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Type:ALLMCQNATMSQ

General Aptitude(10)Engineering Mathematics(9)Electricity and Magnetism(1)Electrical Circuits and Machines(6)Signals and Systems(6)Control Systems(5)Analog Electronics(7)Digital Electronics(6)Measurements(9)Sensors and Industrial Instrumentation(4)Communication and Optical Instrumentation(2)

General Aptitude

10 Questions

GATE→2023→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

The village was nestled in a green spot, _____ the ocean and the hills.

(A)

through

(B)

in

(C)

at

(D)

between

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Disagree : Protest :: Agree : _____ (By word meaning)

(A)

Refuse

(B)

Pretext

(C)

Recommend

(D)

Refute

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

A 'frabjous' number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

(A)

125

(B)

720

(C)

60

(D)

80

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A)

The median is at least as large as the mean.

(B)

The mean is at least as large as the median.

(C)

At most half the candidates have a score that is larger than the median.

(D)

At most half the candidates have a score that is larger than the mean.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Residency is a famous housing complex... Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A)

Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B)

All academicians residing in the complex are well established in their fields.

(C)

Some authors of best-selling books are residents of the complex who are well established in their fields.

(D)

Some academicians residing in the complex are well established in their fields.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Ankita has to climb 5 stairs starting at the ground... The value of $F(5)$ is

(A)

8

(B)

7

(C)

6

(D)

5

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q8

MCQ[2 Marks]

The information contained in DNA is used to synthesize proteins... Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(A)

only (i)

(B)

only (ii)

(C)

both (i) and (ii)

(D)

neither (i) nor (ii)

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Which one of the given figures P, Q, R and S represents the graph of the following function? $f(x) = ||x+2| - |x-1||$

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

An opaque cylinder is suspended in the path of a parallel beam of light... Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

Engineering Mathematics

9 Questions

GATE→2023→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Choose solution set S corresponding to the systems of two equations $x - 2y + z = 0$, $x - z = 0$

(A)

$S = \{\alpha \begin{bmatrix} 1 \\ 1 \end{bmatrix} | \alpha \in \mathbb{R}\}$

(B)

$S = \{\alpha \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} + \beta \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} | \alpha, \beta \in \mathbb{R}\}$

(C)

$S = \{\alpha \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} + \beta \begin{bmatrix} 2 \\ 1 \\ 2 \end{bmatrix} | \alpha, \beta \in \mathbb{R}\}$

(D)

$S = \{\alpha \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix} | \alpha \in \mathbb{R}\is$

Explanation

GATE→2023→Engineering Mathematics→Analysis of Complex Variables

Q12

MCQ[1 Mark]

$F(z) = \frac{1}{1-z}$, when expanded as a power series around $z = 2$, would result in $F(z) = \sum_{k=0}^{\infty} a_{k}(z-2)^{k}$, with the region of convergence (ROC) $|z-2| < 1$. The coefficients $a_{k}, k \ge 0$, are given by the expression

(A)

(-1)^{k}

(B)

(-1)^{k+1}

(C)

(\frac{1}{2})^{k}

(D)

(\frac{-1}{2})^{k+1}

Explanation

GATE→2023→Engineering Mathematics→Differential Equations

Q13

MCQ[1 Mark]

The solution $x(t), t \ge 0$, to the differential equation with initial conditions $x(0) = 1$ and $\dot{x}(0) = 0$ is

(A)

$x(t) = 2e^{-kt} + 2kt - 1$

(B)

$x(t) = 2e^{-kt} - 1$

(C)

$x(t) = 1$

(D)

$x(t) = 2e^{-kt} - kt - 1$

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q14

MCQ[1 Mark]

What is $\lim_{x \to 0} f(x)$ where $f(x) = x \sin\frac{1}{x}$?

(A)

0

(B)

1

(C)

\infty

(D)

Limit does not exist

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q15

NAT[1 Mark]

X is a discrete random variable which takes values 0, 1 and 2... The value of $E[X] - E[X^{2}]$ is (rounded off to one decimal place).

Explanation

GATE→2023→Engineering Mathematics→Analysis of Complex Variables

Q16

MCQ[2 Marks]

Let $f(z) = j \frac{1-z}{1+z}$ where z denotes a complex number and j denotes $\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the real axis to the

(A)

unit circle with centre at the origin

(B)

unit circle with centre not at the origin

(C)

imaginary axis

(D)

real axis

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q17

NAT[2 Marks]

How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with exactly one digit appearing twice?

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q18

NAT[2 Marks]

Consider the real-valued function $g(x) = \max\{(x-2)^{2}, -2x+7\}$, where $x \in (-\infty, \infty)$. The minimum value attained by $g(x)$ is (rounded off to one decimal place).

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q19

NAT[2 Marks]

The rank of the matrix A given below is one. The ratio $\frac{\alpha}{\beta}$ is (rounded off to the nearest integer).

Explanation

Electricity and Magnetism

1 Question

GATE→2023→Electricity and Magnetism→Electric and Magnetic Fields & Laws

Q20

NAT[1 Mark]

The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them is 10 \mu\text{N/m}. When the gap is doubled, the force per unit length will be \mu\text{N/m} (rounded off to one decimal place).

Explanation

Electrical Circuits and Machines

6 Questions

GATE→2023→Electrical Circuits and Machines→Electrical Circuits

Q21

NAT[1 Mark]

In the circuit given, the Thevenin equivalent resistance $R_{th}$ across the terminals 'a' and 'b' is \Omega (rounded off to one decimal place).

Explanation

GATE→2023→Electrical Circuits and Machines→Electrical Machines

Q22

NAT[1 Mark]

The no-load steady-state output voltage of a DC shunt generator is 200 V when it is driven in the clockwise direction at its rated speed. If the same machine is driven at the rated speed but in the opposite direction, the steady-state output voltage will be V (rounded off to the nearest integer).

Explanation

GATE→2023→Electrical Circuits and Machines→Electrical Circuits

Q23

NAT[2 Marks]

In the circuit shown, $\omega = 100\pi$ rad/s, $R_{1} = R_{2} = 2.2$ \Omega and $L = 7$ mH. The capacitance C for which $Y_{in}$ is purely real is mF (rounded off to two decimal places).

Explanation

GATE→2023→Electrical Circuits and Machines→Electrical Circuits

Q24

NAT[2 Marks]

The R-L circuit with $R = 10$ k\Omega and $L = 1$ mH is excited by a step current $I_{0}u(t)$... The minimum time taken for the current through the inductor to reach 99% of its final value is \mu\text{s} (rounded off to two decimal places).

Explanation

GATE→2023→Electrical Circuits and Machines→Electrical Circuits

Q25

NAT[2 Marks]

A sinusoidal current of $i_{1}(t) = 1 \sin(200\pi t)$ mA is flowing through a 4 H inductor... The peak energy stored in the circuit is \mu\text{J} (rounded off to two decimal places).

Explanation

GATE→2023→Electrical Circuits and Machines→Electrical Circuits

Q26

NAT[2 Marks]

The voltage source $V_{s} = 10\sqrt{2}\sin(20000\pi t)$ V has an internal resistance of 50 \Omega. The RMS value of the current through R is mA (rounded off to one decimal place).

Explanation

Signals and Systems

6 Questions

GATE→2023→Signals and Systems→Signals and Systems

Q27

MCQ[1 Mark]

A system has the transfer-function $\frac{Y(s)}{X(s)} = \frac{s - \pi}{s + \pi}$. Let $u(t)$ be the unit-step function. The input $x(t)$ that results in a steady-state output $y(t) = \sin(\pi t)$ is

(A)

x(t) = \sin(\pi t)u(t)

(B)

x(t) = \sin(\pi t + \frac{\pi}{2})u(t)

(C)

x(t) = \sin(\pi t - \frac{\pi}{2})u(t)

(D)

x(t) = \cos(\pi t + \frac{\pi}{4})u(t)

Explanation

GATE→2023→Signals and Systems→Signals and Systems

Q28

NAT[1 Mark]

Consider the discrete-time signal $x[n] = u[-n+5] - u[n+3]...$ The smallest n for which $x[n] = 0$ is

Explanation

GATE→2023→Signals and Systems→Signals and Systems

Q29

NAT[1 Mark]

Let $y(t) = x(4t)$, where $x(t)$ is a continuous-time periodic signal with fundamental period of 100 s. The fundamental period of $y(t)$ is s (rounded off to the nearest integer).

Explanation

GATE→2023→Signals and Systems→Signals and Systems

Q30

MCQ[2 Marks]

The impulse response of an LTI system is $h(t) = \delta(t) + 0.5\delta(t-4)$... If the input signal $x(t) = \cos(\frac{7\pi}{4}t)$, the output is

(A)

0.5\cos(\frac{7\pi}{4}t)

(B)

1.5\cos(\frac{7\pi}{4}t)

(C)

0.5\sin(\frac{7\pi}{4}t)

(D)

1.5\sin(\frac{7\pi}{4}t)

Explanation

GATE→2023→Signals and Systems→Signals and Systems

Q31

MCQ[2 Marks]

The Laplace transform of the continuous-time signal $x(t) = e^{-3t}u(t-5)$ is

(A)

\frac{e^{-5s}}{s+3}, \text{Real}\{s\} > -3

(B)

\frac{e^{-5(s-3)}}{s-3}, \text{Real}\{s\} > 3

(C)

\frac{e^{-5(s+3)}}{s+3}, \text{Real}\{s\} > -3

(D)

\frac{e^{-5(s-3)}}{s+3}, \text{Real}\{s\} > -3$

Explanation

GATE→2023→Signals and Systems→Signals and Systems

Q32

MCQ[2 Marks]

A continuous real-valued signal $x(t)$ has finite positive energy and $x(t) = 0, \forall t < 0$. From the list given below, select ALL the signals whose continuous-time Fourier transform is purely imaginary.

(A)

x(t) + x(-t)

(B)

x(t) - x(-t)

(C)

j(x(t) + x(-t))

(D)

j(x(t) - x(-t))

Explanation

Control Systems

5 Questions

GATE→2023→Control Systems→Control Systems and Actuators

Q33

NAT[1 Mark]

The number of zeros of the polynomial $P(s) = s^{3} + 2s^{2} + 5s + 80$ in the right-half plane is

Explanation

GATE→2023→Control Systems→Control Systems and Actuators

Q34

NAT[1 Mark]

The number of times the Nyquist plot of $G(s)H(s) = \frac{1}{2} \frac{(s-1)(s-2)}{(s+1)(s+2)}$ encircles the origin is

Explanation

GATE→2023→Control Systems→Control Systems and Actuators

Q35

MCQ[2 Marks]

The magnitude and phase plots shown in the figure match with the transfer-function

(A)

\frac{10000}{s^{2} + 2s + 10000}

(B)

\frac{10000}{s^{2} + 2s + 10000} e^{-0.05s}

(C)

\frac{10000}{s^{2} + 2s + 10000} e^{-0.5 \times 10^{-12}s}

(D)

\frac{100}{s^{2} + 2s + 100}

Explanation

GATE→2023→Control Systems→Control Systems and Actuators

Q36

NAT[2 Marks]

Consider a standard negative feedback configuration with $G(s)$ and controller $C(s)$... The value of $K_{D}$ is (rounded off to one decimal place).

Explanation

GATE→2023→Control Systems→Control Systems and Actuators

Q37

NAT[2 Marks]

The phase margin of the transfer function $G(s) = \frac{2(1-s)}{(1+s)^{2}}$ is degrees (rounded off to the nearest integer).

Explanation

Analog Electronics

7 Questions

GATE→2023→Analog Electronics→Analog Electronics

Q38

MCQ[1 Mark]

A light emitting diode (LED) emits light when it is _____ biased. A photodiode provides maximum sensitivity to light when it is _____ biased.

(A)

forward, forward

(B)

forward, reverse

(C)

reverse, reverse

(D)

reverse, forward

Explanation

GATE→2023→Analog Electronics→Analog Electronics

Q39

NAT[1 Mark]

The opamp in the circuit shown is ideal, except that it has an input bias current of 1 nA and an input offset voltage of 10 \mu\text{V}. The resulting worst-case output voltage will be \mu\text{V} (rounded off to the nearest integer).

Explanation

GATE→2023→Analog Electronics→Analog Electronics

Q40

NAT[1 Mark]

The diode in the circuit is ideal... The magnitude of the average current flowing through the resistor R is mA (rounded off to two decimal places).

Explanation

GATE→2023→Analog Electronics→Analog Electronics

Q41

NAT[2 Marks]

The figure below shows a feedback amplifier constructed using an nMOS transistor... The ratio $V_{out}/V_{in}$ is (rounded off to two decimal places).

Explanation

GATE→2023→Analog Electronics→Analog Electronics

Q42

NAT[2 Marks]

The opamps in the circuit are ideal. The input signals are $V_{S1} = 3 + 0.10\sin(300t)$ V and $V_{S2} = -2 + 0.11\sin(300t)$ V. The average value of the voltage $V_{0}$ is V (rounded off to two decimal places).

Explanation

GATE→2023→Analog Electronics→Analog Electronics

Q43

NAT[2 Marks]

In the circuit shown, the input voltage $V_{in} = 100$ mV... At $t = 20$ ms, the magnitude of the voltage $V_{0}$ will be mV (rounded off to the nearest integer).

Explanation

GATE→2023→Analog Electronics→Analog Electronics

Q44

NAT[2 Marks]

In the circuit shown, assuming an ideal opamp, the value of the output voltage $V_{0} =$ V (rounded off to one decimal place).

Explanation

Digital Electronics

6 Questions

GATE→2023→Digital Electronics→Digital Electronics and Embedded Systems

Q45

MCQ[1 Mark]

The table shows the present state Q(t), next state Q(t+1), and the control input in a flip-flop. Identify the flip-flop.

(A)

T flip-flop

(B)

D flip-flop

(C)

SR flip-flop

(D)

JK flip-flop

Explanation

GATE→2023→Digital Electronics→Digital Electronics and Embedded Systems

Q46

MCQ[1 Mark]

Match the Exclusive-OR (XOR) operations (i) to (iv) with the results (p) to (s), where X is a Boolean input.

(A)

(i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)

(B)

(i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)

(C)

(i)-(p), (ii)-(s), (iii)-(q), (iv)-(r)

(D)

(i)-(q), (ii)-(p), (iii)-(s), (iv)-(r)

Explanation

GATE→2023→Digital Electronics→Digital Electronics and Embedded Systems

Q47

MCQ[1 Mark]

Choose the fastest logic family among the following:

(A)

Transistor-Transistor Logic

(B)

Emitter-Coupled Logic

(C)

CMOS Logic

(D)

Resistor-Transistor Logic

Explanation

GATE→2023→Digital Electronics→Digital Electronics and Embedded Systems

Q48

MCQ[2 Marks]

The simplified form of the Boolean function $F(W,X,Y,Z) = \Sigma(4,5,10,11,12,13,14,15)$ with the minimum number of terms and smallest number of literals in each term is

(A)

WX + \bar{W}X\bar{Y} + W\bar{X}Y

(B)

WX + WY + X\bar{Y}

(C)

X\bar{Y} + WY

(D)

\bar{X}Y + \bar{W}\bar{Y}

Explanation

GATE→2023→Digital Electronics→Digital Electronics and Embedded Systems

Q49

MCQ[2 Marks]

For the given digital circuit, $A = B = 1$... The frequency of steady-state oscillation of the output Y is

(A)

20 MHz

(B)

15 MHz

(C)

40 MHz

(D)

50 MHz

Explanation

GATE→2023→Digital Electronics→Digital Electronics and Embedded Systems

Q50

MCQ[2 Marks]

In the circuit shown, the initial binary content of shift register A is 1101 and that of shift register B is 1010... What will be the binary content of the shift registers A and B after four clock pulses?

(A)

A = 1101, B = 1101

(B)

A = 1110, B = 1001

(C)

A = 0101, B = 1101

(D)

A = 1010, B = 1111

Explanation

Measurements

9 Questions

GATE→2023→Measurements→Measurements and Instruments

Q51

MCQ[1 Mark]

Inductance of a coil is measured as 10 mH, using an LCR meter... If a pure copper sheet is brought near the coil, the same LCR meter will read

(A)

less than 10 mH

(B)

10 mH

(C)

more than 10 mH

(D)

less than 10 mH initially and then stabilizes to more than 10 mH

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q52

MCQ[1 Mark]

Capacitance 'C' of a parallel plate structure is calculated as 20 pF... If the meter is assumed to be ideal and it introduces no error due to cable capacitance, which one of the following readings is likely to be correct?

(A)

20.5 pF

(B)

20 pF

(C)

19.5 pF

(D)

10 pF

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q53

NAT[1 Mark]

When the bridge given below is balanced, the current through the resistor $R_{a}$ is mA (rounded off to two decimal places).

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q54

NAT[1 Mark]

The full-scale range of the wattmeter shown in the circuit is 100 W... The wattmeter reading will be W (rounded off to the nearest integer).

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q55

NAT[2 Marks]

Five measurements are made using a weighing machine, and the readings are 80 kg, 79 kg, 81 kg, 79 kg and 81 kg. The sample standard deviation of the measurement is kg (rounded off to two decimal places).

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q56

NAT[2 Marks]

Four strain gauges $R_{A}, R_{B}, R_{C}$ and $R_{D}$... If $R = 100$ \Omega, and $\Delta R = 1$ \Omega, the minimum value of resistance $R_{v}$ required to balance the bridge is \Omega (rounded off to two decimal places).

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q57

NAT[2 Marks]

A short-circuit test is conducted on a single-phase transformer... The primary current (RMS) will be A (rounded off to two decimal places).

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q58

NAT[2 Marks]

In the diagram shown, the frequency of the sinusoidal source voltage $V_{S}$ is 50 Hz... The magnitude of the average value of the multiplier output $V_{0}$ is V (rounded off to one decimal place).

Explanation

GATE→2023→Measurements→Measurements and Instruments

Q59

NAT[2 Marks]

A 1.999 V True RMS 3-1/2 digit multimeter... The worst-case absolute error in the multimeter output is V (rounded off to three decimal places).

Explanation

Sensors and Industrial Instrumentation

4 Questions

GATE→2023→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q60

MCQ[1 Mark]

Which of the following flow meters offers the lowest resistance to the flow?

(A)

Turbine flow meter

(B)

Orifice flow meter

(C)

Venturi meter

(D)

Electromagnetic flow meter

Explanation

GATE→2023→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q61

MCQ[1 Mark]

Pair the quantities (p) to (s) with the measuring devices (i) to (iv).

(A)

(i)-(r), (ii)-(s), (iii)-(q), (iv)-(p)

(B)

(i)-(p), (ii)-(s), (iii)-(r), (iv)-(q)

(C)

(i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

(D)

(i)-(q), (ii)-(s), (iii)-(p), (iv)-(r)

Explanation

GATE→2023→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q62

NAT[2 Marks]

A wire-wound 'resistive potentiometer type' angle sensor with 72 turns... The output (wiper) voltage when the wiper is on top of both the turns 35 and 36 is V (rounded off to two decimal places).

Explanation

GATE→2023→Sensors and Industrial Instrumentation→Sensors and Industrial Instrumentation

Q63

NAT[2 Marks]

The two secondaries of a linear variable differential transformer (LVDT) showed a magnitude of 2 V (RMS)... The output for zero displacement is \mu\text{m} (rounded off to one decimal place).

Explanation

Communication and Optical Instrumentation

2 Questions

GATE→2023→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q64

MCQ[2 Marks]

In a p-i-n photodiode, a pulse of light containing $8 \times 10^{12}$ incident photons... The quantum efficiency of the photodiode at this wavelength is

(A)

50%

(B)

54.2%

(C)

62.5%

(D)

80%

Explanation

GATE→2023→Communication and Optical Instrumentation→Communication and Optical Instrumentation

Q65

NAT[2 Marks]

A silica-glass fiber has a core refractive index of 1.47 and a cladding refractive index of 1.44. If the cladding is completely stripped out and the core is dipped in water having a refractive index of 1.33, the numerical aperture of the modified fiber is (rounded off to three decimal places).

Explanation