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General Aptitude(10)Engineering Mathematics(11)Networks, Signals and Systems(9)Electronic Devices(4)Analog Circuits(10)Digital Circuits(5)Control Systems(6)Communications(6)Electromagnetics(4)

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Here are two analogous groups, Group-I and Group-II, that list words in their decreasing order of intensity. Identify the missing word in Group-II. Group-I: Abuse → Insult → Ridicule Group-II: [Missing] → Praise → Appreciate

(A)

Extol

(B)

Prize

(C)

Appropriate

(D)

Espouse

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q2

MCQ[1 Mark]

Had I learnt acting as a child, I ______ a famous film star. Select the most appropriate option to complete the above sentence.

(A)

will be

(B)

can

(C)

am going to be

(D)

could have been

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

The 12 musical notes are given as C, $C^{\#}$, D, $D^{\#}$, E, F, $F^{\#}$, G, $G^{\#}$, A, $A^{\#}$ and B. Frequency of each note is $\sqrt[12]{2}$ times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes $F^{\#}$ and C is:

(A)

$\sqrt[6]{2}$

(B)

$\sqrt{2}$

(C)

$\sqrt[4]{2}$

(D)

2

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is: Note: The figures shown are representative.

(A)

$(\frac{5}{3})^{\frac{n}{2}}$

(B)

$(\frac{5}{3})^{n}$

(C)

$(\frac{5}{3})$

(D)

$(\frac{5}{3})^{n(2n-1)}$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

Which one of the following plots represents $f(x) = -\frac{|x|}{x}$, where x is a non-zero real number? Note: The figures shown are representative.

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed: P. Over time, such adaptations lead to significant evolutionary changes with the potential to shape the development of new species. Q. In natural world, organisms constantly adapt to their environments in response to challenges and opportunities. R. This process of adaptation is driven by the principle of natural selection, where favorable traits increase an organism's chances of survival and reproduction. S. As environments change, organisms that can adapt their behavior, structure and physiology to such changes are more likely to survive.

(A)

$P \rightarrow Q \rightarrow R \rightarrow S$

(B)

$Q \rightarrow S \rightarrow R \rightarrow P$

(C)

$R \rightarrow S \rightarrow Q \rightarrow P$

(D)

$S \rightarrow P \rightarrow R \rightarrow Q$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

A stick of length one meter is broken at two locations at distances of $b_{1}$ and $b_{2}$ from the origin (0), as shown in the figure. Note that $0 < b_{1} < b_{2} < 1$. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces? Note: All lengths are in meter. The figure shown is representative.

(A)

$b_{1} < 0.5$

(B)

$b_{2} > 0.5$

(C)

$b_{2} < b_{1} + 0.5$

(D)

$b_{1} + b_{2} < 1$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction. After the $1^{st}$ round, $4^{th}$ student behind P leaves the game. After $2^{nd}$ round, $5^{th}$ student behind Q leaves the game. After $3^{rd}$ round, $3^{rd}$ student behind V leaves the game. After $4^{th}$ round, $4^{th}$ student behind U leaves the game. Who all are left in the game after the $4^{th}$ round? Note: The figure shown is representative.

(A)

P; T; Q; S

(B)

V; P; T; Q

(C)

W; R; Q;

(D)

Q; T; V; W

Explanation

GATE→2025→General Aptitude→Data Interpretation

Q9

MCQ[2 Marks]

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT? Nation | Gold | Silver | Bronze USA | 40 | 44 | 41 Canada | 39 | 24 | 27 Japan | 12 | 20 | 13 Australia | 19 | 17 | 16 France | 16 | 26 | 22

(A)

France will occupy the third place if the list were made on the basis of the total number of medals won.

(B)

The order of the top two nations will not change even if the list is made on the basis of the total number of medals won.

(C)

USA and Canada together have less than 50% of the medals awarded to the nations in the above table.

(D)

Canada has won twice as many total medals as Japan.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to 5,00,000. For higher fees, the overhead is 1,00,000 plus 10% of the amount by which the fee exceeds 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than ₹10,00,000, what is the maximum consulting fee that the employee can charge?

(A)

7,01,438

(B)

7,24,961

(C)

7,51,232

(D)

7,75,784

Explanation

Engineering Mathematics

11 Questions

GATE→2025→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Consider the matrix A below: $A = \begin{bmatrix} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{bmatrix}$ For which of the following combinations of $\alpha$, $\beta$, and $\gamma$, is the rank of A at least three?

(A)

Only (i), (iii), and (iv)

(B)

Only (iv)

(C)

Only (ii)

(D)

Only (i) and (iii)

Explanation

GATE→2025→Engineering Mathematics→Complex Analysis

Q12

MCQ[1 Mark]

Consider the following series: (i) $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ (ii) $\sum_{n=1}^{\infty} \frac{1}{n(n+1)}$ (iii) $\sum_{n=1}^{\infty} \frac{1}{n!}$ Choose the correct option.

(A)

Only (ii) converges

(B)

Only (ii) and (iii) converge

(C)

Only (iii) converges

(D)

All three converge

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q13

MCQ[1 Mark]

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two balls drawn have different colours?

(A)

$\frac{2}{3}$

(B)

$\frac{1}{3}$

(C)

$\frac{1}{2}$

(D)

1

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q14

MSQ[1 Mark]

Consider the function $f:\mathbb{R} \to \mathbb{R}$ defined as $f(x) = 2x^3 - 3x^2 - 12x + 1$. Which of the following statements is/are correct? (Here, $\mathbb{R}$ is the set of real numbers.)

(A)

f has no global maximizer

(B)

f has no global minimizer

(C)

$x = -1$ is a local minimizer of f

(D)

$x = 2$ is a local maximizer of f

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q15

NAT[1 Mark]

The function $y(t)$ satisfies $t^2 y''(t) - 2ty'(t) + 2y(t) = 0$, where $y'(t)$ and $y''(t)$ denote the first and second derivatives of $y(t)$, respectively. Given $y'(0) = 1$ and $y'(1) = -1$, the maximum value of $y(t)$ over [0,1] is ______ (rounded off to two decimal places).

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q16

MSQ[2 Marks]

Consider a non-negative function $f(x)$ which is continuous and bounded over the interval [2, 8]. Let M and m denote, respectively, the maximum and the minimum values of $f(x)$ over the interval. Among the combinations of $\alpha$ and $\beta$ given below, choose the one(s) for which the inequality $\beta \le \int_2^8 f(x) dx \le \alpha$ is guaranteed to hold.

(A)

$\beta = 5m$, $\alpha = 7M$

(B)

$\beta = 6m$, $\alpha = 5M$

(C)

$\beta = 7m$, $\alpha = 6M$

(D)

$\beta = 7m$, $\alpha = 5M$

Explanation

GATE→2025→Engineering Mathematics→Complex Analysis

Q17

MSQ[2 Marks]

Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle C in the complex plane is/are TRUE?

(A)

$\oint_C e^z dz = 0$

(B)

$\oint_C z^n dz = 0$, where n is an even integer

(C)

$\oint_C \cos z dz \neq 0$

(D)

$\oint_C \sec z dz \neq 0$

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q18

MSQ[2 Marks]

The random variable X takes values in $\{-1, 0, 1\}$ with probabilities $P(X=-1) = P(X=1) = \alpha$ and $P(X=0) = 1-2\alpha$, where $0 < \alpha < \frac{1}{2}$: Let $g(\alpha)$ denote the entropy function of X (in bits), parameterized by $\alpha$. Which of the following statements is/are TRUE?

(A)

$g(0.4) > g(0.3)$

(B)

$g(0.3) > g(0.4)$

(C)

$g(0.3) > g(0.25)$

(D)

$g(0.25) > g(0.3)$

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q19

NAT[2 Marks]

Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable X denote the sum of the outcomes obtained. The expectation of X is ______ (rounded off to two decimal places).

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q20

NAT[2 Marks]

Consider the vectors $a = \begin{bmatrix} 1 \\ 1 \end{bmatrix}$, $b = \begin{bmatrix} 0 \\ 3\sqrt{2} \end{bmatrix}$. For real-valued scalar variable X, the value of $\min_x \|ax - b\|_2$ is ______ (rounded off to two decimal places). ($\|\cdot\|_2$ denotes the Euclidean norm)

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q21

NAT[2 Marks]

X and Y are Bernoulli random variables taking values in $\{0,1\}$. The joint probability mass function of the random variables is given by: $P(X=0, Y=0) = 0.06$, $P(X=0, Y=1) = 0.14$, $P(X=1, Y=0) = 0.24$, $P(X=1, Y=1) = 0.56$. The mutual information $I(X;Y)$ is ______ (rounded off to two decimal places).

Explanation

Networks, Signals and Systems

9 Questions

GATE→2025→Networks, Signals and Systems→LTI Systems

Q22

MCQ[1 Mark]

Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_1[n]$ and $h_2[n]$ denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, $\delta[n]$ is the unit impulse, and $b > 0$. Assuming $h_2[n] \neq \delta[n]$ the overall system (denoted by the dashed box) is

(A)

linear and time invariant

(B)

linear and time variant

(C)

nonlinear and time invariant

(D)

nonlinear and time variant

Explanation

GATE→2025→Networks, Signals and Systems→Continuous-time Signals

Q23

MCQ[1 Mark]

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega) = \int_{-\infty}^{\infty} f(t) \exp(-j \omega t) dt$ exists. Which one of the following statements is always TRUE?

(A)

$|F(\omega)| \le \int_{-\infty}^{\infty} |f(t)| dt$

(B)

$|F(\omega)| > \int_{-\infty}^{\infty} |f(t)| dt$

(C)

$|F(\omega)| \le \int_{-\infty}^{\infty} f(t) dt$

(D)

$|F(\omega)| \ge \int_{-\infty}^{\infty} f(t) dt$

Explanation

GATE→2025→Networks, Signals and Systems→Circuit Analysis

Q24

MCQ[1 Mark]

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3\Omega$ resistor are as indicated. The voltage (in Volts) at node X is ______

(A)

20/3

(B)

32/3

(C)

22/3

(D)

2/3

Explanation

GATE→2025→Networks, Signals and Systems→Circuit Analysis

Q25

MCQ[1 Mark]

Let $i_c$, $i_L$ and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S). Which one of the following is TRUE?

(A)

$i_C = 0.25\angle 180^{\circ}$ A, $i_L = 0.1\angle 0^{\circ}$ A, $i_R = 0.2\angle 90^{\circ}$ A

(B)

$i_C = 4\angle 180^{\circ}$ A, $i_L = 10\angle 0^{\circ}$ A, $i_R = 5\angle 90^{\circ}$ A

(C)

$i_C = 0.25\angle 270^{\circ}$ A, $i_L = 0.1\angle 90^{\circ}$ A, $i_R = 0.2\angle 90^{\circ}$ A

(D)

$i_C = 4\angle 90^{\circ}$ A, $i_L = 10\angle 270^{\circ}$ A, $i_R = 5\angle 0^{\circ}$ A

Explanation

GATE→2025→Networks, Signals and Systems→Discrete-time Signals

Q26

MSQ[1 Mark]

Let $x[n]$ be a discrete-time signal whose Z-transform is $X(z)$. Which of the following statements is/are TRUE?

(A)

The discrete-time Fourier transform (DTFT) of $x[n]$ always exists

(B)

The region of convergence (ROC) of $X(z)$ contains neither poles nor zeros

(C)

The discrete-time Fourier transform (DTFT) exists if the region of convergence (ROC) contains the unit circle

(D)

If $x[n] = \alpha\delta[n]$, where $\delta[n]$ is the unit impulse and a is a scalar, then the region of convergence (ROC) is the entire Z-plane

Explanation

GATE→2025→Networks, Signals and Systems→Continuous-time Signals

Q27

MCQ[2 Marks]

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $[-\omega_c, \omega_c]$, where $\omega_c$ is in rad/sec. The signal $f(t)$ is uniformly sampled to obtain $y(t) = f(t)p(t)$. Here, $p(t) = \sum_{n=-\infty}^{\infty} \delta(t - \tau - nT_s)$, with $\delta(t)$ being the Dirac impulse, $T_s > 0$, and $\tau > 0$. The sampled signal $y(t)$ is passed through an ideal lowpass filter $h(t) = \omega_c T_s \frac{\sin(\omega_c t)}{\pi \omega_c t}$ with cutoff frequency $\omega_c$ and passband gain $T_s$. The output of the filter is given by

(A)

$f(t)$ if $T_s < \pi / \omega_c$

(B)

$f(t-\tau)$ if $T_s < \pi / \omega_c$

(C)

$f(t-\tau)$ if $T_s < 2\pi / \omega_c$

(D)

$T_s f(t)$ if $T_s < 2\pi / \omega_c$

Explanation

GATE→2025→Networks, Signals and Systems→Circuit Analysis

Q28

MCQ[2 Marks]

In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t) = 100 \cos(200 t)$. What should be the value of the variable capacitor C such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A, respectively?

(A)

25 $\mu F$

(B)

4 $\mu F$

(C)

0.25 $\mu F$

(D)

Insufficient information to find C

Explanation

GATE→2025→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q29

MCQ[2 Marks]

The Z-parameter matrix of a two port network relates the port voltages and port currents as follows: $\begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = Z \begin{bmatrix} I_1 \\ I_2 \end{bmatrix}$ The Z-parameter matrix (with each entry in Ohms) of the network shown below is:

(A)

$\begin{bmatrix} 10/3 & 2/3 \\ 2/3 & 10/3 \end{bmatrix}$

(B)

$\begin{bmatrix} 10 & 2 \\ 2 & 10 \end{bmatrix}$

(C)

$\begin{bmatrix} 10/3 & 1/3 \\ 1/3 & 10/3 \end{bmatrix}$

(D)

[Option D]

Explanation

GATE→2025→Networks, Signals and Systems→Continuous-time Signals

Q30

MSQ[2 Marks]

Let $f(t)$ be a periodic signal with fundamental period $T_0 > 0$. Consider the signal $y(t) = f(\alpha t)$, where $\alpha > 1$. The Fourier series expansions of $f(t)$ and $y(t)$ are given by $f(t) = \sum_{k=-\infty}^{\infty} c_k e^{j \frac{2\pi}{T_0} k t}$ and $y(t) = \sum_{k=-\infty}^{\infty} d_k e^{j \frac{2\pi \alpha}{T_0} k t}$. Which of the following statements is/are TRUE?

(A)

$c_k = d_k$ for all k

(B)

$y(t)$ is periodic with a fundamental period $\alpha T_0$

(C)

$c_k = d_k / \alpha$ for all k

(D)

$y(t)$ is periodic with a fundamental period $T_0 / \alpha$

Explanation

Electronic Devices

4 Questions

GATE→2025→Electronic Devices→Semiconductor Physics and Carrier Transport

Q31

MSQ[1 Mark]

Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).

(A)

Arsenic

(B)

Boron

(C)

Gallium

(D)

Phosphorous

Explanation

GATE→2025→Electronic Devices→Semiconductor Physics and Carrier Transport

Q32

MCQ[2 Marks]

The intrinsic carrier concentration of a semiconductor is $2.5 \times 10^{16} / m^3$ at 300 K. If the electron and hole mobilities are $0.15~m^2/Vs$ and $0.05~m^2/Vs$, respectively, then the intrinsic resistivity of the semiconductor (in $k\Omega \cdot m$) at 300 K is (Charge of an electron $e = 1.6 \times 10^{-19} C$.)

(A)

1.65

(B)

1.25

(C)

0.85

(D)

1.95

Explanation

GATE→2025→Electronic Devices→Semiconductor Physics and Carrier Transport

Q33

MCQ[2 Marks]

The electron mobility $\mu_n$ in a non-degenerate germanium semiconductor at 300 K is $0.38~m^2/Vs$. The electron diffusivity $D_n$ at 300 K (in $cm^2/s$, rounded off to the nearest integer) is (Consider the Boltzmann constant $k_B = 1.38 \times 10^{-23} J/K$ and the charge of an electron $e = 1.6 \times 10^{-19} C$.)

(A)

26

(B)

98

(C)

38

(D)

10

Explanation

GATE→2025→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q34

NAT[2 Marks]

An ideal p-n junction germanium diode has a reverse saturation current of $10~\mu A$ at 300 K. The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of 100 mA at 300 K is ______ (Consider the Boltzmann constant $k_B = 1.38 \times 10^{-23} J/K$ and the charge of an electron $e = 1.6 \times 10^{-19} C$.)

Explanation

Analog Circuits

10 Questions

GATE→2025→Analog Circuits→BJT and MOSFET Amplifiers

Q35

MCQ[1 Mark]

A simplified small-signal equivalent circuit of a BJT-based amplifier is given below. The small-signal voltage gain $v_o / v_S$ (in V/V) is

(A)

$\frac{-\beta R_L}{R_S + r_\pi}$

(B)

$\frac{+\beta R_L}{R_S}$

(C)

$\frac{-\beta R_L}{R_S}$

(D)

$\frac{+\beta R_L}{R_S + r_\pi}$

Explanation

GATE→2025→Analog Circuits→BJT and MOSFET Amplifiers

Q36

MCQ[1 Mark]

The ideal BJT in the circuit given below is biased in the active region with a $\beta$ of 100. If $I_B$ is $10~\mu A$, then $V_{CE}$ (in Volts, rounded off to two decimal places) is

(A)

4.95

(B)

3.03

(C)

1.92

(D)

2.50

Explanation

GATE→2025→Analog Circuits→Op-amp Circuits and Compensation

Q37

MSQ[1 Mark]

Which of the following statements is/are TRUE with respect to an ideal opamp?

(A)

It has an infinite input resistance

(B)

It has an infinite output resistance

(C)

It has an infinite open-loop differential gain

(D)

It has an infinite open-loop common-mode gain

Explanation

GATE→2025→Analog Circuits→BJT and MOSFET Amplifiers

Q38

MSQ[1 Mark]

Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?

(A)

The common-gate amplifier has an infinite input resistance

(B)

The common-source amplifier has an infinite input resistance

(C)

The input and output voltages of the common-source amplifier are in phase

(D)

The input and output voltages of the common-drain amplifier are in phase

Explanation

GATE→2025→Analog Circuits→Op-amp Circuits and Compensation

Q39

NAT[1 Mark]

All the components in the bandpass filter given below are ideal. The lower -3 dB frequency of the filter is 1 MHz. The upper -3 dB frequency (in MHz, rounded off to the nearest integer) is ______

Explanation

GATE→2025→Analog Circuits→Op-amp Circuits and Compensation

Q40

NAT[1 Mark]

A 4-bit weighted-resistor DAC with inputs $b_3$, $b_2$, $b_1$, and $b_0$ (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bits are logic '1' and open otherwise. When the input $b_3 b_2 b_1 b_0$ changes from 1110 to 1101, the magnitude of the change in the output voltage $V_O$ (in mV, rounded off to the nearest integer) is ______

Explanation

GATE→2025→Analog Circuits→BJT and MOSFET Amplifiers

Q41

MCQ[2 Marks]

The identical MOSFETS $M_1$ and $M_2$ in the circuit given below are ideal and biased in the saturation region. $M_1$ and $M_2$ have a transconductance $g_m$ of 5 mS. The input signals (in Volts) are: $V_1 = 2.5 + 0.01 \sin \omega t$, $V_2 = 2.5 - 0.01 \sin \omega t$. The output signal $V_3$ (in Volts) is

(A)

$3 + 0.05 \sin \omega t$

(B)

$3 - 0.1 \sin \omega t$

(C)

$4 + 0.1 \sin \omega t$

(D)

$4 - 0.05 \sin \omega t$

Explanation

GATE→2025→Analog Circuits→BJT and MOSFET Amplifiers

Q42

MCQ[2 Marks]

In the circuit shown, the identical transistors Q1 and Q2 are biased in the active region with $\beta = 120$. The Zener diode is in the breakdown region with $V_Z = 5$ V and $I_Z = 25$ mA. If $I_L = 12$ mA and $V_{EB1} = V_{EB2} = 0.7$ V then the values of $R_1$ and $R_2$ (in $k\Omega$, rounded off to one decimal place) are respectively.

(A)

0.6 and 0.4

(B)

1.4 and 2.5

(C)

14.0 and 25.0

(D)

6.0 and 4.0

Explanation

GATE→2025→Analog Circuits→Diode Circuits

Q43

MSQ[2 Marks]

All the diodes in the circuit given below are ideal. Which of the following plots is/are correct when $V_I$ (in Volts) is swept from -M to M?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2025→Analog Circuits→Diode Circuits

Q44

NAT[2 Marks]

The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by $V_I = 10 \sin(100\pi t)$, where time t is in seconds. The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is ______

Explanation

Digital Circuits

5 Questions

GATE→2025→Digital Circuits→Number Representations and Combinatorial Circuits

Q45

MCQ[1 Mark]

A 3-input majority logic gate has inputs X, Y, and Z. The output F of the gate is logic '1' if two or more of the inputs are logic '1'. The output F is logic '0' if two or more of the inputs are logic '0'. Which one of the following options is a Boolean expression of the output F?

(A)

$XY + YZ + ZX$

(B)

$XYZ$

(C)

$X + Y + Z$

(D)

$\overline{X}\overline{Y}\overline{Z}$

Explanation

GATE→2025→Digital Circuits→Number Representations and Combinatorial Circuits

Q46

MCQ[1 Mark]

A full adder and an XOR gate are used to design a digital circuit with inputs X, Y, and Z, and output F, as shown below. The input Z is connected to the carry-in input of the full adder. If the input Z is set to logic '1', then the circuit functions as ______ with X and Y as inputs.

(A)

an adder

(B)

a subtractor

(C)

a multiplier

(D)

a binary to Gray code converter

Explanation

GATE→2025→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q47

MCQ[2 Marks]

A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V. For an input sinusoidal signal with frequency 500 kHz, the maximum SNR (in dB, rounded off to two decimal places) and the data rate (in Mbps) at the output of the ADC are respectively.

(A)

61.96 and 10

(B)

61.96 and 5

(C)

33.36 and 10

(D)

33.36 and 5

Explanation

GATE→2025→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q48

MCQ[2 Marks]

A positive-edge-triggered sequential circuit is shown below. There are no timing violations in the circuit. Input P0 is set to logic '0' and P1 is set to logic '1' at all times. The timing diagram of the inputs SEL and S are also shown below. The sequence of output Y from time $T_0$ to $T_3$ is

(A)

1011

(B)

0010

(C)

1101

(D)

0100

Explanation

GATE→2025→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q49

NAT[2 Marks]

In the circuit shown below, the AND gate has a propagation delay of 1 ns. The edge-triggered flip-flops have a set-up time of 2 ns, a hold-time of 0 ns, and a clock-to-Q delay of 2 ns. The maximum clock frequency (in MHz, rounded off to the nearest integer) such that there are no setup violations is ______

Explanation

Control Systems

6 Questions

GATE→2025→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q50

MCQ[1 Mark]

The Nyquist plot of a system is given in the figure below. Let $\omega_P$, $\omega_Q$, $\omega_R$, and $\omega_S$ be the positive frequencies at the points P, Q, R, and S, respectively. Which one of the following statements is TRUE?

(A)

$\omega_S$ is the gain crossover frequency and $\omega_P$ is the phase crossover frequency

(B)

$\omega_Q$ is the gain crossover frequency and $\omega_R$ is the phase crossover frequency

(C)

$\omega_Q$ is the gain crossover frequency and $\omega_S$ is the phase crossover frequency

(D)

$\omega_S$ is the gain crossover frequency and $\omega_Q$ is the phase crossover frequency

Explanation

GATE→2025→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q51

MSQ[1 Mark]

Consider the unity-negative-feedback system shown in Figure (i) below, where gain $K \ge 0$. The root locus of this system is shown in Figure (ii) below. For what value(s) of K will the system in Figure (i) have a pole at $-1+j1$?

(A)

$K = 5$

(B)

$K = \frac{1}{5}$

(C)

For no positive value of K

(D)

For all positive values of K

Explanation

GATE→2025→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q52

MCQ[2 Marks]

Let $G(s) = \frac{1}{10s^2}$ be the transfer function of a second-order system. A controller $M(s)$ is connected to the system $G(s)$ in the configuration shown below. Consider the following statements. (i) There exists no controller of the form $M(s) = \frac{K_I}{s}$, where $K_I$ is a positive real number, such that the closed loop system is stable. (ii) There exists at least one controller of the form $M(s) = K_P + s K_D$, where $K_P$ and $K_D$ are positive real numbers, such that the closed loop system is stable. Which one of the following options is correct?

(A)

(i) is TRUE and (ii) is FALSE

(B)

(i) is FALSE and (ii) is TRUE

(C)

Both (i) and (ii) are FALSE

(D)

Both (i) and (ii) are TRUE

Explanation

GATE→2025→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q53

MCQ[2 Marks]

Consider the polynomial $p(s) = s^5 + 7s^4 + 3s^3 - 33s^2 + 2s - 40$. Let $(L, I, R)$ be defined as follows: L is the number of roots of $p(s)$ with negative real parts. I is the number of roots of $p(s)$ that are purely imaginary. R is the number of roots of $p(s)$ with positive real parts. Which one of the following options is correct?

(A)

$L = 2$, $I = 2$, and $R = 1$

(B)

$L = 3$, $I = 2$, and $R = 0$

(C)

$L = 1$, $I = 2$, and $R = 2$

(D)

$L = 0$, $I = 4$, and $R = 1$

Explanation

GATE→2025→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q54

MSQ[2 Marks]

Consider a system where $x_1(t)$, $x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given by $\frac{d}{dt} \begin{bmatrix} x_1(t) \\ x_2(t) \\ x_3(t) \end{bmatrix} = \begin{bmatrix} 2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} x_1(t) \\ x_2(t) \\ x_3(t) \end{bmatrix} + \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} u(t)$. Which of the following statements is/are TRUE?

(A)

The signals $x_1(t)$, $x_2(t)$ and $x_3(t)$ are bounded for all bounded inputs

(B)

There exists a bounded input such that at least one of the signals $x_1(t)$, $x_2(t)$ and $x_3(t)$ is unbounded

(C)

There exists a bounded input such that the signals $x_1(t)$, $x_2(t)$, and $x_3(t)$ are unbounded

(D)

The signals $x_1(t)$, $x_2(t)$ and $x_3(t)$ are unbounded for all bounded inputs

Explanation

GATE→2025→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q55

MSQ[2 Marks]

Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

Communications

6 Questions

GATE→2025→Communications→Random Processes and Analog Communications

Q56

MCQ[1 Mark]

Consider a frequency-modulated (FM) signal $f(t) = A_c \cos(2\pi f_c t + 3\sin(2\pi f_1 t) + 4\sin(6\pi f_1 t))$, where $A_c$ and $f_c$ are, respectively, the amplitude and frequency (in Hz) of the carrier waveform. The frequency $f_1$ is in Hz, and assume that $f_c > 100 f_1$. The peak frequency deviation of the FM signal in Hz is

(A)

$15 f_1$

(B)

$12 f_1$

(C)

$4 f_1$

(D)

$2 f_1$

Explanation

GATE→2025→Communications→Information Theory and Digital Communications

Q57

MCQ[1 Mark]

Consider an additive white Gaussian noise (AWGN) channel with bandwidth W and noise power spectral density $\frac{N_0}{2}$. Let $P_{av}$ denote the average transmit power constraint. Which one of the following plots illustrates the dependence of the channel capacity C on the bandwidth W (keeping $P_{av}$ and $N_0$ fixed)?

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

Explanation

GATE→2025→Communications→Random Processes and Analog Communications

Q58

MSQ[1 Mark]

Consider a message signal $m(t)$ which is bandlimited to $[-W, W]$, where W is in Hz. Consider the following two modulation schemes for the message signal: Double sideband-suppressed carrier (DSB-SC): $f_{DSB}(t) = A_c m(t) \cos(2\pi f_c t)$ Amplitude modulation (AM): $f_{AM}(t) = A_c (1 + \mu m(t)) \cos(2\pi f_c t)$ Here, $A_c$ and $f_c$ are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM, $\mu$ denotes the modulation index. Consider the following statements: (i) An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t) > 0$ for all t. (ii) An envelope detector can be used for demodulation in the AM scheme only if $m(t) > 0$ for all t.

(A)

(i) is TRUE

(B)

(i) is FALSE

(C)

(ii) is TRUE

(D)

(ii) is FALSE

Explanation

GATE→2025→Communications→Information Theory and Digital Communications

Q59

NAT[1 Mark]

The generator matrix of a $(6,3)$ binary linear block code is given by $G = \begin{bmatrix} 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 & 0 \end{bmatrix}$. The minimum Hamming distance $d_{min}$ between codewords equals ______ (answer in integer).

Explanation

GATE→2025→Communications→Information Theory and Digital Communications

Q60

MCQ[2 Marks]

A source transmits symbol S that takes values uniformly at random from the set $\{-2, 0, 2\}$. The receiver obtains $Y = S + N$ where N is a zero-mean Gaussian random variable independent of S. The receiver uses the maximum likelihood decoder to estimate the transmitted symbol S. Suppose the probability of symbol estimation error $P_e$ is expressed as follows: $P_e = \alpha P(N > 1)$, where $P(N > 1)$ denotes the probability that N exceeds 1. What is the value of $\alpha$?

(A)

$\frac{1}{3}$

(B)

1

(C)

$\frac{2}{3}$

(D)

$\frac{4}{3}$

Explanation

GATE→2025→Communications→Random Processes and Analog Communications

Q61

MCQ[2 Marks]

Consider a real-valued random process $f(t) = \sum_{n=1}^N a_n p(t - nT)$, where $T > 0$ and N is a positive integer. Here, $p(t) = 1$ for $t \in [0, 0.5T]$ and 0 otherwise. The coefficients $a_n$ are pairwise independent, zero-mean unit-variance random variables. Read the following statements about the random process and choose the correct option.

(A)

(i) is TRUE and (ii) is FALSE

(B)

Both (i) and (ii) are TRUE

(C)

Both (i) and (ii) are FALSE

(D)

(i) is FALSE and (ii) is TRUE

Explanation

Electromagnetics

4 Questions

GATE→2025→Electromagnetics→Maxwell's Equations and Plane Waves

Q62

MCQ[2 Marks]

A square metal sheet of $4~m \times 4$ m is placed on the x-y plane as shown in the figure below. If the surface charge density (in $\mu C/m^2$) on the sheet is $\rho_s(x,y) = 4|y|$, then the total charge (in $\mu C$, rounded off to the nearest integer) on the sheet is

(A)

16

(B)

85

(C)

64

(D)

128

Explanation

GATE→2025→Electromagnetics→Maxwell's Equations and Plane Waves

Q63

MCQ[2 Marks]

An electric field of 0.01 V/m is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of $5.8 \times 10^7 S/m$. The current (in Amperes, rounded off to two decimal places) flowing through the wire is

(A)

0.46

(B)

1.82

(C)

0.58

(D)

1.12

Explanation

GATE→2025→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q64

NAT[2 Marks]

A $50~\Omega$ lossless transmission line is terminated with a load $Z_L$ of $(50 - j75)~\Omega$. If the average incident power on the line is 10 mW, then the average power delivered to the load (in mW, rounded off to one decimal place) is ______

Explanation

GATE→2025→Electromagnetics→Maxwell's Equations and Plane Waves

Q65

NAT[2 Marks]

Two resistors are connected in a circuit loop of area $5~m^2$, as shown in the figure below. The circuit loop is placed on the x-y plane. When a time-varying magnetic flux, with flux-density $B(t) = 0.5 t$ (in Tesla), is applied along the positive z-axis, the magnitude of current I (in Amperes, rounded off to two decimal places) in the loop is ______

Explanation