GATE 2023 EC PYQ: all 65 questions with official answers

Q1 · General Aptitude · MCQ · 1 mark

“I cannot support this proposal. My ________ will not permit it.”

(A)
conscious
(B)
consensus
(C)
conscience
(D)
consent

Answer (official key): C

Worked solution: in your report after you take this paper.

Q2 · General Aptitude · MCQ · 1 mark

Courts : _______ : : Parliament : Legislature

(By word meaning)

(A)
Judiciary
(B)
Executive
(C)
Governmental
(D)
Legal

Answer (official key): A

Worked solution: in your report after you take this paper.

Q3 · General Aptitude · MCQ · 1 mark

What is the smallest number with distinct digits whose digits add up to 45?

(A)
123555789
(B)
123457869
(C)
123456789
(D)
99999

Answer (official key): C

Worked solution: in your report after you take this paper.

Q4 · General Aptitude · MCQ · 1 mark

In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies, (ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and (iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

(A)
40
(B)
20
(C)
60
(D)
30

Answer (official key): C

Worked solution: in your report after you take this paper.

Q5 · General Aptitude · MCQ · 1 mark

How many rectangles are present in the given figure?

(A)
8
(B)
9
(C)
10
(D)
12

Answer (official key): C

Worked solution: in your report after you take this paper.

Q6 · General Aptitude · MCQ · 2 marks

Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A)
All creatures with claws are animals.
(B)
Some creatures with claws are non-ferocious.
(C)
Some non-ferocious creatures have claws.
(D)
Some ferocious creatures are creatures with claws.

Answer (official key): D

Worked solution: in your report after you take this paper.

Q7 · General Aptitude · MCQ · 2 marks

Which one of the following options represents the given graph?

(A)
$f(x) = x^2\,2^{-|x|}$
(B)
$f(x) = x\,2^{-|x|}$
(C)
$f(x) = |x|\,2^{-x}$
(D)
$f(x) = x\,2^{-x}$

Answer (official key): A

Read the worked solution

Q8 · General Aptitude · MCQ · 2 marks

Which one of the following options can be inferred from the given passage alone?

When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.

[Excerpt from The Truth about Stories by T. King]

(A)
It is a child’s description of what he or she likes.
(B)
It is an adult’s memory of what he or she liked as a child.
(C)
The child in the passage read stories about interplanetary travel only in parts.
(D)
It teaches us that stories are good for children.

Answer (official key): B

Worked solution: in your report after you take this paper.

Q9 · General Aptitude · MCQ · 2 marks

Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5. (ii) Mix the samples within each set and test the mixed sample for covid. (iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative. (iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A)
700
(B)
600
(C)
800
(D)
1000

Answer (official key): A

Read the worked solution

Q10 · General Aptitude · MCQ · 2 marks

A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm × 1 cm.

The total number of creases visible when the sheet is unfolded is _______.

(A)
32
(B)
5
(C)
31
(D)
63

Answer (official key): C

Worked solution: in your report after you take this paper.

Q11 · Linear Algebra · MCQ · 1 mark

Let $\boldsymbol{v_1} = \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix}$ and $\boldsymbol{v_2} = \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix}$ be two vectors. The value of the coefficient $\alpha$ in the expression $\boldsymbol{v_1} = \alpha\boldsymbol{v_2} + \boldsymbol{e}$ , which minimizes the length of the error vector $\boldsymbol{e}$ , is

(A)
$\dfrac{7}{2}$
(B)
$\dfrac{-2}{7}$
(C)
$\dfrac{2}{7}$
(D)
$\dfrac{-7}{2}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q12 · Calculus · MCQ · 1 mark

The rate of increase, of a scalar field $f(x,y,z) = xyz$ , in the direction $\boldsymbol{v} = (2,1,2)$ at a point $(0,2,1)$ is

(A)
$\dfrac{2}{3}$
(B)
$\dfrac{4}{3}$
(C)
2
(D)
4

Answer (official key): B

Worked solution: in your report after you take this paper.

Q13 · Complex Variables · MCQ · 1 mark

Let $w^4 = 16j$ . Which of the following cannot be a value of $w$ ?

(A)
$2e^{\frac{j2\pi}{8}}$
(B)
$2e^{\frac{j\pi}{8}}$
(C)
$2e^{\frac{j5\pi}{8}}$
(D)
$2e^{\frac{j9\pi}{8}}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q14 · Complex Variables · MCQ · 1 mark

The value of the contour integral, $\oint_C \left(\dfrac{z+2}{z^2+2z+2}\right)dz$ , where the contour C is $\left\{z : \left|z + 1 - \frac{3}{2}j\right| = 1\right\}$ , taken in the counter clockwise direction, is

(A)
$-\pi(1+j)$
(B)
$\pi(1+j)$
(C)
$\pi(1-j)$
(D)
$-\pi(1-j)$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q15 · Linear Algebra · MCQ · 1 mark

Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\{\lambda_k \mid 1 \le k \le n\}$ and $\{\boldsymbol{v}_k \mid 1 \le k \le n\}$ , respectively. For any invertible matrix $P$ , the sets of eigenvalues and eigenvectors of the matrix $A$ , where $B = P^{-1}AP$ , respectively, are

(A)
$\{\lambda_k \det(A) \mid 1 \le k \le n\}$ and $\{P\boldsymbol{v}_k \mid 1 \le k \le n\}$
(B)
$\{\lambda_k \mid 1 \le k \le n\}$ and $\{\boldsymbol{v}_k \mid 1 \le k \le n\}$
(C)
$\{\lambda_k \mid 1 \le k \le n\}$ and $\{P\boldsymbol{v}_k \mid 1 \le k \le n\}$
(D)
$\{\lambda_k \mid 1 \le k \le n\}$ and $\{P^{-1}\boldsymbol{v}_k \mid 1 \le k \le n\}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q16 · Electronic Devices · MCQ · 1 mark

In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

(A)
degenerate n-type.
(B)
degenerate p-type.
(C)
non-degenerate n-type.
(D)
non-degenerate p-type.

Answer (official key): A

Worked solution: in your report after you take this paper.

Q17 · Electronic Devices · MCQ · 1 mark

For an intrinsic semiconductor at temperature $T = 0\,K$ , which of the following statement is true?

(A)
All energy states in the valence band are filled with electrons and all energy states in the conduction band are empty of electrons.
(B)
All energy states in the valence band are empty of electrons and all energy states in the conduction band are filled with electrons.
(C)
All energy states in the valence and conduction band are filled with holes.
(D)
All energy states in the valence and conduction band are filled with electrons.

Answer (official key): A

Worked solution: in your report after you take this paper.

Q18 · Networks, Signals and Systems · MCQ · 1 mark

A series $RLC$ circuit has a quality factor $Q$ of 1000 at a center frequency of $10^6$ rad/s. The possible values of $R, L$ and $C$ are

(A)
$R = 1\,\Omega$ , $L = 1\,\mu H$ and $C = 1\,\mu F$
(B)
$R = 0.1\,\Omega$ , $L = 1\,\mu H$ and $C = 1\,\mu F$
(C)
$R = 0.01\,\Omega$ , $L = 1\,\mu H$ and $C = 1\,\mu F$
(D)
$R = 0.001\,\Omega$ , $L = 1\,\mu H$ and $C = 1\,\mu F$

Answer (official key): D

Worked solution: in your report after you take this paper.

Q19 · Electronic Devices · MCQ · 1 mark

For a MOS capacitor, $V_{fb}$ and $V_t$ are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width ( $W_{dep}$ ) for varying gate voltage ( $V_g$ ) is best represented by

(A)
(B)
(C)
(D)

Answer (official key): B

Read the worked solution

Q20 · Electromagnetics · MCQ · 1 mark

Consider a narrow band signal, propagating in a lossless dielectric medium ( $\varepsilon_r = 4, \mu_r = 1$ ), with phase velocity $v_p$ and group velocity $v_g$ . Which of the following statement is true? ( $c$ is the velocity of light in vacuum.)

(A)
$v_p > c, v_g > c$
(B)
$v_p < c, v_g > c$
(C)
$v_p > c, v_g < c$
(D)
$v_p < c, v_g < c$

Answer (official key): D

Worked solution: in your report after you take this paper.

Q21 · Analog Circuits · MCQ · 1 mark

In the circuit shown below, $V_1$ and $V_2$ are bias voltages. Based on input and output impedances, the circuit behaves as a

(A)
voltage controlled voltage source.
(B)
voltage controlled current source.
(C)
current controlled voltage source.
(D)
current controlled current source.

Answer (official key): D

Worked solution: in your report after you take this paper.

Q22 · Analog Circuits · MCQ · 1 mark

A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when

(A)
the closed loop gain is less than 1 and the phase shift is less than 180°.
(B)
the closed loop gain is greater than 1 and the phase shift is less than 180°.
(C)
the closed loop gain is less than 1 and the phase shift is greater than 180°.
(D)
the closed loop gain is greater than 1 and the phase shift is greater than 180°.

Answer (official key): Marks to all

Everyone who took this paper got the marks for this question. Marks to all in GATE

Worked solution: in your report after you take this paper.

Q23 · Digital Circuits · MCQ · 1 mark

In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

(A)
$Y = PQ$
(B)
$Y = P + Q$
(C)
$Y = \overline{PQ}$
(D)
$Y = \overline{P + Q}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q24 · Digital Circuits · MCQ · 1 mark

The synchronous sequential circuit shown below works at a clock frequency of 1 GHz. The throughput, in Mbits/s, and the latency, in ns, respectively, are

(A)
1000, 3
(B)
333.33, 1
(C)
2000, 3
(D)
333.33, 3

Answer (official key): A

Worked solution: in your report after you take this paper.

Q25 · Control Systems · MCQ · 1 mark

The open loop transfer function of a unity negative feedback system is $G(s) = \dfrac{k}{s(1+sT_1)(1+sT_2)}$ , where $k$ , $T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in rad/s, is

(A)
$\dfrac{1}{\sqrt{T_1T_2}}$
(B)
$\dfrac{1}{T_1T_2}$
(C)
$\dfrac{1}{T_1\sqrt{T_2}}$
(D)
$\dfrac{1}{T_2\sqrt{T_1}}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q26 · Networks, Signals and Systems · MCQ · 1 mark

Consider a system with input $x(t)$ and output $y(t) = x(e^t)$ . The system is

(A)
Causal and time invariant.
(B)
Non-causal and time varying.
(C)
Causal and time varying.
(D)
Non-causal and time invariant.

Answer (official key): B

Worked solution: in your report after you take this paper.

Q27 · Communications · MCQ · 1 mark

Let $m(t)$ be a strictly band-limited signal with bandwidth $B$ and energy $E$ . Assuming $\omega_0 = 10B$ , the energy in the signal $m(t)\cos\omega_0 t$ is

(A)
$\dfrac{E}{4}$
(B)
$\dfrac{E}{2}$
(C)
$E$
(D)
$2E$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q28 · Networks, Signals and Systems · MCQ · 1 mark

The Fourier transform $X(\omega)$ of $x(t) = e^{-t^2}$ is

Note: $\int_{-\infty}^{\infty} e^{-y^2}dy = \sqrt{\pi}$

(A)
$\sqrt{\pi}\,e^{\frac{\omega^2}{2}}$
(B)
$\dfrac{e^{-\frac{\omega^2}{4}}}{2\sqrt{\pi}}$
(C)
$\sqrt{\pi}\,e^{-\frac{\omega^2}{4}}$
(D)
$\sqrt{\pi}\,e^{-\frac{\omega^2}{2}}$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q29 · Networks, Signals and Systems · MCQ · 1 mark

In the table shown below, match the signal type with its spectral characteristics.

Signal type	Spectral characteristics
(i) Continuous, aperiodic	(a) Continuous, aperiodic
(ii) Continuous, periodic	(b) Continuous, periodic
(iii) Discrete, aperiodic	(c) Discrete, aperiodic
(iv) Discrete, periodic	(d) Discrete, periodic

(A)
(i) → (a), (ii) → (b), (iii) → (c), (iv) → (d)
(B)
(i) → (a), (ii) → (c), (iii) → (b), (iv) → (d)
(C)
(i) → (d), (ii) → (b), (iii) → (c), (iv) → (a)
(D)
(i) → (a), (ii) → (c), (iii) → (d), (iv) → (b)

Answer (official key): B

Worked solution: in your report after you take this paper.

Q30 · Networks, Signals and Systems · MSQ · 1 mark

For a real signal, which of the following is/are valid power spectral density/densities?

(A)
$S_X(\omega) = \dfrac{2}{9 + \omega^2}$
(B)
$S_X(\omega) = e^{-\omega^2}\cos^2\omega$
(C)
(D)

Answer (official key): A, B

Worked solution: in your report after you take this paper.

Q31 · Digital Circuits · Numerical · 1 mark

The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is ________ bits (rounded off to the nearest integer).

Answer (official key): 10

Worked solution: in your report after you take this paper.

Q32 · Networks, Signals and Systems · Numerical · 1 mark

In the circuit shown below, the current $i$ flowing through 200 Ω resistor is _______ mA (rounded off to two decimal places).

Answer (official key): 1.3 to 1.4

Read the worked solution

Q33 · Networks, Signals and Systems · Numerical · 1 mark

For the two port network shown below, the [Y]-parameters is given as

$[Y] = \frac{1}{100}\begin{bmatrix} 2 & -1 \\ -1 & 4/3 \end{bmatrix} S$

The value of load impedance $Z_L$ , in Ω, for maximum power transfer will be _______ (rounded off to the nearest integer).

Answer (official key): 80

Worked solution: in your report after you take this paper.

Q34 · Digital Circuits · Numerical · 1 mark

For the circuit shown below, the propagation delay of each NAND gate is 1 ns. The critical path delay, in ns, is __________ (rounded off to the nearest integer).

Answer (official key): 2

Worked solution: in your report after you take this paper.

Q35 · Networks, Signals and Systems · Numerical · 1 mark

In the circuit shown below, switch S was closed for a long time. If the switch is opened at $t = 0$ , the maximum magnitude of the voltage $V_R$ , in volts, is _________ (rounded off to the nearest integer).

Answer (official key): 4

Worked solution: in your report after you take this paper.

Q36 · Probability and Statistics · MCQ · 2 marks

A random variable X, distributed normally as $N(0,1)$ , undergoes the transformation $Y = h(X)$ , given in the figure. The form of the probability density function of $Y$ is

(In the options given below, $a, b, c$ are non-zero constants and $g(y)$ is piece-wise continuous function)

(A)
$a\delta(y-1) + b\delta(y+1) + g(y)$
(B)
$a\delta(y+1) + b\delta(y) + c\delta(y-1) + g(y)$
(C)
$a\delta(y+2) + b\delta(y) + c\delta(y-2) + g(y)$
(D)
$a\delta(y+2) + b\delta(y-2) + g(y)$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q37 · Calculus · MCQ · 2 marks

The value of the line integral $\int_P^Q (z^2\,dx + 3y^2\,dy + 2xz\,dz)$ along the straight line joining the points $P\,(1,1,2)$ and $Q\,(2,3,1)$ is

(A)
20
(B)
24
(C)
29
(D)
-5

Answer (official key): B

Worked solution: in your report after you take this paper.

Q38 · Linear Algebra · MCQ · 2 marks

Let $\boldsymbol{x}$ be an $n \times 1$ real column vector with length $l = \sqrt{\boldsymbol{x}^T\boldsymbol{x}}$ . The trace of the matrix $P = \boldsymbol{x}\boldsymbol{x}^T$ is

(A)
$l^2$
(B)
$\dfrac{l^2}{4}$
(C)
$l$
(D)
$\dfrac{l^2}{2}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q39 · Analog Circuits · MCQ · 2 marks

The $\frac{V_{OUT}}{V_{IN}}$ of the circuit shown below is

(A)
$-\dfrac{R_4}{R_3}$
(B)
$\dfrac{R_4}{R_3}$
(C)
$1 + \dfrac{R_4}{R_3}$
(D)
$1 - \dfrac{R_4}{R_3}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q40 · Analog Circuits · MCQ · 2 marks

In the circuit shown below, $D_1$ and $D_2$ are silicon diodes with cut-in voltage of 0.7 V. $V_{IN}$ and $V_{OUT}$ are input and output voltages in volts. The transfer characteristic is

(A)
(B)
(C)
(D)

Answer (official key): A

Worked solution: in your report after you take this paper.

Q41 · Control Systems · MCQ · 2 marks

A closed loop system is shown in the figure where $k > 0$ and $\alpha > 0$ . The steady state error due to a ramp input ( $R(s) = \alpha/s^2$ ) is given by

(A)
$\dfrac{2\alpha}{k}$
(B)
$\dfrac{\alpha}{k}$
(C)
$\dfrac{\alpha}{2k}$
(D)
$\dfrac{\alpha}{4k}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q42 · Control Systems · MCQ · 2 marks

In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as $Y(s) = G_1(s)R(s) + G_2(s)D(s)$ .

$G_1(s)$ and $G_2(s)$ are given by

(A)
$G_1(s) = \dfrac{G(s)}{1 + G(s) + G(s)H(s)}$ and $G_2(s) = \dfrac{G(s)}{1 + G(s) + G(s)H(s)}$
(B)
$G_1(s) = \dfrac{G(s)}{1 + G(s) + H(s)}$ and $G_2(s) = \dfrac{G(s)}{1 + G(s) + H(s)}$
(C)
$G_1(s) = \dfrac{G(s)}{1 + G(s) + H(s)}$ and $G_2(s) = \dfrac{G(s)}{1 + G(s) + G(s)H(s)}$
(D)
$G_1(s) = \dfrac{G(s)}{1 + G(s) + G(s)H(s)}$ and $G_2(s) = \dfrac{G(s)}{1 + G(s) + H(s)}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q43 · Control Systems · MCQ · 2 marks

The state equation of a second order system is

$\dot{\boldsymbol{x}}(t) = A\boldsymbol{x}(t)$ , $\boldsymbol{x}(0)$ is the initial condition.

Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of $A$ and $\boldsymbol{v}_1$ and $\boldsymbol{v}_2$ are the corresponding eigenvectors. For constants $\alpha_1$ and $\alpha_2$ , the solution, $\boldsymbol{x}(t)$ , of the state equation is

(A)
$\sum_{i=1}^{2}\alpha_i e^{\lambda_i t}\boldsymbol{v}_i$
(B)
$\sum_{i=1}^{2}\alpha_i e^{2\lambda_i t}\boldsymbol{v}_i$
(C)
$\sum_{i=1}^{2}\alpha_i e^{3\lambda_i t}\boldsymbol{v}_i$
(D)
$\sum_{i=1}^{2}\alpha_i e^{4\lambda_i t}\boldsymbol{v}_i$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q44 · Networks, Signals and Systems · MCQ · 2 marks

The switch $S_1$ was closed and $S_2$ was open for a long time. At $t = 0$ , switch $S_1$ is opened and $S_2$ is closed, simultaneously. The value of $i_c(0^+)$ , in amperes, is

(A)
1
(B)
−1
(C)
0.2
(D)
0.8

Answer (official key): B

Worked solution: in your report after you take this paper.

Q45 · Communications · MCQ · 2 marks

Let a frequency modulated (FM) signal

$x(t) = A\cos\left(\omega_c t + k_f\int_{-\infty}^{t} m(\lambda)d\lambda\right)$ , where $m(t)$ is a message signal of bandwidth W. It is passed through a non-linear system with output $y(t) = 2x(t) + 5(x(t))^2$ . Let $B_T$ denote the FM bandwidth. The minimum value of $\omega_c$ required to recover $x(t)$ from $y(t)$ is

(A)
$B_T + W$
(B)
$\dfrac{3}{2}B_T$
(C)
$2B_T + W$
(D)
$\dfrac{5}{2}B_T$

Answer (official key): B

Worked solution: in your report after you take this paper.

Q46 · Networks, Signals and Systems · MCQ · 2 marks

The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain $\frac{V_{out}}{V_s}$ is

(A)
$h_{11} = 0, h_{12} = 0, h_{21} =$ very high and $h_{22} = 0$
(B)
$h_{11} =$ very high, $h_{12} = 0, h_{21} =$ very high and $h_{22} = 0$
(C)
$h_{11} = 0, h_{12} =$ very high, $h_{21} =$ very high and $h_{22} = 0$
(D)
$h_{11} = 0, h_{12} = 0, h_{21} =$ very high and $h_{22} =$ very high

Answer (official key): Marks to all

Everyone who took this paper got the marks for this question. Marks to all in GATE

Worked solution: in your report after you take this paper.

Q47 · Networks, Signals and Systems · MCQ · 2 marks

Consider a discrete-time periodic signal with period $N = 5$ . Let the discrete-time Fourier series (DTFS) representation be $x[n] = \sum_{k=0}^{4} a_k e^{\frac{jk2\pi n}{5}}$ , where $a_0 = 1, a_1 = 3j, a_2 = 2j, a_3 = -2j$ and $a_4 = -3j$ . The value of the sum $\sum_{n=0}^{4} x[n]\sin\frac{4\pi n}{5}$ is

(A)
−10
(B)
10
(C)
−2
(D)
2

Answer (official key): A

Worked solution: in your report after you take this paper.

Q48 · Networks, Signals and Systems · MCQ · 2 marks

Let an input $x[n]$ having discrete time Fourier transform

$X(e^{j\Omega}) = 1 - e^{-j\Omega} + 2e^{-3j\Omega}$ be passed through an LTI system. The frequency response of the LTI system is $H(e^{j\Omega}) = 1 - \frac{1}{2}e^{-j2\Omega}$ . The output $y[n]$ of the system is

(A)
$\delta[n] + \delta[n-1] - \frac{1}{2}\delta[n-2] - \frac{5}{2}\delta[n-3] + \delta[n-5]$
(B)
$\delta[n] - \delta[n-1] - \frac{1}{2}\delta[n-2] - \frac{5}{2}\delta[n-3] + \delta[n-5]$
(C)
$\delta[n] - \delta[n-1] - \frac{1}{2}\delta[n-2] + \frac{5}{2}\delta[n-3] - \delta[n-5]$
(D)
$\delta[n] + \delta[n-1] + \frac{1}{2}\delta[n-2] + \frac{5}{2}\delta[n-3] + \delta[n-5]$

Answer (official key): C

Worked solution: in your report after you take this paper.

Q49 · Networks, Signals and Systems · MCQ · 2 marks

Let $x(t) = 10\cos(10.5Wt)$ be passed through an LTI system having impulse response $h(t) = \pi\left(\dfrac{\sin Wt}{\pi t}\right)^2\cos 10Wt$ . The output of the system is

(A)
$\left(\frac{15W}{4}\right)\cos(10.5Wt)$
(B)
$\left(\frac{15W}{2}\right)\cos(10.5Wt)$
(C)
$\left(\frac{15W}{8}\right)\cos(10.5Wt)$
(D)
$(15W)\cos(10.5Wt)$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q50 · Communications · MCQ · 2 marks

Let $x_1(t)$ and $x_2(t)$ be two band-limited signals having bandwidth $B = 4\pi \times 10^3$ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

(A)
$20\pi \times 10^3$
(B)
$40\pi \times 10^3$
(C)
$8\pi \times 10^3$
(D)
$32\pi \times 10^3$

Answer (official key): D

Worked solution: in your report after you take this paper.

Q51 · Electromagnetics · MCQ · 2 marks

The S-parameters of a two port network is given as

$[S] = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix}$

with reference to $Z_0$ . Two lossless transmission line sections of electrical lengths $\theta_1 = \beta l_1$ and $\theta_2 = \beta l_2$ are added to the input and output ports for measurement purposes, respectively. The S-parameters $[S']$ of the resultant two port network is

(A)
$\begin{bmatrix} S_{11}e^{-j2\theta_1} & S_{12}e^{-j(\theta_1+\theta_2)} \\ S_{21}e^{-j(\theta_1+\theta_2)} & S_{22}e^{-j2\theta_2} \end{bmatrix}$
(B)
$\begin{bmatrix} S_{11}e^{j2\theta_1} & S_{12}e^{-j(\theta_1+\theta_2)} \\ S_{21}e^{-j(\theta_1+\theta_2)} & S_{22}e^{j2\theta_2} \end{bmatrix}$
(C)
$\begin{bmatrix} S_{11}e^{j2\theta_1} & S_{12}e^{j(\theta_1+\theta_2)} \\ S_{21}e^{j(\theta_1+\theta_2)} & S_{22}e^{j2\theta_2} \end{bmatrix}$
(D)
$\begin{bmatrix} S_{11}e^{-j2\theta_1} & S_{12}e^{j(\theta_1+\theta_2)} \\ S_{21}e^{j(\theta_1+\theta_2)} & S_{22}e^{-j2\theta_2} \end{bmatrix}$

Answer (official key): A

Worked solution: in your report after you take this paper.

Q52 · Electromagnetics · MSQ · 2 marks

The standing wave ratio on a 50 Ω lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance $R_m$ of the same line. The value of $R_m$ and $l_m$ , respectively, are

(A)
$R_m = 100\,\Omega$ , $l_m = 20$ cm
(B)
$R_m = 25\,\Omega$ , $l_m = 20$ cm
(C)
$R_m = 100\,\Omega$ , $l_m = 5$ cm
(D)
$R_m = 25\,\Omega$ , $l_m = 5$ cm

Answer (official key): B, C

Read the worked solution

Q53 · Electromagnetics · MSQ · 2 marks

The electric field of a plane electromagnetic wave is

$\boldsymbol{E} = \boldsymbol{a}_x C_{1x}\cos(\omega t - \beta z) + \boldsymbol{a}_y C_{1y}\cos(\omega t - \beta z + \theta)$ V/m.

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

(A)
$C_{1x} = 1, C_{1y} = 1, \theta = \pi/4$
(B)
$C_{1x} = 2, C_{1y} = 1, \theta = \pi/2$
(C)
$C_{1x} = 1, C_{1y} = 2, \theta = 3\pi/2$
(D)
$C_{1x} = 2, C_{1y} = 1, \theta = 3\pi/4$

Answer (official key): A, B, D

Worked solution: in your report after you take this paper.

Q54 · Electromagnetics · MSQ · 2 marks

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

(A)
(B)
(C)
(D)

Answer (official key): B, C, D

Worked solution: in your report after you take this paper.

Q55 · Calculus · Numerical · 2 marks

The value of the integral $\iint_R xy\,dx\,dy$ over the region R, given in the figure, is _______ (rounded off to the nearest integer).

Answer (official key): 0

Worked solution: in your report after you take this paper.

Q56 · Electronic Devices · Numerical · 2 marks

In an extrinsic semiconductor, the hole concentration is given to be $1.5n_i$ where $n_i$ is the intrinsic carrier concentration of $1 \times 10^{10}\ cm^{-3}$ . The ratio of electron to hole mobility for equal hole and electron drift current is given as __________ (rounded off to two decimal places).

Answer (official key): 2.2 to 2.3

Worked solution: in your report after you take this paper.

Q57 · Control Systems · Numerical · 2 marks

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $G(s) = \dfrac{k(s+z)^a}{s^b(s+p)^c}$ , where $k, z, p, a, b$ and $c$ are positive constants. The value of $(a + b + c)$ is __________ (rounded off to the nearest integer).

Answer (official key): 4

Worked solution: in your report after you take this paper.

Q58 · Networks, Signals and Systems · Numerical · 2 marks

Let $x_1(t) = u(t + 1.5) - u(t - 1.5)$ and $x_2(t)$ is shown in the figure below. For $y(t) = x_1(t) * x_2(t)$ , the $\int_{-\infty}^{\infty} y(t)dt$ is ____________ (rounded off to the nearest integer).

Answer (official key): 15

Worked solution: in your report after you take this paper.

Q59 · Communications · Numerical · 2 marks

Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2}$ W/Hz. If $X(t)$ is input to an LTI system with impulse response $e^{-t}u(t)$ . The average power of the system output is __________ W (rounded off to two decimal places).

Answer (official key): 0.24 to 0.26

Worked solution: in your report after you take this paper.

Q60 · Electromagnetics · Numerical · 2 marks

A transparent dielectric coating is applied to glass ( $\varepsilon_r = 4, \mu_r = 1$ ) to eliminate the reflection of red light ( $\lambda_0 = 0.75\ \mu$ m). The minimum thickness of the dielectric coating, in µm, that can be used is _________ (rounded off to two decimal places).

Answer (official key): 0.12 to 0.14

Worked solution: in your report after you take this paper.

Q61 · Electronic Devices · Numerical · 2 marks

In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is $1 \times 10^{19}\,\text{cm}^{-3}$ . The thermal equilibrium hole concentration in silicon at 400 K is ___________ × $10^{13}\,\text{cm}^{-3}$ (rounded off to two decimal places).

Given kT at 300 K is 0.026 eV.

Answer (official key): 60 to 70

Worked solution: in your report after you take this paper.

Q62 · Analog Circuits · Numerical · 2 marks

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 µs. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is _______ µs (rounded off to two decimal places).

Answer (official key): 8.3 to 8.34

Worked solution: in your report after you take this paper.

Q63 · Digital Circuits · Numerical · 2 marks

In a given sequential circuit, initial states are $Q_1 = 1$ and $Q_2 = 0$ . For a clock frequency of 1 MHz, the frequency of signal $Q_2$ in kHz, is ___________ (rounded off to the nearest integer).

Answer (official key): 250

Worked solution: in your report after you take this paper.

Q64 · Analog Circuits · Numerical · 2 marks

In the circuit below, the voltage $V_L$ is ____________ V (rounded off to two decimal places).

Answer (official key): 2

Worked solution: in your report after you take this paper.

Q65 · Communications · Numerical · 2 marks

The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of “yes/no” questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______ (rounded off to two decimal places).

Symbols	a	b	c	d	e	f	g	h
Frequency of occurrence	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{16}$	$\frac{1}{32}$	$\frac{1}{64}$	$\frac{1}{128}$	$\frac{1}{128}$

Answer (official key): 1.97 to 1.99

Worked solution: in your report after you take this paper.

All 65 questions of GATE 2023 EC

Q1 · General Aptitude · MCQ · 1 mark

Q2 · General Aptitude · MCQ · 1 mark

Q3 · General Aptitude · MCQ · 1 mark

Q4 · General Aptitude · MCQ · 1 mark

Q5 · General Aptitude · MCQ · 1 mark

Q6 · General Aptitude · MCQ · 2 marks

Q7 · General Aptitude · MCQ · 2 marks

Q8 · General Aptitude · MCQ · 2 marks

Q9 · General Aptitude · MCQ · 2 marks

Q10 · General Aptitude · MCQ · 2 marks

Q11 · Linear Algebra · MCQ · 1 mark

Q12 · Calculus · MCQ · 1 mark

Q13 · Complex Variables · MCQ · 1 mark

Q14 · Complex Variables · MCQ · 1 mark

Q15 · Linear Algebra · MCQ · 1 mark

Q16 · Electronic Devices · MCQ · 1 mark

Q17 · Electronic Devices · MCQ · 1 mark

Q18 · Networks, Signals and Systems · MCQ · 1 mark

Q19 · Electronic Devices · MCQ · 1 mark

Q20 · Electromagnetics · MCQ · 1 mark

Q21 · Analog Circuits · MCQ · 1 mark

Q22 · Analog Circuits · MCQ · 1 mark

Q23 · Digital Circuits · MCQ · 1 mark

Q24 · Digital Circuits · MCQ · 1 mark

Q25 · Control Systems · MCQ · 1 mark

Q26 · Networks, Signals and Systems · MCQ · 1 mark

Q27 · Communications · MCQ · 1 mark

Q28 · Networks, Signals and Systems · MCQ · 1 mark

Q29 · Networks, Signals and Systems · MCQ · 1 mark

Q30 · Networks, Signals and Systems · MSQ · 1 mark

Q31 · Digital Circuits · Numerical · 1 mark

Q32 · Networks, Signals and Systems · Numerical · 1 mark

Q33 · Networks, Signals and Systems · Numerical · 1 mark

Q34 · Digital Circuits · Numerical · 1 mark

Q35 · Networks, Signals and Systems · Numerical · 1 mark

Q36 · Probability and Statistics · MCQ · 2 marks

Q37 · Calculus · MCQ · 2 marks

Q38 · Linear Algebra · MCQ · 2 marks

Q39 · Analog Circuits · MCQ · 2 marks

Q40 · Analog Circuits · MCQ · 2 marks

Q41 · Control Systems · MCQ · 2 marks

Q42 · Control Systems · MCQ · 2 marks

Q43 · Control Systems · MCQ · 2 marks

Q44 · Networks, Signals and Systems · MCQ · 2 marks

Q45 · Communications · MCQ · 2 marks

Q46 · Networks, Signals and Systems · MCQ · 2 marks

Q47 · Networks, Signals and Systems · MCQ · 2 marks

Q48 · Networks, Signals and Systems · MCQ · 2 marks

Q49 · Networks, Signals and Systems · MCQ · 2 marks

Q50 · Communications · MCQ · 2 marks

Q51 · Electromagnetics · MCQ · 2 marks

Q52 · Electromagnetics · MSQ · 2 marks

Q53 · Electromagnetics · MSQ · 2 marks

Q54 · Electromagnetics · MSQ · 2 marks

Q55 · Calculus · Numerical · 2 marks

Q56 · Electronic Devices · Numerical · 2 marks

Q57 · Control Systems · Numerical · 2 marks

Q58 · Networks, Signals and Systems · Numerical · 2 marks

Q59 · Communications · Numerical · 2 marks

Q60 · Electromagnetics · Numerical · 2 marks

Q61 · Electronic Devices · Numerical · 2 marks

Q62 · Analog Circuits · Numerical · 2 marks

Q63 · Digital Circuits · Numerical · 2 marks

Q64 · Analog Circuits · Numerical · 2 marks

Q65 · Communications · Numerical · 2 marks