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General Aptitude(10)Engineering Mathematics(5)Networks, Signals and Systems(12)Electronic Devices(5)Analog Circuits(7)Digital Circuits(8)Control Systems(4)Communications(8)Electromagnetics(6)

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

Among the following options, the antonym of the word 'nocturnal' is

(A)

normal

(B)

diurnal

(C)

abnormal

(D)

exceptional

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is 150. (S1) The highest score is 100. (S2) The fourth highest score is 76. (S3) There are at least four students whose scores are within 25 of each other. Which one of the following options is necessarily correct?

(A)

(S1) and (S2) together imply (S3)

(B)

(S1) and (S3) together imply (S2)

(C)

(S2) and (S3) together imply (S1)

(D)

(S1) implies (S3)

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

The figure below has exactly three intersecting line segments with a rectangular portion WXYZ missing. Which one of the following options P, Q, R, and S is the missing portion WXYZ?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

Real numbers y, p, and n (all greater than 1) satisfy $(\log_{p^{1/n}}y)(\log_{y^{1/n}}p)=16$ where the logarithms are taken to the bases $p^{1/n}$ and $y^{1/n}.$ The value of n is

(A)

2

(B)

4

(C)

8

(D)

16

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

The following observation is made about the scores obtained by 100 students in an exam: 'For each student, there exists another student in the class such that their scores are at most ten marks away.' If the above statement is false, which one of the following statements is necessarily true?

(A)

For each student, the scores of all the other students are more than 10 marks away.

(B)

There exists at least one student in the class for whom the scores of all the other students are more than 10 marks away.

(C)

There is exactly one student in the class for whom the scores of some students are more than 10 marks away.

(D)

For each student, the score of exactly one other student is more than 10 marks away.

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Each one of the following clues contains a keyword that is partially filled. Clue 1: Synonym of recognize (8 letters): _D_NT_FY Clue 2: A story long enough to fill a book (5 letters): EL Clue 3: Two of something (6 letters): PLE Clue 4: A fraction of something, split equally into two parts (4 letters): _F The first letter of each of the keywords can be rearranged to form a four-letter word. Which one of the options below is a possible choice for the four-letter word?

(A)

CHIN

(B)

COIN

(C)

ITCH

(D)

NOSE

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

Three children P, Q, R and two grown-ups X, Y play a badminton doubles tournament. X and Y are parents to two of the children playing. The child of X is not the same as the child of Y. Exactly one of the children does not have a parent playing in the tournament. The following rules are followed: (i) A parent and his/her child cannot be on the same team. (ii) A match can feature at most one parent and his/her child, that is, a maximum of one parent-child pair can play in a match. The following matches were played: MATCH 1: TEAM 1: Q and R, TEAM 2: P and X MATCH 2: TEAM 1: X and Y, TEAM 2: P and R MATCH 3: TEAM 1: R and X, TEAM 2: Q and Y Which one of the following options is correct?

(A)

P does not have any parent playing

(B)

Q does not have any parent playing

(C)

R does not have any parent playing

(D)

X does not have a child playing

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

Let $P_{k}$ represent the perimeter of a square with sides of length k. The value of the expression $P_{1}+P_{2}+P_{3}+\cdot\cdot\cdot+P_{10}$ is

(A)

55

(B)

110

(C)

220

(D)

440

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was 2.5 stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths BC and CD), and the outer pair is three stades wide each (lengths DE and EF). The ratio of the surface area of the land to that of the water in the city of Atlantis is ______ (round off to two decimal places).

(A)

0.45

(B)

0.60

(C)

0.75

(D)

0.90

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q10

MCQ[2 Marks]

If Ref Fig $\rightarrow$ gîⅎ ʇǝᴚ 12 34 $\rightarrow$ AꞮ εS Then GATE - 2026 $\rightarrow$ ? Aptitude Test

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

Engineering Mathematics

5 Questions

GATE→2026→Engineering Mathematics→Differential Equations

Q11

MCQ[1 Mark]

Consider the differential equation $\dot{\vec{w}}=A\vec{w}$ , with $\vec{w}(t=0)=[\begin{matrix}1\\ 1\end{matrix}]$ If $\vec{w}(t)=e^{t}\vec{u}_{x}+e^{-2t}\vec{u}_{y}$ be the solution to the equation where $\vec{u}_{x}$ and $\vec{u}_{y}$ are unit vectors along the positive x and y axes respectively, then which of the following options is the correct matrix representing A?

(A)

$[\begin{matrix}1&0\\ 0&-2\end{matrix}]$

(B)

$[\begin{matrix}-1&0\\ 0&2\end{matrix}]$

(C)

$[\begin{matrix}0&-2\\ 1&0\end{matrix}]$

(D)

$[\begin{matrix}0&2\\ -1&0\end{matrix}]$

Explanation

GATE→2026→Engineering Mathematics→Vector Analysis

Q12

MCQ[1 Mark]

A surface is given by $z^{2}=2x^{2}-y^{2}$ and $\vec{n}$ and $-\vec{n}$ are unit normal vectors to the surface at the point $\vec{P}=\hat{i}+\sqrt{2}\hat{k}.$ Which of the following vectors can be $\vec{n}$ where î, and $\hat{k}$ are the unit vectors along x, y and z axes, respectively?

(A)

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

(B)

$\frac{2}{3}\hat{i}-\frac{1}{3}\hat{k}$

(C)

$\sqrt{2}\hat{i}-\sqrt{3}\hat{k}$

(D)

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

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q13

MSQ[1 Mark]

Consider the matrix $M=[\begin{matrix}2&1&1\\ 1&3&0\\ -1&a&b\end{matrix}].$ Which of the following options is/are TRUE if $det(M)\ne0$?

(A)

$b=-\frac{1}{2}$ $a=-\frac{1}{2}$

(B)

$a=\frac{1}{2}$ and $b=\frac{1}{2}$

(C)

$a=-3$ and $b=0$

(D)

$a=\frac{1}{2}$ and $b=-3$

Explanation

GATE→2026→Engineering Mathematics→Complex Analysis

Q14

MCQ[2 Marks]

Consider the two series, $S_{A}$ and $S_{B}$ where $S_{A}=\Sigma_{n=1}^{\infty}\frac{n^{2}}{2^{n}}$ $S_{B}=1+\frac{1}{2}+\frac{1}{8}+\frac{1}{16}+\frac{1}{64}+\frac{1}{128}+\frac{1}{512}+\cdot\cdot\cdot$ Which of the following statements is correct for the two given series?

(A)

Both $S_{A}$ and $S_{B}$ converge.

(B)

Neither $S_{A}$ nor SB converges.

(C)

$S_{A}$ converges but $S_{B}$ does not converge.

(D)

$S_{B}$ converges but $S_{A}$ does not converge.

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q15

NAT[2 Marks]

Consider the square region R in the X-Y plane as shown with the dark shading in the Figure. The value of $\iint_{R}(x^{2}+y^{2}-1)dxdy$ is ______ (rounded off to two decimal places)

Explanation

Networks, Signals and Systems

12 Questions

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q16

MCQ[1 Mark]

The Laplace Transform of the signal $x(t)=u(t-2)*(tu(t))$ is given by which of the following expressions? ["*" represents convolution operator]

(A)

$\frac{e^{-2s}}{s^{2}(s-2)}$

(B)

$\frac{e^{-2(s-2)}}{s^{3}}$

(C)

$\frac{se^{-2s}}{(s-2)^{2}}$

(D)

$\frac{e^{-2s}}{s^{3}}$

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q17

MCQ[1 Mark]

Two analog signals $x_{1}(t)$ and $x_{2}(t)$ (t in second), are sampled at a rate $F_{s}=40~Hz,$ where $x_{1}(t)=cos(20\pi t)$, $t\ge0$ and $x_{2}(t)=cos(100\pi t)$, $t\ge0$. The first ten samples (starting from $t=0$) are considered for the analysis. Which of the following statements is TRUE?

(A)

All of the first three samples of $x_{1}(t)$ are greater than the corresponding samples of $x_{2}(t)$.

(B)

All of the last three samples of $x_{1}(t)$ are greater than the corresponding samples of $x_{2}(t)

(C)

All of the samples of $x_{2}(t)$ are greater than the corresponding samples of $x_{1}(t).$

(D)

All of the fourth to seventh samples of $x_{1}(t)$ are equal to the corresponding samples of $x_{2}(t).

Explanation

GATE→2026→Networks, Signals and Systems→Discrete-time Signals

Q18

MCQ[1 Mark]

The response of a discrete time system $y[n]$ obeys the following relation: $y[n]=\frac{5}{6}y[n-1]-\frac{1}{6}y[n-2]+x[n].$ The input to the system is $x[n]=\delta[n]-\frac{1}{3}\delta[n-1]$ Which of the following options is TRUE for $y[n]$?

(A)

Stable and causal response

(B)

Stable and non-causal response

(C)

Unstable and causal response

(D)

Unstable and non-causal response

Explanation

GATE→2026→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q19

MCQ[1 Mark]

The relation between the input current ($I$) and the output voltage $(V)$ of a circuit is governed by the equation: $C\frac{dV}{dt}=I(t)-m(t)$ . The circuit is excited by $I(t)=q\delta(t)$, where q is a real valued constant. V at $t=0^{-}$ is $V_{0}.$ Which of the following is an equivalent representation of the above case?

(A)

$C\frac{dV}{dt}=-m(t)$ , with $V(t=0^{-})=V_{0}+q/C$

(B)

$C\frac{dV}{dt}=-m(t)$ , with $V(t=0^{-})=V_{0}+q/C+m(t=0^{-})$

(C)

$C\frac{dv}{dt}=-m(t)$ with $V(t=0^{-})=V_{0}-q/C+m(t=0^{-})$

(D)

$C\frac{dv}{dt}=-m(t)$ with $V(t=0^{-})=q/C$

Explanation

GATE→2026→Networks, Signals and Systems→Circuit Analysis

Q20

NAT[1 Mark]

The output voltage $V_{o}$ (in Volt) for the network given in the Figure is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q21

NAT[1 Mark]

Consider the circuit shown in the Figure, where the input $v_{i}(t)$ is in Volt. The average power (in mW) dissipated in the load resistance of $1~k\Omega$ at the resonant frequency is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q22

MCQ[2 Marks]

The continuous time signal $x(t)$ is real, periodic with period T and satisfies the Dirichlet conditions. The Fourier series representation of $x(t)=\Sigma_{-\infty}^{\infty}a_{n}e^{j(\frac{2\pi nt}{T})}$ and $x(t)$ satisfies the following: $x(t-\frac{T}{2})=-x(t).$ For any integer m, which of the following options is correct?

(A)

$a_{2m}=0$

(B)

$a_{2m}=1$

(C)

$a_{2m}=a_{2m+1}$

(D)

$a_{2m}=-1$

Explanation

GATE→2026→Networks, Signals and Systems→Circuit Analysis

Q23

MCQ[2 Marks]

In the given circuit, $L=1\mu H$ and $C=1~\mu F$. The phasor diagram for Ic and IL is also shown. Assume that the phase $(\theta_{1}+\theta_{2})$ is $90^{\circ}$ at a frequency of 159.15 kHz. Among the following options, what is the nearest integer value of $R_{C}\times R_{L};$

(A)

0

(B)

1

(C)

2

(D)

10

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q24

MCQ[2 Marks]

Consider a real signal $x(t)$, $-\infty<t<\infty$, such that $x(t)=0$ for $t<0$ $x(t)=2$ for $0\le t<1$ and $x(t)=0$ for $t\ge1$. Let $E[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2}dt$. Which of the following options correctly represents the ratio, $E[x(t)]/E[3~x(-3t+5)]$?

(A)

3

(B)

1

(C)

$1/3$

(D)

$1/9$

Explanation

GATE→2026→Networks, Signals and Systems→LTI Systems

Q25

MCQ[2 Marks]

Consider the discrete time system (S) with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_{1}[n]$ and $h_{2}[n]$ are linear and time invariant. Which of the following statements is necessarily TRUE?

(A)

S is causal.

(B)

S is linear and time invariant.

(C)

S is linear and time varying.

(D)

S is non-linear.

Explanation

GATE→2026→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q26

MCQ[2 Marks]

Consider the two-port network as shown in the Figure. Which of the following options provides the correct set of values of A, B, C and D parameters?

(A)

$A=1/2$, $B=3\times10^{3}S$, $C=10^{-3}\Omega^{-1}$, $D=1/2$

(B)

$A=2$, $B=3~\Omega$ $C=1~\Omega^{-1}$ $D=2$

(C)

$A=2$, $B=6\times10^{3}\Omega$ $C=2\times10^{-3}\Omega^{-1}$ $D=2$

(D)

$B=3\times10^{3}$ Ω, $C=10^{-3}\Omega^{-1}$, $D=2$ $A=2$

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q27

MSQ[2 Marks]

Let $x_{1}(t)=cos(2\pi nt)$ and $x_{2}(t)=2~sin(4\pi nt)$ represent two sinusoids for a positive integer n and $-\infty<t<\infty$. Which of the following statements about $x_{1}(t)$ and $x_{2}(t)$ is/are valid?

(A)

$x_{1}(t)$ and $x_{2}(t)$ are orthogonal to each other over $0\le t<1/n$.

(B)

$x_{1}(t)$ and $x_{2}(t)$ are orthonormal to each other over $0\le t<1/n$.

(C)

$x_{2}(t)$ is a harmonic of $x_{1}(t).$

(D)

$x_{1}(t)$ and $x_{2}(t)$ are non-orthogonal to each other over $0\le t<1/(2n)$.

Explanation

Electronic Devices

5 Questions

GATE→2026→Electronic Devices→Semiconductor Physics and Carrier Transport

Q28

MCQ[1 Mark]

Consider carrier transport in a Zener diode in the breakdown region. Which is the dominant transport mechanism for current flow in this case?

(A)

Drift

(B)

Diffusion

(C)

Tunneling

(D)

Ballistic transport

Explanation

GATE→2026→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q29

MSQ[1 Mark]

Consider a p-n junction diode when it is forward biased with 2 V. Which of the following is/are the correct magnitude(s) of the energy difference between quasi Fermi-levels, $E_{fn}$ in the n-side and $E_{fp}$ in the p-side?

(A)

2 eV

(B)

1 eV

(C)

2 V

(D)

1 V

Explanation

GATE→2026→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q30

MSQ[1 Mark]

Figure shows the output characteristics of two different Bipolar Junction Transistors (BJT), BJT 1 with magnitude of Early voltage $|V_{A1}|$, and BJT 2 with magnitude of Early voltage $|V_{A2}|$. Which of the following options is/are correct regarding the Early voltages?

(A)

$|V_{A1}|>|V_{A2}|$ dak

(B)

$|V_{A1}|$ is infinitely large

(C)

$|V_{A1}|<|V_{A2}|$

(D)

$|V_{A2}|$ is finite

Explanation

GATE→2026→Electronic Devices→Diodes, BJTs, MOS Capacitors, MOSFETs, and Optoelectronic Devices

Q31

MSQ[2 Marks]

Consider an LED based on a direct bandgap semiconductor material with energy bandgap 1.3 eV. Given: Plank's constant, $h=6.63\times10^{-34}$ Js and speed of light in free space is $3\times10^{8}ms^{-1}$ In which of the following wavelength ranges the LED will NOT emit?

(A)

$1410\pm20~nm$

(B)

$1090\pm20~nm$

(C)

$950\pm20~nm$

(D)

$510\pm20~nm$

Explanation

GATE→2026→Electronic Devices→Semiconductor Physics and Carrier Transport

Q32

NAT[2 Marks]

Consider that the concentration of electrons in a semiconductor bar varies linearly from $2\times10^{17}cm^{-3}$ at $x=1~\mu m$ to $1\times10^{16}cm^{-3}$ at $x=4~\mu m$ along the x-direction. Assume that the concentration of electrons is not varying along other directions (that is along y- and z-directions). [Given: the mobility of electron is $1400~cm^{2}V^{-1}s^{-1}$, thermal voltage is 25 mV and electronic charge is $1.6\times10^{-19}$ Coulomb.] The density of electron diffusion current $(in~A/mm^{2})$ is ______ (rounded off to two decimal places)

Explanation

Analog Circuits

7 Questions

GATE→2026→Analog Circuits→Op-amp Circuits and Compensation

Q33

MCQ[1 Mark]

The ideal OP-AMP circuit shown in the Figure produces output voltage $V_{o}=x$ when the Switch, S, is open. Which of the options represents the output voltage when S is closed?

(A)

X

(B)

$\frac{2}{3}x$

(C)

$\frac{3}{4}x$

(D)

$\frac{1}{2}x$

Explanation

GATE→2026→Analog Circuits→BJT and MOSFET Amplifiers

Q34

MCQ[1 Mark]

Consider the circuit shown in the Figure with $V_{i}=3$ V and $V_{CC}=12~V.$ Assume $V_{BE}=0.7~V$ and $\beta_{dc}=99$ for the BJT. Which of the following options is the correct value of the current $I_{o}$?

(A)

$60~\mu A$

(B)

6 μΑ

(C)

$3~\mu A$

(D)

$30~\mu A$

Explanation

GATE→2026→Analog Circuits→BJT and MOSFET Amplifiers

Q35

MCQ[2 Marks]

A small signal source, $V_{i}(t)=A~cos(10^{5}t)+B~sin(10^{7}t)$ is applied to a BJT circuit as shown in the Figure. Assume zero source resistance, $V_{BE}=0.7~V.$ $\beta_{dc}=99$, Early voltage $=100~V$ and Thermal voltage $=25~mV$. Effect of internal parasitic capacitances of the BJT may be neglected. Which expression is the best approximation of the output voltage $V_{o}(t)$?

(A)

$-9.1[A~cos(10^{5}t)+B~sin(10^{7}t)]$

(B)

$9.1[A~cos(10^{5}t)-B~sin(10^{7}t)]$

(C)

$-190.4[A~cos(10^{5}t)+B~sin(10^{7}t)]$

(D)

$190.4[A~cos(10^{5}t)-B~sin(10^{7}t)]$

Explanation

GATE→2026→Analog Circuits→Op-amp Circuits and Compensation

Q36

MCQ[2 Marks]

A circuit using an ideal OP-AMP is shown in the Figure. Which of the following options gives the correct value of the current $I_{X}$?

(A)

2.0 mA

(B)

1.5 mA

(C)

3.0 mA

(D)

0 mA

Explanation

GATE→2026→Analog Circuits→BJT and MOSFET Amplifiers

Q37

NAT[2 Marks]

An n-channel MOSFET is connected as shown in the Figure. Assume $V_{TH}=1~V$, $V_{DD}=5~V,$ and $\mu C_{ox}(\frac{W}{L})=2~mA~V^{-2}$ and neglect channel length modulation effects. The gate voltage $(V_{G})$ of the n-channel MOSFET (in Volt) is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Analog Circuits→Op-amp Circuits and Compensation

Q38

NAT[2 Marks]

Consider an ideal OP-AMP circuit as shown in the Figure. The resistances $R_{1}=R_{2}=R_{3}=R_{4}=50$ ΚΩ. The magnitude of the closed loop gain is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Analog Circuits→Diode Circuits

Q39

NAT[2 Marks]

Consider the ideal diodes D1 and D2 as shown in the Figure with cut-in voltage $V_{\gamma}=0$ Volt and $v_{i}(t)$ is in Volt. The maximum voltage (Volt) of the output $v_{o}(t)$ is ______ (rounded off to two decimal places)

Explanation

Digital Circuits

8 Questions

GATE→2026→Digital Circuits→Number Representations and Combinatorial Circuits

Q40

MCQ[1 Mark]

In the circuit shown in the Figure, A and B are logic inputs and Y is the logic output. Which of the following logic operations is realized by the circuit?

(A)

NOR

(B)

OR

(C)

XOR

(D)

AND

Explanation

GATE→2026→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q41

MSQ[1 Mark]

A binary ripple counter is designed to count $(0)_{10}$ to $(64)_{10}.$ Which of the following is/are the number of flip-flops required to design the counter?

(A)

6

(B)

7

(C)

4

(D)

5

Explanation

GATE→2026→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q42

NAT[1 Mark]

The negative edge triggered JK flip-flop in the Figure has J and K inputs tied to Logic High and a square wave of 10 cycles/second is applied to its clock (C) input. The frequency of the output Q (in cycles/second) is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Digital Circuits→Computer Organization

Q43

MCQ[2 Marks]

The address of the first location of a 256 kilo byte (KB) memory is (2500)н. Choose the correct address of the last location of the memory.

(A)

(2FFF)H

(B)

(124FF)H

(C)

(424FF)H

(D)

(324FF)H

Explanation

GATE→2026→Digital Circuits→Number Representations and Combinatorial Circuits

Q44

MCQ[2 Marks]

What is the $10^{\prime}s$ complement of (47) 10?

(A)

52

(B)

53

(C)

54

(D)

55

Explanation

GATE→2026→Digital Circuits→Number Representations and Combinatorial Circuits

Q45

MCQ[2 Marks]

A Boolean function, $f(x,y,z)$ with x as MSB and z as LSB is realized by 4:1 multiplexer (MUX) with select lines, $S_{1}$ and $S_{0}$ (S1 is MSB, $S_{0}$ is LSB) and inputs, Io, $I_{1}$, $I_{2}$, $I_{3}$ as shown in the Figure. Which of the following options is the correct expression of $f(x,y,z)$?

(A)

$xz+y$

(B)

$x\overline{y}+z$

(C)

$xy+z$

(D)

$\overline{x}y+\overline{z}$

Explanation

GATE→2026→Digital Circuits→Sequential Circuits, Data Converters, and Memories

Q46

MCQ[2 Marks]

A shift-left Shift Register (SR) and a D flip-flop are connected to a synchronized clock as shown in the Figure. Assume that the SR and D flip-flops are initially cleared and the XOR gate has no propagation delay. Which of the following options gives the correct binary representation ($b_{7}b_{6}b_{5}b_{4}b_{3}b_{2}b_{1}b_{0}$) of the content of the shift register immediately after the $5^{th}$ clock transition (positive edge)?

(A)

00011111

(B)

10111111

(C)

00111111

(D)

11000011

Explanation

GATE→2026→Digital Circuits→Number Representations and Combinatorial Circuits

Q47

MSQ[2 Marks]

Consider the four-variable Boolean function, $f(w,x,y,z)=\Sigma m(0,2,5,7,8,10,13,14,15)$ with 'w' as MSB and 'z' as LSB. Which of the following expressions is/are the valid form(s) of $f(w,x,y,z)$?

(A)

$\overline{x}\overline{z}+xz+wxy$

(B)

$xz+wxy+w\overline{x}\overline{z}+\overline{w}xy\overline{z}$

(C)

$\overline{x}\overline{z}+wxy+w\overline{x}\overline{z}+\overline{w}xy\overline{z}$

(D)

$\overline{x}\overline{z}+xz+wy\overline{z}$

Explanation

Control Systems

4 Questions

GATE→2026→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q48

MCQ[1 Mark]

A control system is shown in the Figure. Which option represents the correct transfer function of the system?

(A)

$\frac{1}{(s+4)^{2}}$

(B)

$\frac{1}{(s+4)}$

(C)

$\frac{2}{(s+4)}$

(D)

$\frac{1}{(s^{2}+8s+17)}$

Explanation

GATE→2026→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q49

MCQ[2 Marks]

For the control system shown in the Figure, the transfer function of a plant, $G(s)=\frac{1}{(s+1)(s+2)}$ is connected in cascade with a compensator $C(s)=K(s+\alpha)$, where K and a are positive real valued constants. Which of the following pairs $(K,\alpha)$ represent the correct values for the closed loop system to have poles at $(-3\pm j\sqrt{5})$?

(A)

2,3

(B)

3,4

(C)

2,4

(D)

3,3

Explanation

GATE→2026→Control Systems→Frequency Response, Compensators, Controllers, and State Variable Models

Q50

MCQ[2 Marks]

The state and output equations for a control system are: $\dot{x}=[\begin{matrix}-4&-1.5\\ 4&0\end{matrix}]x+[\begin{matrix}2\\ 0\end{matrix}]u$ $y=[\begin{matrix}1.5&0.625\end{matrix}]x$ Which of the following expressions correctly represents the transfer function $\frac{Y(s)}{U(s)}$ of the system with zero initial conditions?

(A)

$\frac{3s}{s^{2}+4s-6}$

(B)

$\frac{3s+5}{s^{2}+4s-6}$

(C)

$\frac{3s+5}{s^{2}+4s+6}$

(D)

$\frac{3s}{s^{2}+4s+6}$

Explanation

GATE→2026→Control Systems→Control System Components, Transfer Functions, and Stability Analysis

Q51

NAT[2 Marks]

Consider the unity negative feedback control system shown in the Figure. The value of gain $K(>0)$ at which the given system will remain marginally stable is ______ (Answer in integer)

Explanation

Communications

8 Questions

GATE→2026→Communications→Information Theory and Digital Communications

Q52

MCQ[1 Mark]

Consider a discrete memoryless source with an alphabet of four source symbols. $s(t)$ is a multi-level $(-1,0,+1,+2)$ signal representing a long sequence of random symbols from the above source which is generating $10^{4}$ symbols per second. Which of the following options is the correct value of equivalent Nyquist bandwidth of $s(t)$?

(A)

10 kHz

(B)

64 kHz

(C)

5 kHz

(D)

20 kHz

Explanation

GATE→2026→Communications→Information Theory and Digital Communications

Q53

NAT[1 Mark]

A wireless digital transmission scheme is using 16-QAM over an additive white Gaussian noise channel and a maximum-likelihood receiver. Consider the information bit rate from source to be $4\times10^{6}$ bits per second. The minimum transmission bandwidth (in MHz) of the modulated signal necessary for optimum recovery of information at the receiver is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Communications→Random Processes and Analog Communications

Q54

MCQ[2 Marks]

Let X, N, Y and Z be random variables. The variables X and N are independent of each other. X is uniformly distributed between -1 and 1; N follows Normal distribution with zero mean and unity variance. Y and Z are defined as, $Y=X+N$ and $Z=X^{2}+N$ Which of the following pairs represents the values of correlation between X and Y and that between X and Z?

(A)

$1/3$ and 0

(B)

$1/3$ and $1/9$

(C)

$1/3$ and $1/3$

(D)

1 and 0

Explanation

GATE→2026→Communications→Information Theory and Digital Communications

Q55

MCQ[2 Marks]

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an Eb/N = 8.4 dB at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator. Assume the complimentary error function $erfc(u)\cong[1/(u\sqrt{\pi})]exp(-u^{2})$. Which is the nearest bit error rate (BER) at the output of the demodulator?

(A)

$10^{-3}$

(B)

$10^{-4}$

(C)

$10^{-5}$

(D)

$10^{-6}$

Explanation

GATE→2026→Communications→Random Processes and Analog Communications

Q56

MCQ[2 Marks]

Consider a real baseband signal $x(t)=e^{-2t}$ for t (in seconds) $\ge0.$ If 99% of energy of $x(t)$ lies within B Hz, then which of the following options is TRUE for the value of B?

(A)

$B>1~kHz$

(B)

$63/\pi~Hz<B<64/\pi~Hz$

(C)

126/π Hz < Β < 128/π Hz

(D)

$B<1~Hz$

Explanation

GATE→2026→Communications→Information Theory and Digital Communications

Q57

MSQ[2 Marks]

Let the relevant bandwidth (B) of a digital communication system be 1 MHz and $kT=-174~dBm/Hz$, where k is Boltzmann's constant and '7" is equivalent noise temperature of the receiver. The power (S) of signal received through an additive Gaussian channel is -80 dBm. Which of the following options is/are TRUE about Shannon capacity (C) of the channel?

(A)

$C=B$

(B)

$C=2B$

(C)

$C>3B$

(D)

$C<B$

Explanation

GATE→2026→Communications→Random Processes and Analog Communications

Q58

MSQ[2 Marks]

Consider a real, narrowband signal $x(t)=A(t)cos[2\pi f_{c}t+\theta(t)]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_{M}$ and $f_{c}(=1000f_{M})$ respectively. Which of the following statements is/are correct for∞ $-\infty<t<\infty$?

(A)

$x(t)$ represents a PSK modulated signal for suitable choices of $A(t)$ and $\theta(t).$

(B)

$x(t)$ represents an amplitude modulated signal for suitable choices of $A(t)$ and $\theta(t)$ gegen

(C)

$x(t)$ represents a band-limited Gaussian noise process.

(D)

$x(t)$ never represents a narrowband FM signal.

Explanation

GATE→2026→Communications→Information Theory and Digital Communications

Q59

NAT[2 Marks]

The average bit error rate at the input of a (7, 4, 1) Hamming decoder is 0.10. The probability that the decoder will fail to decode a received word correctly is ______ (rounded off to two decimal places)

Explanation

Electromagnetics

6 Questions

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q60

MCQ[1 Mark]

Consider the Friis' transmission equation $P_{R}=(P_{T}G_{T}G_{R}\lambda^{2})/(4\pi D)^{2}$, where $P_{R}$ and $P_{T}$ are the received and the transmitted powers, respectively. $G_{T}$ and $G_{R}$ are the gain of transmitting and receiving antennas, respectively, D is the distance between the transmitting and receiving antennas, and $\lambda$ is the wavelength in free space. Given: $G_{T}=G_{R}=1.0$, $\lambda=0.30$ m and $P_{T}=+10$ dBm. Choose the distance (D), in km, from the following options at which the received power, $P_{R}=-90$ dBm?

(A)

$\frac{15}{4\pi}$

(B)

$\frac{15}{2\pi}$

(C)

$\frac{75}{2\pi}$

(D)

$\frac{3}{4\pi}$

Explanation

GATE→2026→Electromagnetics→Maxwell's Equations and Plane Waves

Q61

MCQ[1 Mark]

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by $\vec{E}(z,t)=E_{0}[\hat{x}cos(\omega t-kz)+\hat{y}sin(\omega t-kz)]$ in a right-handed orthogonal co-ordinate system. Which of the following is the correct polarization of the electromagnetic wave?

(A)

Right-handed circularly polarized

(B)

Left-handed circularly polarized

(C)

Linearly polarized

(D)

Linearly polarized with $-45^{\circ}$ angle to

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q62

MSQ[1 Mark]

Which option(s) represents/ represent the dielectric loss tangent of a substrate?

(A)

Ratio of the real to imaginary parts of the total displacement current

(B)

$(\omega\epsilon^{\prime\prime}+\sigma)/(\omega\epsilon^{\prime})$

(C)

Ratio of the electric susceptibility to permittivity

(D)

Ratio of the polarization vector $\vec{P}$ to the displacement vector $\vec{D}$

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q63

NAT[1 Mark]

The cutoff frequency (in GHz) for the dominant $TE_{10}$ mode of an air-filled rectangular waveguide of inner dimension $0.28~inch\times0.14$ inch is ______ (rounded off to two decimal places).

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q64

NAT[1 Mark]

For a lossless passive two-port network, $|S_{11}|$ and $|S_{21}|$ intersect at -3 dB. For a lossy passive two-port network, $|S_{11}|$ and $|S_{21}|$ intersect at -4 dB. The percentage of power dissipated in the lossy network at the intersection frequency is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q65

MCQ[2 Marks]

A complex load (in $\Omega$) is represented as $\Gamma_{L}=0.5\angle30^{\circ}$ on the Smith chart. A co-axial cable with a characteristic impedance of $50~\Omega$ is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same VSWR circle on the Smith chart. Which option is the nearest input impedance of the cable connected load (in Ω)?

(A)

$20.7-j5.1$

(B)

$17.7-j11.8$

(C)

$97.5-j65.0$

(D)

$97.5+j65.0$

Explanation