GATE 2026 Instrumentation Engineering (IN) Question Paper with Solutions PDF

Suresh said, "I did it yesterday."
Which one of the following options is the correct form of this sentence in indirect speech?

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

To continue the sequence of tiles shown, the tile indicated by the question mark should be:

• (A)

• (B)

• (C)

• (D)

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 ________.

• (A) 2
• (B) 3
• (C) 4
• (D) 5

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

A coin with heads facing up is shown as a circled letter "H", and a coin with tails facing up is shown as a circled letter "T".
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 to the Final Arrangement, as shown in the figure, is ________.

• (A) 3
• (B) 6
• (C) 9
• (D) 12

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

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?

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

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

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.
Based on these observations, the youngest person is ______.

• (A) P
• (B) Q
• (C) R
• (D) S

Circles \(C_1\), \(C_2\), and \(C_3\), with centers \(O_1\), \(O_2\), and \(O_3\), and radii \(r_1\), \(r_2\), and \(r_3\), respectively, touch each other as shown in the following figure. Given \(r_1 = 2\) cm, \(r_2 = 1\) cm and the angle \(\angle O_1O_3O_2\) is \(90^{\circ}\), \(r_3 =\) _____ cm.

• (A) \(\dfrac{1}{2}\left(-3+\sqrt{17}\right)\)
• (B) \(\dfrac{1}{2}\left(3+\sqrt{17}\right)\)
• (C) \(\dfrac{1}{2}\left(-2+\sqrt{17}\right)\)
• (D) \(\dfrac{1}{2}\left(-3+2\sqrt{17}\right)\)

A matrix \(P\in\mathbb{R}^{3\times3}\) satisfies \(P^3-4P^2+5P-2I=0\), where \(I\) is a \(3\times3\) identity matrix.
The set of all possible eigenvalues of matrix \(P\) is ____.

• (A) \(\{1,2,3\}\)
• (B) \(\{1\}\)
• (C) \(\{1,2\}\)
• (D) \(\{2\}\)

Which one among the following statements is true for the function \(f(x)=x|x|\)?

• (A) \(f(x)\) is discontinuous but not differentiable at \(x=0\).
• (B) \(f(x)\) is discontinuous and differentiable at \(x=0\).
• (C) \(f(x)\) is continuous but not differentiable at \(x=0\).
• (D) \(f(x)\) is continuous and differentiable at \(x=0\).

Consider a function \(f(z)=z^2+z+1\), where \(z\in\mathbb{C}\) is a complex variable. A simple closed contour \(\gamma\) in the \(z\)-plane encloses the point \(z=1+0j\).
The value of the integral
\[\oint_{\gamma}\frac{f(z)}{z-1}\,dz\]
is ______.

• (A) \(6\pi j\)
• (B) \(3\pi j\)
• (C) \(12\pi j\)
• (D) \(\pi j\)

Consider a matrix
\[ A=\begin{bmatrix}1 & 0 & 2\\ -1 & 1 & 0\\ 0 & 1 & 2\end{bmatrix} \]
Let \(b=\begin{bmatrix}1\\3\\0\end{bmatrix}\) and \(x=\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\).
The number of solutions to the linear system of equations \(Ax=b\) is _____.

• (A) \(0\)
• (B) \(1\)
• (C) \(6\)
• (D) infinitely many

An electric field has a potential of \(V(x,y,z)=\sqrt{x^2+y^2+z^2}\) V.
A charge of \(1\) coulomb placed at \((\hat{i}+\hat{j}+\hat{k})\) experiences a force of
\[\vec{F}=(a\hat{i}+b\hat{j}+c\hat{k})\text{ N}\]
The values of \((a,b,c)\) are ______.

• (A) \(a=\dfrac{1}{\sqrt3},\ b=\dfrac{1}{\sqrt3},\ c=\dfrac{1}{\sqrt3}\)
• (B) \(a=\dfrac{1}{3},\ b=\dfrac{1}{3},\ c=\dfrac{1}{3}\)
• (C) \(a=0,\ b=1,\ c=\dfrac{1}{\sqrt3}\)
• (D) \(a=0,\ b=1,\ c=\dfrac{1}{3}\)

The RLC filter shown below acts as a ________.

• (A) low pass filter
• (B) high pass filter
• (C) band pass filter
• (D) band stop filter

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 \(Z_2\). The impedance \(Z_2\) when referred to the primary winding is denoted by \(Z_2'\). Which of the following conditions is true?

• (A) \(Z_2' = Z_2\)
• (B) \(0.5\,Z_2 < Z_2' < Z_2\)
• (C) \(Z_2' > Z_2\)
• (D) \(Z_2' \leq 0.5\,Z_2\)

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

Given \(x(t) = 4\sin(15\pi t) + 7\cos(4\pi t)\), where \(t\) is in seconds.
The fundamental period of \(x(t)\) is _____ seconds.

• (A) 15
• (B) 60
• (C) 30
• (D) 2

Among the following, the differential equation(s) not representative of a linear dynamical system is/are ____.
(i) \[ \frac{d^2x}{dt^2} + 2t\frac{dx}{dt} + x(t) = u(t) \]
(ii) \[ \left(\frac{dx}{dt}\right)^2 + 2\frac{dx}{dt} + x(t) = u(t) \]
(iii) \[ \frac{d^2x}{dt^2} + 2\frac{dx}{dt} + x(t) = u(t) \]

• (A) (i) and (ii) only
• (B) (i) only
• (C) (ii) only
• (D) (ii) and (iii) only

A common gate amplifier represents a _____________.

• (A) voltage controlled voltage source
• (B) current controlled current source
• (C) voltage controlled current source
• (D) current controlled voltage source

In the circuit shown, the BJT has a \(\beta\) of \(100\). The base-emitter junction voltage is \(0.65\) V. The quiescent collector current, \(I_C\), is _______ mA.

• (A) \(0.365\)
• (B) \(0.435\)
• (C) \(0.625\)
• (D) \(0.862\)

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

• (A) \(48\)
• (B) \(68\)
• (C) \(88\)
• (D) \(98\)

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

• (A) low ; three-terminal
• (B) low ; four-terminal
• (C) high ; three-terminal
• (D) high ; four-terminal

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) \(160\)

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) \(8.5\)

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.

• (A) \(16\)
• (B) \(48\)
• (C) \(19.2\)
• (D) \(54\)

The slope efficiency of a laser diode 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.

• (A) \(0\)
• (B) \(20\)
• (C) \(40\)
• (D) \(60\)

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

• (A) \((500 \pm 37.5)\) mW
• (B) \((500 \pm 12.5)\) mW
• (C) \(500\) mW \(\pm 7.5\%\)
• (D) \(500\) mW \(\pm 2.5\%\)

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.

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)

The potential difference between nodes \(A\) and \(B\) in a circuit is \(v_A - v_B = 5\) V. The work done in moving a charge of \(1\) coulomb from point \(B\) to \(A\) is ____ J. (answer in integer)

In a series \(RL\) circuit shown in the figure, the current through the resistor lags the AC source voltage by \(45^{\circ}\). Let \(R = 100\pi\) \(\Omega\) and \(L = 2\) H.

In the circuit below the maximum value of \(v_{out}\) is ________ V. (rounded off to the nearest integer)

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

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) \(\dfrac{3}{5}\)
• (B) \(\dfrac{3}{20}\)
• (C) \(\dfrac{3}{10}\)
• (D) \(\dfrac{2}{5}\)

An electric field in free space is
\[ \vec{E} = (2x+5y+6z)\hat{i} + (5x+4y+10z)\hat{j} + (6x+10y+2z)\hat{k} \ \text{V/m} \]
The charge density is \(\_\_\_\_\) \(\text{C/m}^3\). (\(\epsilon_0\) is the permittivity of free space)

• (A) \(8\epsilon_0\)
• (B) \(10\epsilon_0\)
• (C) \(6\epsilon_0\)
• (D) \(4\epsilon_0\)

A straight thin wire carrying a current of \(I=1\) A in the direction
\[ \hat{n} = \frac{1}{\sqrt6}\hat{i}+\frac{2}{\sqrt6}\hat{j}+\frac{1}{\sqrt6}\hat{k} \]
is placed inside a magnetic field of \(\vec{B} = (2\hat{i}+2\hat{k})\) T.
The force per unit length on the wire is \(\_\_\_\_\_\) N/m.

• (A) \(2\sqrt6\,\hat{i} - 2\sqrt6\,\hat{k}\)
• (B) \(\sqrt{\dfrac{3}{2}}\,\hat{i} - \sqrt{\dfrac{3}{4}}\,\hat{j} + \sqrt{\dfrac{3}{4}}\,\hat{k}\)
• (C) \(\dfrac{4}{\sqrt6}\,\hat{i} - \dfrac{4}{\sqrt6}\,\hat{k}\)
• (D) \(\sqrt{\dfrac{3}{2}}\,\hat{i} + \sqrt{\dfrac{3}{4}}\,\hat{j} + \sqrt{\dfrac{3}{4}}\,\hat{k}\)

A two-port network has z-parameters \(z_{11}=z_{22}=10\ \Omega\), and \(z_{12}=z_{21}=5\ \Omega\).
The value of \(R_L\) such that maximum power is transferred to \(R_L\) is \(\_\_\_\_\_\_\_\_\) \(\Omega\).
Port 1 of the network is driven by a 5 V source in series with a 5 \(\Omega\) resistor, and the load \(R_L\) is connected across port 2, as shown in the figure.

• (A) 5.67
• (B) 8.33
• (C) 10.33
• (D) 25.67

In the circuit shown below, the value of the output voltage \(V_0\) is \(\_\_\_\_\_\) V.

• (A) 2
• (B) 3
• (C) 4
• (D) 8

A signal \(x(t)\) is shown below.

• (A)

• (B)

• (C)

• (D)

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 ______.

• (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

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 ______.

• (A) \(\dfrac{e^{-3s}\left[e^{s}-1\right]}{s(s+4)}\)
• (B) \(\dfrac{e^{-s}\left[e^{-3s}-1\right]}{(s+3)(s+4)}\)
• (C) \(\dfrac{e^{-3s}\left[1-e^{s}\right]}{(s+3)(s+4)}\)
• (D) \(\dfrac{e^{-3s}\left[1-e^{s}\right]}{s(s+4)}\)

A linear time invariant (LTI) system is described by:
\[ \begin{bmatrix}\dot{x}_1\\ \dot{x}_2\end{bmatrix}=\begin{bmatrix}0 & 1\\ -10 & -7\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}+\begin{bmatrix}1\\ 1\end{bmatrix}u \]
\[ y=\begin{bmatrix}1 & 1\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix} \]
The poles of the system are ______.

• (A) \(-2,\ -5\)
• (B) \(2,\ 5\)
• (C) \(-2,\ 5\)
• (D) \(2,\ -5\)

In the circuit shown below, \(R\) is \(1\ \text{k}\Omega\) and \(R_f\) is \(10\ \text{k}\Omega\). If \(V_{in}\) is \(100\) mV and the op-amps have supply voltages of \(\pm15\) V, then \(V_{out}\) is ______ V.

• (A) \(-15\)
• (B) \(15\)
• (C) \(2.1\)
• (D) \(1.1\)

In the following active filter circuit with ideal op-amps, \(R\) is \(1\ \text{k}\Omega\), \(C\) is \(1\ \mu\text{F}\), and \(V_{in}\) has an amplitude of \(1\) V at \(1000\) rad/s.

• (A) 0.5
• (B) 0.707
• (C) 1.0
• (D) 1.414

The initial state of \(Q_3Q_2Q_1Q_0\) in the digital circuit shown below is 1011.

• (A) 1101
• (B) 0101
• (C) 1010
• (D) 1011

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

If the definition of SI unit 'X' is required to define SI unit 'Y', the dependency is indicated as \(X \rightarrow Y\). A valid order of dependencies, as per present convention, is __________.

• (A) \(\text{metre} \rightarrow \text{second} \rightarrow \text{kilogram} \rightarrow \text{kelvin}\)
• (B) \(\text{second} \rightarrow \text{metre} \rightarrow \text{kilogram} \rightarrow \text{kelvin}\)
• (C) \(\text{metre} \rightarrow \text{second} \rightarrow \text{kelvin} \rightarrow \text{kilogram}\)
• (D) \(\text{second} \rightarrow \text{kilogram} \rightarrow \text{kelvin} \rightarrow \text{metre}\)

A parallel plate capacitive displacement sensor has a plate area of \(2\ \text{cm}^2\). 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 \(\epsilon_0 = 8.854 \times 10^{-12}\ \text{F/m}\))

• (A) 10.0
• (B) 14.1
• (C) 25.0
• (D) 30.0

The emitted radiant energy from a piece of metal was measured using a pyrometer. The temperature was calculated to be \(1000^{\circ}\text{C}\), 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 ______ \(^{\circ}\text{C}\).

• (A) \(1043\)
• (B) \(958\)
• (C) \(1033\)
• (D) \(967\)

An amplitude modulated voltage signal \(x(t)\) drives a load of \(1\,\Omega\).
\[ x(t) = K\cos(300\pi t) + L\cos(240\pi t) + L\cos(360\pi t) \]
If the efficiency is \(60\%\) and the carrier power is \(50\) W, the value of \(L\) is ______ V.

• (A) \(8.66\)
• (B) \(1.22\)
• (C) \(0.81\)
• (D) \(17.32\)

Given \(f(x,y) = x^2 -2xy+ y^2\).
The complete contour of the equation \(f(x,y) = 1\) is described by the option(s) ___.

• (A) A line, \(x-y= 1\)
• (B) A circle with radius \(1\)
• (C) An ellipse with length of major axis equal to \(1\)
• (D) A line, \(x-y= -1\)

Given a differential equation \(\dfrac{d^2x}{dt^2} + x= 0\) with \(x(0) \neq 0\).
Which of the following statements is/are true?

• (A) \(|x(t)|^2 + \left|\dfrac{dx(t)}{dt}\right|^2= 0\) for all \(t\geq0\)
• (B) \(|x(t)|^2 + \left|\dfrac{dx(t)}{dt}\right|^2= c\) for all \(t\geq0\), for some real constant \(c>0\)
• (C) \(|x(t)|^2 + \left|\dfrac{dx(t)}{dt}\right|^2= e^{jt}\) for all \(t\geq0\)
• (D) \(|x(t)|^2 + \left|\dfrac{dx(t)}{dt}\right|^2= \sin t\) for all \(t\geq0\)

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

• (A) \(f= \overline{A} + \overline{B}\cdot\overline{C}\)
• (B) \(f= \overline{A+BC}\)
• (C) \(f= \overline{A}\cdot(\overline{B} + \overline{C})\)
• (D) \(f= \overline{A\cdot(B + C)}\)

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).

Let \[ f(t)= \begin{cases} 1, & t\in[0,2] \\ -t+3, & t\in[2,3] \\ 0, & \text{otherwise} \end{cases} \] Then \[ \int_{-\infty}^{\infty} f(\tau)\,d\tau = \_\_\_\_\_. \] (rounded off to one decimal place)

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
Measured power = 363 W
Measured current = 2.75 A
Magnetizing reactance \(X_m\) referred to the high voltage winding is ________ \(\Omega\). (rounded off to the nearest integer)

A linear time invariant (LTI) system has a transfer function \[ G(s)=\frac{10(s+1)}{s(s^2+2s+5)} \] The system is placed in unity negative feedback configuration.
For a unit ramp reference, the steady state error is ________. (rounded off to two decimal places)

The system \[ G(s)=\frac{K}{(s+1)^4} \] has a gain margin of 20 dB. The value of \(K\) is ________. (rounded off to two decimal places)

In the phase-locked-loop (PLL) circuit shown below, the output of the VCO (voltage-controlled oscillator) is a digital square wave.

A digital counter increments its count every \(0.1\) \(\mu\text{s}\). 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).

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 \(4 \times 10^{-4}\) \(\text{m}^3/\text{C}\), the value of the incident magnetic field is T (rounded off to two decimal places).

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).

A photodiode has a responsivity of \(0.8\) A/W. If the input optical power to the photodiode is \(2\) mW, the power delivered to a \(50\) \(\Omega\) load is \(\mu\text{W}\) (rounded off to the nearest integer).