at 100 kHz. The maximum error in the measured frequency is _____ kHz.
(rounded off to the nearest integer)

Q.63 A current carrying semiconductor of thickness 0.7 mm is placed in a transverse
magnetic field. The measured Hall voltage is 0.9 mV and the current is 6 mA. If
the Hall coefficient is 4 x 10-4 m3/C, the value of the incident magnetic field
is _______ T. (rounded off to two decimal places)

Q.64 For a fiber Bragg grating-based sensor, the shift in the Bragg wavelength gives
information about the value of the measurand. For a Bragg wavelength of 1550 nm
and effective index of 1.44, the grating period is _______ nm.

(rounded off to two decimal places)

Q.65 A photodiode has a responsivity 0.8 A/W. If the input optical power to the
photodiode is 2 mW, the power delivered to a 50 W load is _______ W.

(rounded off to the nearest integer)

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