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General Aptitude(10)Engineering Mathematics(9)Electricity and Magnetism(2)Electrical Circuits and Machines(6)Signals and Systems(5)Control Systems(5)Analog Electronics(5)Digital Electronics(5)Measurements(10)Sensors and Industrial Instrumentation(7)Communication and Optical Instrumentation(1)

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Despite his initial hesitation, Rehman's _____ to contribute to the success of the project never wavered. Select the most appropriate option to complete the above sentence.

(A)

ambivalence

(B)

satisfaction

(C)

resolve

(D)

revolve

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Bird : Nest :: Bee : _____ Select the correct option to complete the analogy.

(A)

Kennel

(B)

Hammock

(C)

Hive

(D)

Lair

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

If $Pe^{x} = Qe^{-x}$ for all real values of x, which one of the following statements is true?

(A)

$P = Q = 0$

(B)

$P = Q = 1$

(C)

$P = 1; Q = -1$

(D)

\frac{P}{Q} = 0

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

Let $p_{1}$ and $p_{2}$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_{1}$ and $p_{2}$?

(A)

$p_{1} + p_{2}$ is not a prime number.

(B)

$p_{1}p_{2}$ is not a prime number.

(C)

$p_{1} + p_{2} + 1$ is a prime number.

(D)

$p_{1}p_{2} + 1$ is a prime number.

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Based only on the conversation below, identify the logically correct inference: "Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine.

(A)

Ramya knew that Josephine was in the hospital.

(B)

Ramya did not know that Josephine was in the hospital.

(C)

Ramya and Josephine were once close friends; but now, they are not.

(D)

Josephine was in the hospital due to an injury to her leg.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH ?

(A)

CEADP

(B)

IDBFC

(C)

JGIBC

(D)

IBCEC

Explanation

GATE→2025→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

Which one of the following options is correct for the given data in the table?

(A)

$X(i) = X(i-1) + I(i); Y(i) = Y(i-1)I(i); i > 0$

(B)

$X(i) = X(i-1)I(i); Y(i) = Y(i-1) + I(i); i > 0$

(C)

$X(i) = X(i-1)I(i); Y(i) = Y(i-1)I(i); i > 0$

(D)

$X(i) = X(i-1) + I(i); Y(i) = Y(i-1)I(i-1); i > 0$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square. What is the area (in $\text{cm}^{2}$) of the rectangle PLMN?

(A)

$2\sqrt{2}$

(B)

2

(C)

8

(D)

4

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?

(A)

Bridges on P, Q, and T

(B)

Bridges on P, Q, S, and T

(C)

Bridges on Q, R, T, and V

(D)

Bridges on P, Q, S, U, and V

Explanation

Engineering Mathematics

9 Questions

GATE→2025→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

A $2n \times 2n$ matrix $A = [a_{ij}]$ has its elements as $a_{ij} = \begin{cases} \beta & \text{if } (i+j) \text{ is odd}, \\ -\beta & \text{if } (i+j) \text{ is even} \end{cases}$, where n is any integer greater than 2 and $\beta$ is any non-zero real number. The rank of A is

(A)

1

(B)

2

(C)

n

(D)

2n

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q12

MCQ[1 Mark]

The solution of the differential equation $\frac{dy}{dx} = 9 \frac{x}{y}$ represents

(A)

a hyperbola

(B)

a parabola

(C)

an ellipse

(D)

a circle

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q13

NAT[1 Mark]

If one of the eigenvectors of the matrix $A = \begin{bmatrix} -1 & -1 \\ x & -4 \end{bmatrix}$ is along the direction $\begin{bmatrix} \alpha \\ 2\alpha \end{bmatrix}$, where \alpha is any non-zero real number, then the value of x is (in integer).

Explanation

GATE→2025→Engineering Mathematics→Analysis of Complex Variables

Q14

NAT[1 Mark]

Consider the function $f(z) = \frac{2z + 1}{z^{2} - z}$, where z is a complex variable. The sum of the residues at singular points of $f(z)$ is (in integer).

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q15

MCQ[2 Marks]

The value of the surface integral $\iint_{S} (2x+z) dy dz + (2x+z) dx dz + (2z+y) dx dy$ over the sphere $S: x^{2} + y^{2} + z^{2} = 9$ is

(A)

$72\pi$

(B)

$144\pi$

(C)

$36\pi$

(D)

$432\pi$

Explanation

GATE→2025→Engineering Mathematics→Numerical Methods

Q16

MCQ[2 Marks]

Newton-Raphson method is used to compute the inverse of the number 1.6. Among the following options, the initial guess of the solution that results in non-convergence of the iterative process is

(A)

0.55

(B)

0.75

(C)

1.15

(D)

1.25

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q17

MCQ[2 Marks]

The value of the integral $\int_{-\pi}^{\pi} (\cos^{6}x + \cos^{4}x) dx$ is

(A)

\frac{\pi}{2}

(B)

\frac{5\pi}{8}

(C)

\frac{11\pi}{8}

(D)

\frac{9\pi}{8}

Explanation

GATE→2025→Engineering Mathematics→Analysis of Complex Variables

Q18

MSQ[2 Marks]

Choose the correct statement(s) from the following options, regarding Cauchy's theorem on complex integration $\oint_{C} f(z) dz$ where C is a simple closed path in a simply connected domain D.

(A)

Cauchy's theorem cannot be directly applied to conclude that $\oint f(z) dz = 0$ when $f(z) = \frac{1}{z^{2}}$ and C is the unit circle

(B)

If $f(z)$ is analytic in D, then it can be concluded that $\oint_{C} f(z) dz = 0$ for any simple closed path C in D

(C)

The function $f(z)$ must be analytic in D to conclude $\oint_{C} f(z) dz = 0$ for any simple closed path C in D

(D)

$\oint_{C} f(z) dz \neq 0$ when $f(z) = \frac{1}{z^{2}}$, since the function is not analytic at $z=0$

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q19

NAT[2 Marks]

The probability of a student missing a class is 0.1. In a total number of 10 classes, the probability that the student will not miss more than one class is (rounded off to two decimal places).

Explanation

Electricity and Magnetism

2 Questions

GATE→2025→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q20

MCQ[1 Mark]

An infinite sheet of uniform charge $\rho_{s} = 10 \text{ C/m}^{2}$ is placed on $z = 0$ plane. The medium surrounding the sheet has a relative permittivity of 10. The electric flux density, in $\text{C/m}^{2}$, at a point $P(0,0,5)$, is

(A)

5

(B)

0.25

(C)

10

(D)

0.5

Explanation

GATE→2025→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q21

MCQ[1 Mark]

A 60 V DC source with an internal resistance $R_{int} = 0.5$ \Omega is connected through a switch to a pair of infinitely long rails separated by $l = 1$ m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density $B = 0.5$ T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is

(A)

60 N in the direction of motion

(B)

60 N opposite to the direction of motion

(C)

120 N in the direction of motion

(D)

120 N opposite to the direction of motion

Explanation

Electrical Circuits and Machines

6 Questions

GATE→2025→Electrical Circuits and Machines→Electrical Circuits

Q22

MCQ[1 Mark]

The circuit shown in Figure (a) can be represented using its equivalent T-model as shown in Figure (b). The values of the inductances $L_{1}, L_{2}$, and $L_{3}$ in the equivalent T-model are

(A)

$L_{1} = 7$ H, $L_{2} = 6$ H, $L_{3} = -4$ H

(B)

$L_{1} = -1$ H, $L_{2} = -2$ H, $L_{3} = 4$ H

(C)

$L_{1} = 3$ H, $L_{2} = 2$ H, $L_{3} = 9$ H

(D)

$L_{1} = 1$ H, $L_{2} = -2$ H, $L_{3} = -4$ H

Explanation

GATE→2025→Electrical Circuits and Machines→Electrical Circuits

Q23

MCQ[1 Mark]

Three parallel admittances $Y_{a} = -j0.2$ S, $Y_{b} = 0.3$ S, and $Y_{c} = j0.4$ S connected in parallel with a voltage source $V_{s} = 10 \angle 45^{\circ}$ V, draw a total current $I_{s}$ from the source. The currents flowing through each of these admittances are $I_{a}, I_{b}$ and $I_{c}$ respectively. Let $I = I_{b} + I_{c}$. The phase relation between I and $I_{s}$ is

(A)

I leads $I_{s}$ by $19.44^{\circ}$

(B)

I lags $I_{s}$ by $19.44^{\circ}$

(C)

I leads $I_{s}$ by $33.69^{\circ}$

(D)

I lags $I_{s}$ by $33.69^{\circ}$

Explanation

GATE→2025→Electrical Circuits and Machines→Electrical Machines

Q24

MCQ[2 Marks]

A 2-pole, 50 Hz, 3-phase induction motor supplies power to a certain load at 2970 rpm. The torque-speed curve of this machine follows a linear relationship between synchronous speed and 95% of synchronous speed. Assume mechanical and stray losses to be zero. If the load torque of the motor is doubled, the new operating speed of the motor, in rpm, is

(A)

2940

(B)

2812

(C)

2970

(D)

2850

Explanation

GATE→2025→Electrical Circuits and Machines→Electrical Circuits

Q25

NAT[2 Marks]

The circuit given in the figure is driven by a voltage source $V_{s} = 25\sqrt{2} \angle 30^{\circ}$ V... The average power dissipated, in W, in the 50 k\Omega resistance is (rounded off to two decimal places).

Explanation

GATE→2025→Electrical Circuits and Machines→Electrical Circuits

Q26

NAT[2 Marks]

In the circuit shown, the switch is opened at $t = 0$ s. The current $i(t)$ at $t = 2$ ms is mA (rounded off to two decimal places).

Explanation

GATE→2025→Electrical Circuits and Machines→Electrical Circuits

Q27

NAT[2 Marks]

For the circuit shown in the figure, the active power supplied by the source is W (rounded off to one decimal place).

Explanation

Signals and Systems

5 Questions

GATE→2025→Signals and Systems→Signals and Systems

Q28

MCQ[1 Mark]

Let a continuous-time signal be $x(t) = e^{j9t} + e^{j5t}$, where $j = \sqrt{-1}$ and t is in seconds. The fundamental period of magnitude of $x(t)$, in seconds, is

(A)

\pi

(B)

\frac{\pi}{2}

(C)

\frac{\pi}{5}

(D)

\frac{\pi}{9}

Explanation

GATE→2025→Signals and Systems→Signals and Systems

Q29

MCQ[2 Marks]

Let $y[n] = \frac{1}{\alpha}y[n-1] + x[n]$, where $\alpha > 1$ and real, represent a difference equation of a causal discrete-time linear time invariant system. The system is initially at rest. If $x[n] = \delta[n-p]$ where $p > 10$, the value of $y[p+1]$ is

(A)

0

(B)

1

(C)

\frac{1}{\alpha}

(D)

\frac{1}{\alpha^{2}}

Explanation

GATE→2025→Signals and Systems→Signals and Systems

Q30

MCQ[2 Marks]

Let $f(t)$ and $g(t)$ represent continuous-time real-valued signals. If $h(t)$ denotes cross-correlation between $f(t)$ and $g(-t)$, its continuous-time Fourier transform $H(j\omega)$ equals

(A)

$F(j\omega)G(j\omega)$

(B)

$F(-j\omega)G(j\omega)$

(C)

$F(j\omega)G(-j\omega)$

(D)

$-F(j\omega)G(-j\omega)$

Explanation

GATE→2025→Signals and Systems→Signals and Systems

Q31

MSQ[2 Marks]

Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems from the following options.

(A)

$e^{j \frac{2\pi}{3} t}$

(B)

\cos(\frac{2\pi}{3} t)

(C)

$2^{t}$

(D)

\sin(\frac{2\pi}{3} t)

Explanation

GATE→2025→Signals and Systems→Signals and Systems

Q32

NAT[2 Marks]

Let $X(e^{j\omega})$ represent the discrete time Fourier transform of a 4-length sequence $x[n]...$ The value of $y[0]$ is (in integer).

Explanation

Control Systems

5 Questions

GATE→2025→Control Systems→Control Systems and Actuators

Q33

MCQ[1 Mark]

For the transfer function $G(s) = 1 + \frac{2s - 1}{s^{3} + 5s^{2} + 3s + 22}$, the number of zeros lying in the left half of the s-plane is

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2025→Control Systems→Control Systems and Actuators

Q34

MCQ[1 Mark]

Consider the control system block diagram given in Figure (a)... Choose the correct statement from the following options for closed loop stability of the system.

(A)

The locus of $G(s)H(s)$ should encircle the origin twice in the counterclockwise direction

(B)

The locus of $1 + G(s)H(s)$ should encircle the origin twice in the clockwise direction

(C)

The locus of $G(s)H(s)$ should encircle the point $-1 + j0$ twice in the counterclockwise direction

(D)

The locus of $1 + G(s)H(s)$ should encircle the point twice in the clockwise direction

Explanation

GATE→2025→Control Systems→Control Systems and Actuators

Q35

MCQ[2 Marks]

The figure shows a closed-loop system with a plant $G(s) = \frac{1}{s^{2}}$ and a lead compensator $C(s)$. The compensator is designed to place the dominant closed-loop poles at $-1.5 \pm j\frac{\sqrt{27}}{2}$. From the following options, choose the phase lead that the compensator needs to contribute.

(A)

30^{\circ}

(B)

60^{\circ}

(C)

90^{\circ}

(D)

120^{\circ}

Explanation

GATE→2025→Control Systems→Control Systems and Actuators

Q36

MSQ[2 Marks]

The plant in the feedback control system shown in the figure is $P(s) = \frac{a}{s^{2} - b^{2}}$ where $a > 0$ and $b > 0$. The type(s) of controller $C(s)$ that CANNOT stabilize the plant is/are

(A)

proportional (P) controller

(B)

integral (I) controller

(C)

proportional-integral (PI) controller

(D)

proportional-derivative (PD) controller

Explanation

GATE→2025→Control Systems→Control Systems and Actuators

Q37

NAT[2 Marks]

A feedback control system is shown in the figure. The maximum allowable value of n such that the output $y(t)$, due to any step disturbance signal $d(t)$, becomes zero at steady-state, is (in integer).

Explanation

Analog Electronics

5 Questions

GATE→2025→Analog Electronics→Analog Electronics

Q38

MCQ[1 Mark]

For the ideal opamp based circuit shown in the figure, the ratio $\frac{V}{I}$ is

(A)

$(\frac{R_{3} + R_{4}}{R_{1} + R_{3}}) R_{1}$

(B)

$(\frac{R_{2} + R_{4}}{R_{1} + R_{3}}) R_{3}$

(C)

$R_{1} + R_{3}$

(D)

$R_{3} + R_{4}$

Explanation

GATE→2025→Analog Electronics→Analog Electronics

Q39

MSQ[1 Mark]

The circuits mentioned in the following options are realized using ideal opamp. Among these, the circuit(s) performing non-linear operation on the input signal is/are

(A)

Instrumentation amplifier

(B)

Schmitt trigger

(C)

Logarithmic amplifier

(D)

Precision rectifier

Explanation

GATE→2025→Analog Electronics→Analog Electronics

Q40

NAT[1 Mark]

In the circuit shown, assume that the BJT in the circuit has very high \beta and $V_{BE} = 0.7$ V, and the Zener diode has $V_{Z} = 4.7$ V. The current through the LED is mA (rounded off to two decimal places).

Explanation

GATE→2025→Analog Electronics→Analog Electronics

Q41

MCQ[2 Marks]

An chopper amplifier shown in the figure is designed to process a biomedical signal $v_{in}(t)$ to generate conditioned output $v_{out}(t)...$

(A)

The minimum frequency of $s(t)$ required is 100 Hz and $v_{os}(t)$ gets attenuated by the system

(B)

The minimum frequency of $s(t)$ required is 100 Hz and $v_{os}(t)$ also gets amplified by the system by a factor $\frac{200}{\pi}$

(C)

The minimum frequency of $s(t)$ required is 80 Hz and $v_{os}(t)$ gets attenuated by the system

(D)

The minimum frequency of $s(t)$ required is 80 Hz and $v_{os}(t)$ also gets amplified by the system by a factor $\frac{200}{\pi}$

Explanation

GATE→2025→Analog Electronics→Analog Electronics

Q42

MCQ[2 Marks]

A 3-bit DAC is implemented using ideal opamp and switches as shown in the figure... For a digital input of 110, the resistance $R_{in}$ seen from the reference source and the current I, are

(A)

$R_{in} = 2$ \Omega and $I = 3$ mA

(B)

$R_{in} = 12$ k\Omega and $I = 0.5$ mA

(C)

$R_{in} = \infty$ and $I = 1$ mA

(D)

$R_{in} = \infty$ and $I = 3$ mA

Explanation

Digital Electronics

5 Questions

GATE→2025→Digital Electronics→Digital Electronics and Embedded Systems

Q43

MCQ[1 Mark]

The minimized expression of the Boolean function $Y(P,Q,R)$ implemented by the multiplexer (MUX) circuit shown in the figure is

(A)

$Y = R + (P \oplus Q)$

(B)

$Y = R(P \oplus Q)$

(C)

$Y = R + (P \odot Q)$

(D)

$Y = R \oplus (P \oplus Q)$

Explanation

GATE→2025→Digital Electronics→Digital Electronics and Embedded Systems

Q44

MCQ[1 Mark]

The 4-bit signed 2's complement form of $(5)_{10} + (5)_{10}$ is

(A)

$(-6)_{10}$

(B)

$(-7)_{10}$

(C)

$(-5)_{10}$

(D)

$(-8)_{10}$

Explanation

GATE→2025→Digital Electronics→Digital Electronics and Embedded Systems

Q45

MCQ[1 Mark]

A Boolean function X is given as $X = \overline{A}\overline{B} + \overline{A}\overline{C}$. The reduced form of $\overline{X}$ is

(A)

\overline{A} + \overline{B} + \overline{C}

(B)

A + BC

(C)

\overline{A} + \overline{B} + C

(D)

B + AC

Explanation

GATE→2025→Digital Electronics→Digital Electronics and Embedded Systems

Q46

MCQ[2 Marks]

The clock frequency of the digital circuit shown in the figure is 12 MHz. The frequencies of the output (F) corresponding to Control = 0 and Control = 1, respectively, are

(A)

4 MHz and 6 MHz

(B)

6 MHz and 4 MHz

(C)

3 MHz and 4 MHz

(D)

3 MHz and 6 MHz

Explanation

GATE→2025→Digital Electronics→Digital Electronics and Embedded Systems

Q47

MCQ[2 Marks]

An 8-bit microprocessor has 16-bit address bus $(A_{15}-A_{0})$ where $A_{0}$ is the LSB... The address range for the newly added RAM is

(A)

1000 H - 4FFF H

(B)

3000 H - 6FFF H

(C)

4000 H - 7FFF H

(D)

8000 H - BFFF H

Explanation

Measurements

10 Questions

GATE→2025→Measurements→Measurements and Instruments

Q48

MCQ[1 Mark]

In a single-phase AC circuit, the power consumed by load resistance $R_{L}$ for an excitation Vs is measured using a wattmeter. The same wattmeter is connected in two different topologies, Topology-A and Topology-B, as shown in the figure. Among the following options, the condition that ensures low error in the wattmeter reading for both the topologies is

(A)

$V_{L} \gg V_{C}$ for Topology-A and $I_{L} \gg I_{P}$ for Topology-B

(B)

$V_{L} \gg V_{C}$ for Topology-A and $I_{L} \ll I_{P}$ for Topology-B

(C)

$V_{L} \ll V_{C}$ for Topology-A and $I_{L} \ll I_{P}$ for Topology-B

(D)

$V_{L} \ll V_{C}$ for Topology-A and $I_{L} \gg I_{P}$ for Topology-B

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q49

MCQ[1 Mark]

A $3\frac{1}{2}$ digit digital voltmeter has a specified accuracy of $\pm(0.5\% + 1)$. If it is used to measure 10V DC voltage, the error in the measurement would be

(A)

\pm 0.4\%

(B)

\pm 1.5\%

(C)

\pm 0.6\%

(D)

\pm 1\%

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q50

MCQ[1 Mark]

An oscilloscope has an input resistance of $1 \text{ M}\Omega$. A $10\times$ passive attenuating probe is connected to it to increase the input voltage range as well as the effective input resistance. The effective input resistance, in $\text{M}\Omega$, seen into the probe tip is

(A)

0.9

(B)

9.1

(C)

10

(D)

11

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q51

NAT[1 Mark]

A dual-slope ADC has a fixed integration time of 100 ms. The reference voltage of the ADC is -5 V. The time taken by the ADC to measure an input voltage of 1.25 V is ms (rounded off to the nearest integer).

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q52

MCQ[2 Marks]

Power consumed by a three-phase balanced load is measured using two-wattmeter method. The per-phase average power drawn by the load is 30 kW at $\frac{\sqrt{3}}{2}$ lagging power factor. The readings of the wattmeters will be

(A)

15 kW and 15 kW

(B)

22.5 kW and 7.5 kW

(C)

60 kW and 30 kW

(D)

45 kW and 45 kW

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q53

MCQ[2 Marks]

The bridge circuit, shown in Figure (a), can be equivalently represented using the circuit shown in Figure (b). The values of R1, R2, and Vc in the equivalent circuit are

(A)

$R_{1} = 6$ k\Omega, $R_{2} = 3$ k\Omega, and $V_{C} = 9$ V

(B)

$R_{1} = 3$ k\Omega, $R_{2} = 6$ k\Omega, and $V_{C} = 4.5$ V

(C)

$R_{1} = 2$ k\Omega, $R_{2} = 2$ k\Omega, and $V_{C} = 9$ V

(D)

$R_{1} = 2$ k\Omega, $R_{2} = 2$ k\Omega, and $V_{C} = 4.5$ V

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q54

NAT[2 Marks]

Consider an AC bridge shown in the figure... At the bridge balance condition, the frequency of the excitation source $V_{s}$ is kHz (rounded off to two decimal places).

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q55

NAT[2 Marks]

In the circuit shown, the galvanometer (G) has an internal resistance of 100 \Omega. The galvanometer current $I_{G}$ is \mu\text{A} (rounded off to the nearest integer).

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q56

NAT[2 Marks]

A series RLC circuit resonates at 7500 rad/s for inductance $L = 20$ mH and resistance $R = 10$ \Omega... The percentage uncertainty in the measurement of quality factor is % (rounded off to one decimal place).

Explanation

GATE→2025→Measurements→Measurements and Instruments

Q57

NAT[2 Marks]

A signal $V_{M} = 5 \sin(\pi t / 3)$ V is applied... If S is opened at $t = 0.5$ s, the value of $V_{x}$ at $t = 1.5$ s will be V (rounded off to two decimal places).

Explanation

Sensors and Industrial Instrumentation

7 Questions

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q58

MCQ[1 Mark]

The working of the hand-held metal detector most widely used by security personnel for human frisking is based on the principle of

(A)

change in reluctance of an iron core in presence of a metallic object

(B)

change in conductance of an iron core in presence of a metallic object

(C)

electric field induced by a metallic object

(D)

eddy current generation in a metallic object

Explanation

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q59

MCQ[1 Mark]

The primary coil of a linear variable differential transformer (LVDT) is supplied with AC voltage as shown in the figure. The secondary coils are connected in series opposition and the output is measured using a true RMS voltmeter. The displacement x of the core is indicated in mm on a linear scale. At the null position $x=0$ the voltmeter reads 0 V. If the voltmeter reads 0.2 V for a displacement of $x = +2$ mm, then for a displacement of $x = -3$ mm, the voltmeter reading, in V, is

(A)

-0.3

(B)

-0.1

(C)

0.3

(D)

0.1

Explanation

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q60

MCQ[1 Mark]

In the force transducer shown in Figure (a), four identical strain gauges S1, S2, S3, and S4 are mounted on a cantilever at equal distance from its base. S1 and S2 are mounted on the top surface and S3 and S4 are mounted on the bottom surface, as shown in the Figure (a). These strain gauges are to be connected to form a Wheatstone bridge consisting of four arms A, B, C, and D, as shown in the Figure (b). From the following options, the correct order to maximize the measurement sensitivity is

(A)

$A \to S1, B \to S2, C \to S4, D \to S3$

(B)

$A \to S1, B \to S4, C \to S3, D \to S2$

(C)

$A \to S1, B \to S2, C \to S3, D \to S4$

(D)

$A \to S1, B \to S4, C \to S2, D \to S3$

Explanation

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q61

MCQ[1 Mark]

Match the following sensors with their most suitable applications.

(A)

P-II, Q-III, R-I, S-IV

(B)

P-II, Q-IV, R-I, S-III

(C)

P-III, Q-IV, R-II, S-I

(D)

P-III, Q-IV, R-I, S-II

Explanation

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q62

NAT[2 Marks]

A metallic strain-gauge (SG) with resistance $R_{SG}$ is connected as shown in the figure... The measured value of tensile strain is $\times 10^{-3}$ (rounded off to two decimal places).

Explanation

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q63

NAT[2 Marks]

An air filled parallel plate electrostatic actuator is shown in the figure... The magnitude of minimum charge (Q) required to momentarily close the gap between the plates is $\times 10^{-14}$ C (rounded off to two decimal places).

Explanation

GATE→2025→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q64

NAT[2 Marks]

The resistance of a thermistor is measured to be 2.25 k\Omega at $30^{\circ}\text{C}$ and 1.17 k\Omega at $60^{\circ}\text{C}$. Its material constant \beta is K (rounded off to two decimal places).

Explanation

Communication and Optical Instrumentation

1 Question

GATE→2025→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q65

NAT[2 Marks]

A schematic of a Michelson interferometer... If a 532 nm laser beam produces 30 interference fringes on the screen, then the number of fringes produced by a 632.8 nm laser beam will be (rounded off to one decimal place).

Explanation