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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(10)Electricity and Magnetism(2)Electrical Circuits and Machines(5)Signals and Systems(7)Control Systems(6)Analog Electronics(5)Digital Electronics(2)Measurements(11)Sensors and Industrial Instrumentation(5)Communication and Optical Instrumentation(2)

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

If '$\rightarrow$' denotes increasing order of intensity, then the meaning of the words [drizzle $\rightarrow$ rain $\rightarrow$ downpour] is analogous to [$\rule{1cm}{0.15mm}$ $\rightarrow$ quarrel $\rightarrow$ feud]. Which one of the given options is appropriate to fill the blank?

(A)

bicker

(B)

bog

(C)

dither

(D)

dodge

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Statements: 1. All heroes are winners. 2. All winners are lucky people.\nInferences:\nI. All lucky people are heroes.\nII. Some lucky people are heroes.\nIII. Some winners are heroes.\nWhich of the above inferences can be logically deduced from statements 1 and 2?

(A)

Only I and II

(B)

Only II and III

(C)

Only I and III

(D)

Only II

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

A student was supposed to multiply a positive real number p with another positive real number q. Instead, the student divided p by q. If the percentage error in the student's answer is 80%, the value of q is

(A)

5

(B)

\sqrt{2}

(C)

0.2

(D)

\sqrt{5}

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

If the sum of the first 20 consecutive positive odd numbers is divided by $20^{2}$, the result is

(A)

1

(B)

20

(C)

2

(D)

1/2

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is

(A)

150

(B)

200

(C)

250

(D)

175

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.\nYoko Roi stands (i) as an author for standing (ii) as an honorary fellow, after she stood (iii) the freedom of her writings that stand (iv) .

(A)

(i) out, (ii) down, (iii) in, (iv) up

(B)

(i) down, (ii) out, (iii) in, (iv) up

(C)

(i) down, (ii) out, (iii) up, (iv) in

(D)

(i) out, (ii) down, (iii) up, (iv) in

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder... The ratio of the occupied space to the empty space of the container is

(A)

5/2

(B)

7/2

(C)

9/2

(D)

11/2

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q8

MCQ[2 Marks]

The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true?

(A)

The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk reduction on increasing the steps/day from 10000 to 20000.

(B)

The risk reduction on increasing the steps/day from 0 to 5000 is less than the risk reduction on increasing the steps/day from 15000 to 20000.

(C)

For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000.

(D)

For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000.

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B. If viewed from direction Y, Figure A will appear as

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is

(A)

120^{\circ}

(B)

60^{\circ}

(C)

90^{\circ}

(D)

180^{\circ}

Explanation

Engineering Mathematics

10 Questions

GATE→2024→Engineering Mathematics→Analysis of Complex Variables

Q11

MCQ[1 Mark]

Let $z = x + iy$ be a complex variable and $\bar{z}$ be its complex conjugate. The equation $\bar{z}^{2} + z^{2} = 2$ represents a

(A)

parabola

(B)

hyperbola

(C)

ellipse

(D)

circle

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

A matrix M is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as $M = \begin{bmatrix} v_{1} & v_{2} & v_{3} \end{bmatrix}$. Choose the set of vectors from the following options such that $rank(M) = 3$.

(A)

v_{1} = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}, v_{2} = \begin{bmatrix} 0 \\ -1 \\ 0 \end{bmatrix}, v_{3} = \begin{bmatrix} 1 \\ -1 \\ 1 \end{bmatrix}

(B)

v_{1} = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, v_{2} = \begin{bmatrix} -1 \\ 0 \\ 1 \end{bmatrix}, v_{3} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}

(C)

v_{1} = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}, v_{2} = \begin{bmatrix} -1 \\ 0 \\ 1 \end{bmatrix}, v_{3} = \begin{bmatrix} 1 \\ -1 \\ 1 \end{bmatrix}

(D)

v_{1} = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}, v_{2} = \begin{bmatrix} -1 \\ 1 \\ -1 \end{bmatrix}, v_{3} = \begin{bmatrix} 0 \\ -1 \\ 0 \end{bmatrix}

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q13

NAT[1 Mark]

A 3 x 3 matrix P with all real elements has eigenvalues $\frac{1}{4}$, 1, and -2. The value of $|P^{-1}|$ is (rounded off to nearest integer).

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q14

NAT[1 Mark]

Consider a system given by the following first order differential equation: $\frac{dy}{dt} = y + 2t - t^{2}$ where, $y(0) = 1$ and $0 \le t < \infty$. Using a step size $h = 0.1$ for the improved Euler method, the value of $y(t)$ at $t = 0.1$ is (rounded off to two decimal places).

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q15

NAT[1 Mark]

Indian Premier League has divided the sixteen cricket teams into two equal pools... the probability that one team has a blue logo jersey and another has a red logo jersey is (rounded off to one decimal place).

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

Let C be the closed curve in the xy-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at (0,0), (2,0), (2,1), (0,1). The value of the line integral $\oint_{C} (-e^{y} dx + e^{x} dy)$ is

(A)

e^{2} + 2e - 3

(B)

e^{2} - 2e - 3

(C)

e^{2} + e - 1

(D)

e^{2} + e + 1

Explanation

GATE→2024→Engineering Mathematics→Analysis of Complex Variables

Q17

MSQ[2 Marks]

The complex functions $f(z) = u(x,y) + i v(x,y)$ and $\overline{f(z)} = u(x,y) - i v(x,y)$ are both analytic in a given domain. Choose the correct option(s) from the following.

(A)

\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} = 0

(B)

\frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x} \neq 0

(C)

\frac{df(z)}{dz} = 0

(D)

\frac{df(z)}{dz} \neq 0

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q18

NAT[2 Marks]

The readings recorded from a 20-psig pressure gauge are given in the Table... The regression coefficient of determination, $R^{2} =$ (rounded off to three decimal places).

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q19

NAT[2 Marks]

The solution of an ordinary differential equation $y''' + 3y'' + 3y' + y = 30e^{-t}$ is $y(t) = (c_{0} + c_{1}t - c_{2}t^{2} + c_{3}t^{3})e^{-t}$... The value of $(c_{0} + c_{1} + c_{2} + c_{3})$ is (rounded off to nearest integer).

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q20

NAT[2 Marks]

A random variable X has a probability density function... The probability of $X > 2$ is (rounded off to three decimal places).

Explanation

Electricity and Magnetism

2 Questions

GATE→2024→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q21

MCQ[1 Mark]

The capacitance formed between two concentric spherical metal shells having radii x and y with $y > x$ is

(A)

4\pi\epsilon \left(\frac{xy}{y-x}\right)

(B)

4\pi\epsilon \left(\frac{x^{2}}{y-x}\right)

(C)

4\pi\epsilon \left(\frac{y^{2}}{y-x}\right)

(D)

4\pi\epsilon \left(\frac{y^{2}-xy}{x}\right)

Explanation

GATE→2024→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q22

MCQ[2 Marks]

A wire of circular cross section with radius a is shown in the figure. The current density is given by $J = ks^{2}$, where k is a constant, s is the radial distance from the axis and $0 \le s \le a$. The total current I in the wire is

(A)

\frac{\pi ka^{4}}{2}

(B)

\frac{2\pi ka^{3}}{3}

(C)

\frac{\pi ka^{3}}{2}

(D)

\frac{\pi ka^{4}}{4}

Explanation

Electrical Circuits and Machines

5 Questions

GATE→2024→Electrical Circuits and Machines→Electrical Circuits

Q23

NAT[1 Mark]

The switch in the following figure has been closed for a long time ($t < 0$). It is opened at $t = 0$ seconds. The value of $dv_{c}/dt$ at $t = 0^{+}$ is V/s (rounded off to nearest integer).

Explanation

GATE→2024→Electrical Circuits and Machines→Electrical Circuits

Q24

NAT[2 Marks]

In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t = 2$ ms is V (rounded off to one decimal place).

Explanation

GATE→2024→Electrical Circuits and Machines→Electrical Machines

Q25

NAT[2 Marks]

A 50 kVA transformer has an efficiency of 95% at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer at 75% of the full load and 0.8 power factor is % (rounded off to one decimal place).

Explanation

GATE→2024→Electrical Circuits and Machines→Electrical Machines

Q26

NAT[2 Marks]

A three-phase squirrel-cage induction motor has a starting torque of 100% of the full load torque and a maximum torque of 300% of the full load torque. Neglecting the stator impedance, the slip at the maximum torque is % (rounded off to two decimal places).

Explanation

GATE→2024→Electrical Circuits and Machines→Electrical Circuits

Q27

NAT[2 Marks]

Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of 500 mH. When connected in series-opposing configuration, the coils have a total inductance of 300 mH. If the self-inductance of both the coils are equal, then the coupling coefficient is (rounded off to two decimal places).

Explanation

Signals and Systems

7 Questions

GATE→2024→Signals and Systems→Signals and Systems

Q28

MCQ[1 Mark]

A discrete-time sequence is given by $x[n] = [1, 2, 3, 4]$ for $0 \le n \le 3$. The zero lag auto-correlation value of $x[n]$ is

(A)

1

(B)

10

(C)

20

(D)

30

Explanation

GATE→2024→Signals and Systems→Signals and Systems

Q29

NAT[1 Mark]

Consider a filter defined by the difference equation $y[n] - 0.5y[n-2] = a x[n-4]$... The value of a is (rounded off to two decimal places).

Explanation

GATE→2024→Signals and Systems→Signals and Systems

Q30

NAT[1 Mark]

The number of complex multiplications required for computing a 16-point DFT using the decimation-in-time radix-2 FFT is (in integer).

Explanation

GATE→2024→Signals and Systems→Signals and Systems

Q31

NAT[1 Mark]

The Nyquist sampling frequency for $x(t) = 10 \sin^{2}(200\pi t)$ is Hz (rounded off to nearest integer).

Explanation

GATE→2024→Signals and Systems→Signals and Systems

Q32

MCQ[2 Marks]

Consider a discrete-time sequence $x[n] = \begin{cases} (0.2)^{n}, & 0 \le n \le 7 \\ 0, & \text{otherwise} \end{cases}$. The region of convergence of $X(z)$, the z-transform of $x[n]$ consists of

(A)

all values of z except $z = 0.2$

(B)

all values of z

(C)

all values of z except $z = 0$

(D)

all values of z except $z = \infty$

Explanation

GATE→2024→Signals and Systems→Signals and Systems

Q33

MCQ[2 Marks]

Laplace transform of a signal $x(t)$ is $X(s) = \frac{1}{s^{2} + 13s + 42}$. Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if the region of convergence is $-7 < \text{Re}\{s\} < -6$.

(A)

-e^{-6t}u(t) - e^{-7t}u(-t)

(B)

-e^{-6t}u(-t) - e^{-7t}u(t)

(C)

e^{-6t}u(t) - e^{-7t}u(-t)

(D)

-e^{-6t}u(-t) - e^{-7t}u(-t)

Explanation

GATE→2024→Signals and Systems→Signals and Systems

Q34

NAT[2 Marks]

The 4-point DFTs of two sequences $x[n]$ and $y[n]$... the value of $z[0]$ is (rounded off to nearest integer).

Explanation

Control Systems

6 Questions

GATE→2024→Control Systems→Control Systems and Actuators

Q35

MCQ[1 Mark]

The pressure drop across a control valve is constant. The control valve with inherent characteristic has decreasing sensitivity. If x represents the fraction of maximum stem position of the control valve, then the function $f(x)$ representing the fraction of maximum flow is

(A)

\alpha^{x-1}, where \alpha is constant

(B)

\sqrt{x}

(C)

x

(D)

x^{2}

Explanation

GATE→2024→Control Systems→Control Systems and Actuators

Q36

MCQ[1 Mark]

Consider the state-space representation of a system $\dot{x} = Ax + Bu$... Choose the matrix A from the following options such that the system has a pole at the origin.

(A)

\begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}

(B)

\begin{bmatrix} 1 & -1.5 \\ -2 & 3 \end{bmatrix}

(C)

\begin{bmatrix} 1 & 1.5 \\ 2 & -3 \end{bmatrix}

(D)

\begin{bmatrix} 0 & 1 \\ -2 & 3 \end{bmatrix}

Explanation

GATE→2024→Control Systems→Control Systems and Actuators

Q37

MCQ[1 Mark]

The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T > 0$, is

(A)

1 - j\omega T

(B)

\frac{1 - j\omega T}{1 + j\omega T}

(C)

1 + j\omega T

(D)

\frac{1}{1 + j\omega T}

Explanation

GATE→2024→Control Systems→Control Systems and Actuators

Q38

MCQ[2 Marks]

Consider the feedback control system shown in the figure. The steady-state error $e_{ss} = \lim_{t \to \infty}(r(t) - y(t))$ due to unit step reference $r(t)$ is

(A)

\frac{K-1}{K}

(B)

\frac{1}{2}

(C)

0

(D)

1-K

Explanation

GATE→2024→Control Systems→Control Systems and Actuators

Q39

MCQ[2 Marks]

The transfer function of a system is $G(s) = \frac{\omega_{n}^{2}}{s^{2} + 2\xi\omega_{n}s + \omega_{n}^{2}}$. Choose the range of $\xi$ and $\omega_{n}$ (in rad/s) from the following options such that the poles lie on the shaded region of the s-plane as shown in the figure.

(A)

\xi \ge \frac{1}{2} and \omega_{n} \ge 2

(B)

\xi \ge \frac{1}{4} and \omega_{n} \ge 2

(C)

\xi \ge \frac{1}{2} and \omega_{n} \ge \sqrt{3}

(D)

\xi \ge \frac{1}{4} and \omega_{n} \ge \sqrt{3}

Explanation

GATE→2024→Control Systems→Control Systems and Actuators

Q40

NAT[2 Marks]

Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the points $s = j\alpha$, $\alpha > 0$, lies on the root locus, the value of $\alpha$ is (rounded off to nearest integer).

Explanation

Analog Electronics

5 Questions

GATE→2024→Analog Electronics→Analog Electronics

Q41

NAT[1 Mark]

Consider the circuit shown in the figure... The corresponding maximum value of resistance $R_{Z}$ is k\Omega (rounded off to one decimal place).

Explanation

GATE→2024→Analog Electronics→Analog Electronics

Q42

NAT[1 Mark]

Figure shows an amplifier using an NMOS transistor... The drain current of the transistor at the operating point is \mu\text{A} (rounded off to nearest integer).

Explanation

GATE→2024→Analog Electronics→Analog Electronics

Q43

MCQ[2 Marks]

In the figure shown, both the opamps $A_{1}$ and $A_{2}$ are ideal, except that the opamp $A_{1}$ has an offset voltage $(V_{os})$ of 1 mV. For $V_{in} = 0$ V, the values of the output voltages $V_{out1}$ and $V_{out2}$, respectively, are

(A)

3 mV and -1 mV

(B)

1 mV and 0 mV

(C)

1 mV and -1 mV

(D)

2 mV and 0 mV

Explanation

GATE→2024→Analog Electronics→Analog Electronics

Q44

MCQ[2 Marks]

In the figure shown, $R = 1$ k\Omega and $C = 0.1$ \mu\text{F}. For a dc gain of -10, the 3 dB cut-off frequency (rounded off to one decimal place) is Hz. Assume the opamp is ideal.

(A)

159.1 Hz

(B)

1591.5 Hz

(C)

1750.7 Hz

(D)

175.0 Hz

Explanation

GATE→2024→Analog Electronics→Analog Electronics

Q45

NAT[2 Marks]

In the figure shown, the diode current is given by $I_{D} = I_{S} e^{\frac{\alpha V_{D}}{T}}$... The change in the output voltage $(V_{out})$ per Kelvin change in temperature is mV (rounded off to one decimal place).

Explanation

Digital Electronics

2 Questions

GATE→2024→Digital Electronics→Digital Electronics and Embedded Systems

Q46

MCQ[1 Mark]

Among the given options, the simplified form of the Boolean function $F = (A + \bar{A}.B) + \bar{A}.(A + \bar{B}).C$ is

(A)

$A + B + C$

(B)

$A . B . C$

(C)

$B + \bar{A}.C$

(D)

\bar{A} + B.C

Explanation

GATE→2024→Digital Electronics→Digital Electronics and Embedded Systems

Q47

MCQ[2 Marks]

In the figure shown, the positive edge triggered D flip-flops are initially reset to $Q=0$... The sequence of output Y from the $3^{rd}$ clock to the $5^{th}$ clock, $Y_{3}Y_{4}Y_{5}$ is

(A)

001

(B)

010

(C)

000

(D)

101

Explanation

Measurements

11 Questions

GATE→2024→Measurements→Measurements and Instruments

Q48

MCQ[1 Mark]

Match the following measuring devices with their principle of measurement.

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q49

NAT[1 Mark]

The resistance of a 20 k\Omega resistor is measured six consecutive times using an LCR meter... the last reading is k\Omega (rounded off to nearest integer).

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q50

NAT[1 Mark]

The voltage applied and the current drawn by a circuit are... The average power absorbed by the circuit is W (rounded off to nearest integer).

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q51

NAT[1 Mark]

The current $i(t)$ drawn by a circuit is given as... The root-mean-square value of $i(t)$ is A (rounded off to one decimal place).

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q52

MCQ[2 Marks]

The measured values from a flow instrument, whose range is between 0 and 2 flow units, are shown in the histogram. The systematic error (bias) and the maximum error (in flow units), respectively are

(A)

0.25 and 0.14

(B)

0.12 and 0.14

(C)

0.01 and 0.10

(D)

0.04 and 0.12

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q53

MCQ[2 Marks]

In the bridge circuit shown in the figure, under balanced condition, the values of R and C respectively, are

(A)

1.010 \Omega and 19.802 \mu\text{F}

(B)

9.901 \Omega and 0.505 \mu\text{F}

(C)

19.802 \Omega and 1.01 \mu\text{F}

(D)

39.604 \Omega and 2.02 \mu\text{F}

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q54

MCQ[2 Marks]

In the figure shown, assume... When the load has a lagging phase angle of \alpha, which one of the following options is correct?

(A)

\alpha = -\gamma \pm \delta \pm \theta - \beta

(B)

\alpha = -\gamma \pm \delta \pm \theta + \beta

(C)

\alpha = \gamma \pm \delta \pm \theta + \beta

(D)

\alpha = \gamma \pm \delta \pm \theta - \beta

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q55

NAT[2 Marks]

In the figure shown, $R = 4.5$ k\Omega, $\Delta R = 1.5$ k\Omega, and INA is assumed to be ideal. The equivalent resistance between A and B is k\Omega (rounded off to nearest integer).

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q56

NAT[2 Marks]

Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is \Omega (rounded off to nearest integer).

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q57

NAT[2 Marks]

A shielded cable with $C_{stray} = 20$ pF and $R_{wire} = 10$ \Omega is used to connect the inductive sensors as shown in the figure. The RMS value of $V_{out}$ is V (rounded off to two decimal places).

Explanation

GATE→2024→Measurements→Measurements and Instruments

Q58

NAT[2 Marks]

In the figure shown, Sw is a switch... the voltmeter reading is V (rounded off to nearest integer).

Explanation

Sensors and Industrial Instrumentation

5 Questions

GATE→2024→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q59

MCQ[1 Mark]

The capacitor shown in the figure has parallel plates... If $d_{1}$ is decreased by $\delta d_{1}$ the resultant capacitance becomes

(A)

\frac{\epsilon_{0}A}{d_{1} - \delta d_{1} + \frac{d_{2}}{\epsilon_{2}}}

(B)

\frac{\epsilon_{0}A}{d_{2} + \frac{d_{1}}{\epsilon_{2}}}

(C)

\frac{\epsilon_{0}A}{d_{2} - \delta d_{2} + \frac{d_{1}}{\epsilon_{2}}}

(D)

\frac{\epsilon_{0}A}{d_{1} + \delta d_{1} + \frac{d_{2}}{\epsilon_{2}}}

Explanation

GATE→2024→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q60

NAT[1 Mark]

A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is mA/$^{\circ}\text{C}$ (rounded off to two decimal places).

Explanation

GATE→2024→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q61

NAT[1 Mark]

Consider the readout circuit of a piezoelectric sensor shown in the figure... the corresponding change in the voltage $V_{out}$ is V (rounded off to nearest integer).

Explanation

GATE→2024→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q62

NAT[1 Mark]

A linear potentiometer (0-10 k\Omega) is used to measure the water level... If $V_{out} = 5$ V, the water level is cm (rounded off to one decimal place).

Explanation

GATE→2024→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q63

NAT[2 Marks]

Consider the capacitive sensor circuit and its output voltage shown in the figure... The frequency of the output voltage $V_{0}$ is kHz (rounded off to two decimal places).

Explanation

Communication and Optical Instrumentation

2 Questions

GATE→2024→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q64

MCQ[2 Marks]

Consider an ultrasonic measurement system shown in the figure... the modulation index (\beta) and the frequency deviation in $y(t)$, respectively, are

(A)

0.25 \text{ and } \pm 250 Hz

(B)

0.5 \text{ and } \pm 500 Hz

(C)

1 \text{ and } \pm 1000 Hz

(D)

0.75 \text{ and } \pm 1000 Hz

Explanation

GATE→2024→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q65

NAT[2 Marks]

An ADC has a full scale voltage of 1.4 V, resolution of 200 mV... The data rate at the output of the parallel-to-serial converter is Gbps (rounded off to nearest integer).

Explanation