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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(9)Electricity and Magnetism(4)Electrical Circuits and Machines(7)Signals and Systems(5)Control Systems(4)Analog Electronics(4)Digital Electronics(5)Measurements(5)Sensors and Industrial Instrumentation(6)Communication and Optical Instrumentation(6)

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

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.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

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

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

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

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

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

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

A coin with heads facing up is shown as H and a coin with tails facing up is shown as 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

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

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

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

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.

Explanation

GATE→2026→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

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.\nThen the number of patients who have both diabetes and high BP is

(A)

0

(B)

15

(C)

20

(D)

10

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Four people P, Q, R, and S, of different ages, make the following observations.\nP - I am younger than S.\nQ - I am neither the youngest nor the oldest.\nR - P is older than me.\nBased on these observations, the youngest person is

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

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 angle O1O3O2 is 90 degrees, r3 = ____ cm.

(A)

\frac{1}{2}(-3+\sqrt{17})

(B)

\frac{1}{2}(3+\sqrt{17})

(C)

\frac{1}{2}(-2+\sqrt{17})

(D)

\frac{1}{2}(-3+2\sqrt{17})

Explanation

Engineering Mathematics

9 Questions

GATE→2026→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

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

(A)

{1, 2, 3}

(B)

{1}

(C)

{1, 2}

(D)

{2}

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q12

MCQ[1 Mark]

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 $x=0$.

Explanation

GATE→2026→Engineering Mathematics→Analysis of Complex Variables

Q13

MCQ[1 Mark]

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

(A)

$6\pi j$

(B)

$3\pi i$

(C)

$12\pi i$

(D)

$\pi i$

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q14

MCQ[1 Mark]

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

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q15

NAT[1 Mark]

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)

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q16

MCQ[2 Marks]

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)

\frac{3}{5}

(B)

\frac{3}{20}

(C)

\frac{3}{10}

(D)

\frac{2}{5}

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q17

MSQ[2 Marks]

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, $x - y = -1$

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q18

MSQ[2 Marks]

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

(A)

$|x(t)|^{2} + |\frac{dx(t)}{dt}|^{2} = 0$ for all $t \ge 0$

(B)

$|x(t)|^{2} + |\frac{dx(t)}{dt}|^{2} = c$ for all $t \ge 0$, for some real constant $c > 0$

(C)

$|x(t)|^{2} + |\frac{dx(t)}{dt}|^{2} = e^{jt}$ for all $t \ge 0$

(D)

$|x(t)|^{2} + |\frac{dx(t)}{dt}|^{2} = \sin t$ for all $t \ge 0$

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q19

NAT[2 Marks]

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

Explanation

Electricity and Magnetism

4 Questions

GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q20

MCQ[1 Mark]

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 $\vec{F} = (a\hat{i}+b\hat{j}+c\hat{k})$ N. The values of (a, b, c) are

(A)

$a=\frac{1}{\sqrt{3}}, b=\frac{1}{\sqrt{3}}, c=\frac{1}{\sqrt{3}}$

(B)

$a=\frac{1}{3}, b=\frac{1}{3}, c=\frac{1}{3}$

(C)

$a=0, b=1, c=\frac{1}{\sqrt{3}}$

(D)

$a=0, b=1, c=\frac{1}{3}$

Explanation

GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q21

NAT[1 Mark]

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)

Explanation

GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q22

MCQ[2 Marks]

An electric field in free space is $\vec{E} = (2x+5y+6z)\hat{i} + (5x+4y+10z)\hat{j} + (6x+10y+2z)\hat{k}$ V/m. The charge density is $\epsilon_{0}$ is the permittivity of free space)

(A)

$8\epsilon_{0}$

(B)

$10\epsilon_{0}$

(C)

$6\epsilon_{0}$

(D)

$4\epsilon_{0}$

Explanation

GATE→2026→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q23

MCQ[2 Marks]

A straight thin wire carrying a current of $I = 1$ A in the direction $\hat{n} = \frac{1}{\sqrt{6}}\hat{i} + \frac{2}{\sqrt{6}}\hat{j} + \frac{1}{\sqrt{6}}\hat{k}$ 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)

$2\sqrt{6}\hat{i} - 2\sqrt{6}\hat{k}$

(B)

$\sqrt{\frac{3}{2}}\hat{i} - \sqrt{\frac{3}{4}}\hat{j} + \sqrt{\frac{3}{4}}\hat{k}$

(C)

$\frac{4}{\sqrt{6}}\hat{i} - \frac{4}{\sqrt{6}}\hat{k}$

(D)

$\sqrt{\frac{3}{2}}\hat{i} + \sqrt{\frac{3}{4}}\hat{j} + \sqrt{\frac{3}{4}}\hat{h}$

Explanation

Electrical Circuits and Machines

7 Questions

GATE→2026→Electrical Circuits and Machines→Electrical Circuits

Q24

MCQ[1 Mark]

The RLC filter shown below acts as a

(A)

low pass filter

(B)

high pass filter

(C)

band pass filter

(D)

band stop filter

Explanation

GATE→2026→Electrical Circuits and Machines→Electrical Circuits

Q25

MCQ[1 Mark]

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)

$Z_{2}' \le 0.5 Z_{2}$

Explanation

GATE→2026→Electrical Circuits and Machines→Electrical Circuits

Q26

NAT[1 Mark]

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

Explanation

GATE→2026→Electrical Circuits and Machines→Electrical Circuits

Q27

NAT[1 Mark]

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

Explanation

GATE→2026→Electrical Circuits and Machines→Electrical Circuits

Q28

MCQ[2 Marks]

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.

(A)

5.67

(B)

8.33

(C)

10.33

(D)

25.67

Explanation

GATE→2026→Electrical Circuits and Machines→Electrical Circuits

Q29

MCQ[2 Marks]

In the circuit shown below, the value of the output voltage $V_{0}$ is V.

(A)

2

(B)

3

(C)

4

(D)

8

Explanation

GATE→2026→Electrical Circuits and Machines→Electrical Machines

Q30

NAT[2 Marks]

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)

Explanation

Signals and Systems

5 Questions

GATE→2026→Signals and Systems→Signals and Systems

Q31

MCQ[1 Mark]

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

Explanation

GATE→2026→Signals and Systems→Signals and Systems

Q32

MCQ[1 Mark]

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

(A)

15

(B)

60

(C)

30

(D)

2

Explanation

GATE→2026→Signals and Systems→Signals and Systems

Q33

MCQ[2 Marks]

A signal $x(t)$ is shown below. The plot of $y(t) = 1 - x(4-t)$ is shown in

(A)

Plot A

(B)

Plot B

(C)

Plot C

(D)

Plot D

Explanation

GATE→2026→Signals and Systems→Signals and Systems

Q34

MCQ[2 Marks]

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

Explanation

GATE→2026→Signals and Systems→Signals and Systems

Q35

MCQ[2 Marks]

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)

\frac{e^{-3s}[e^{s}-1]}{s(s+4)}

(B)

\frac{e^{-s}[e^{-3s}-1]}{(s+3)(s+4)}

(C)

\frac{e^{-3s}[1-e^{s}]}{(s+3)(s+4)}

(D)

\frac{e^{-3s}[1-e^{s}]}{s(s+4)}

Explanation

Control Systems

4 Questions

GATE→2026→Control Systems→Control Systems and Actuators

Q36

MCQ[1 Mark]

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

(A)

(i) and (ii) only

(B)

(i) only

(C)

(ii) only

(D)

(ii) and (iii) only

Explanation

GATE→2026→Control Systems→Control Systems and Actuators

Q37

MCQ[2 Marks]

A linear time invariant (LTI) system is described by state space matrices. The poles of the system are

(A)

-2, -5

(B)

2, 5

(C)

-2, 5

(D)

2, -5

Explanation

GATE→2026→Control Systems→Control Systems and Actuators

Q38

NAT[2 Marks]

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)

Explanation

GATE→2026→Control Systems→Control Systems and Actuators

Q39

NAT[2 Marks]

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

Explanation

Analog Electronics

4 Questions

GATE→2026→Analog Electronics→Analog Electronics

Q40

MCQ[1 Mark]

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

Explanation

GATE→2026→Analog Electronics→Analog Electronics

Q41

MCQ[1 Mark]

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

Explanation

GATE→2026→Analog Electronics→Analog Electronics

Q42

MCQ[2 Marks]

In the circuit shown below, R is 1 k\Omega and R_{f} is 10 k\Omega. If V_{in} is 100 mV and the op-amps have supply voltages of \pm 15 V, then $V_{out}$ is V.

(A)

-15

(B)

15

(C)

2.1

(D)

1.1

Explanation

GATE→2026→Analog Electronics→Analog Electronics

Q43

MCQ[2 Marks]

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

(A)

0.5

(B)

0.707

(C)

1.0

(D)

1.414

Explanation

Digital Electronics

5 Questions

GATE→2026→Digital Electronics→Digital Electronics and Embedded Systems

Q44

MCQ[1 Mark]

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

Explanation

GATE→2026→Digital Electronics→Digital Electronics and Embedded Systems

Q45

NAT[1 Mark]

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

Explanation

GATE→2026→Digital Electronics→Digital Electronics and Embedded Systems

Q46

MCQ[2 Marks]

The initial state of $Q_{3}Q_{2}Q_{1}Q_{0}$ in the digital circuit shown below is 1011. The new value of $Q_{3}Q_{2}Q_{1}Q_{0}$ after two rising edges of the clock (CLK) will be

(A)

1101

(B)

0101

(C)

1010

(D)

1011

Explanation

GATE→2026→Digital Electronics→Digital Electronics and Embedded Systems

Q47

MSQ[2 Marks]

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)

$f = \overline{A \cdot (B + C)}$

Explanation

GATE→2026→Digital Electronics→Digital Electronics and Embedded Systems

Q48

MSQ[2 Marks]

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).

Explanation

Measurements

5 Questions

GATE→2026→Measurements→Measurements and Instruments

Q49

MCQ[1 Mark]

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

Explanation

GATE→2026→Measurements→Measurements and Instruments

Q50

MSQ[1 Mark]

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

(A)

$(500 \pm 37.5)$ mW

(B)

$(500 \pm 12.5)$ mW

(C)

$500 \text{ mW} \pm 7.5\%$

(D)

$500 \text{ mW} \pm 2.5\%$

Explanation

GATE→2026→Measurements→Measurements and Instruments

Q51

MCQ[2 Marks]

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

Explanation

GATE→2026→Measurements→Measurements and Instruments

Q52

MCQ[2 Marks]

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

(A)

$metre \to second \to kilogram \to kelvin$

(B)

$second \to metre \to kilogram \to kelvin$

(C)

$metre \to second \to kelvin \to kilogram$

(D)

$second \to kilogram \to kelvin \to metre$

Explanation

GATE→2026→Measurements→Measurements and Instruments

Q53

NAT[2 Marks]

A digital counter increments its count every 0.1 \mu 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)

Explanation

Sensors and Industrial Instrumentation

6 Questions

GATE→2026→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q54

MCQ[1 Mark]

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

Explanation

GATE→2026→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q55

MCQ[1 Mark]

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

Explanation

GATE→2026→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q56

MSQ[1 Mark]

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.

Explanation

GATE→2026→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q57

MCQ[2 Marks]

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 $\epsilon_{0} = 8.854 \times 10^{-12}$ F/m)

(A)

10.0

(B)

14.1

(C)

25.0

(D)

30.0

Explanation

GATE→2026→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q58

MCQ[2 Marks]

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

Explanation

GATE→2026→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q59

NAT[2 Marks]

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)

Explanation

Communication and Optical Instrumentation

6 Questions

GATE→2026→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q60

MCQ[1 Mark]

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

Explanation

GATE→2026→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q61

MCQ[1 Mark]

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

Explanation

GATE→2026→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q62

MCQ[2 Marks]

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

Explanation

GATE→2026→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q63

NAT[2 Marks]

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

Explanation

GATE→2026→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q64

NAT[2 Marks]

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)

Explanation

GATE→2026→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q65

NAT[2 Marks]

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 \Omega load is \mu W. (rounded off to the nearest integer)

Explanation