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GATE EC 2016 Set 3

All 65 solved GATE EC 2016 Set 3 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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100

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Difficulty mixEasy 21Medium 37Hard 7

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65 of 65 questions

Question typeDifficultyYour progress

Electronics and Communication Engineering (Set 3)

11
Q11MCQ1 markEasy
Consider a $2 \times 2$ square matrix $A = \begin{bmatrix} \sigma & x \\ \omega & \sigma \end{bmatrix}$ where x is unknown. If the eigenvalues of the matrix A are…
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Question
$2 \times 2$
Your answer
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A. $+ j\omega$ B. $-j\omega$ C. $+\omega$ D. $-\omega$
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$2 \times 2$
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12
Q12NAT1 markEasy
For $f(z) = \frac{\sin(z)}{z^2}$ , the residue of the pole at $z = 0$ is
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Question
$f(z) = \frac{\sin(z)}{z^2}$
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$f(z) = \frac{\sin(z)}{z^2}$
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13
Q13NAT1 markEasy
The probability of getting a “head” in a single toss of a biased coin is $0.3$ . The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the…
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Question
$0.3$
Your answer
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$P(H) = 0.3$
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14
Q14NAT1 markEasy
The integral $\int_{0}^{1} \frac{dx}{\sqrt{(1-x)}}$ is equal to __________
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Question
$\int_{0}^{1} \frac{dx}{\sqrt{(1-x)}}$
Your answer
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$I = \int_{0}^{1} \frac{dx}{\sqrt{1-x}}$
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15
Q15NAT1 markHard
Consider the first order initial value problem $y' = y + 2x - x^2, y(0) = 1, (0 \leq x < \infty)$ with exact solution $y(x) = x^2 + e^x$ . For $x = 0.1$ , the percentage difference…
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Question
$y' = y + 2x - x^2, y(0) = 1, (0 \leq x < \infty)$
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$x = 0.1$
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16
Q16MCQ1 markMedium
Consider the signal $x(t) = \cos(6\pi t) + \sin(8\pi t)$ , where $t$ is in seconds. The Nyquist sampling rate (in samples/second) for the signal $y(t) = x(2t + 5)$ is
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Question
$x(t) = \cos(6\pi t) + \sin(8\pi t)$
Your answer
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A. $8$ B. $12$ C. $16$ D. $32$
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$x(t) = \cos(6\pi t) + \sin(8\pi t)$
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17
Q17MCQ1 markEasy
If the signal $x(t) = \frac{\sin(t)}{\pi t} * \frac{\sin(t)}{\pi t}$ with $*$ denoting the convolution operation, then $x(t)$ is equal to
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Question
$x(t) = \frac{\sin(t)}{\pi t} * \frac{\sin(t)}{\pi t}$
Your answer
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A. $\pi$ B. $\pi$ C. $\pi$ D. $\pi$
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$g(t) = \frac{\sin(t)}{\pi t}$
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18
Q18MCQ1 markEasy
A discrete-time signal $x[n] = \delta[n - 3] + 2 \delta[n - 5]$ has z-transform $X(z)$ . If $Y(z) = X(-z)$ is the z-transform of another signal $y[n]$ , then
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Question
$x[n] = \delta[n - 3] + 2 \delta[n - 5]$
Your answer
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A. $y[n] = x[n]$ B. $y[n] = x[-n]$ C. $y[n] = -x[n]$ D. $y[n] = -x[-n]$
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$x[n] \leftrightarrow X(z)$
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19
Q19MCQ1 markMedium
In the RLC circuit shown in the figure, the input voltage is given by $v_i(t) = 2 \cos(200t) + 4 \sin(500t)$ . The output voltage $v_o(t)$ is
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Question
$v_i(t) = 2 \cos(200t) + 4 \sin(500t)$
Your answer
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A. $\cos(200t) + 2 \sin(500t)$ B. $2\cos(200t) + 4 \sin(500t)$ C. $\sin(200t) + 2 \cos(500t)$ D. $2\sin(200t) + 4 \cos(500t)$
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$\omega_1 = \frac{1}{\sqrt{L_1 C_1}} = \frac{1}{\sqrt{0.25 \times 100 \times 10^{-6}}} = 200$
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20
Q20MCQ1 markMedium
The I-V characteristics of three types of diodes at the room temperature, made of semiconductors X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped…
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Question
$E_{gX}$
Your answer
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A. $E_{gX} > E_{gY} > E_{gZ}$ B. $E_{gX} = E_{gY} = E_{gZ}$ C. $E_{gX} < E_{gY} < E_{gZ}$ D. $no relationship among these band gaps exists.$
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$V_{\gamma}$
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21
Q21MCQ1 markMedium
The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in [figure]
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Question
$The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in$
Your answer
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A. $inversion$ B. $accumulation$ C. $depletion$ D. $flat band$
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$E_i$
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22
Q22NAT1 markMedium
The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of power $100\text{ mW/cm}^2$ . The solar cell has an area of $3\text{ cm}^2$ and a…
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Question
$100\text{ mW/cm}^2$
Your answer
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$P_{in}$
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23
Q23NAT1 markMedium
The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is very large compared to the time period of the ac voltage. Assuming that the diodes…
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Question
$V_O$
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$C$
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24
Q24NAT1 markMedium
Consider the circuit shown in the figure. Assuming $V_{BE1} = V_{EB2} = 0.7$ volt, the value of the dc voltage $V_{C2}$ (in volt) is __________
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Question
$V_{BE1} = V_{EB2} = 0.7$
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$V_{B1} = V_{CC} = 2.5V$
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25
Q25NAT1 markMedium
In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin 3 is __________
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Question
$In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin 3 is__________$
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$f = \frac{1.44}{(R_A + 2R_B)C}$
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26
Q26MCQ1 markMedium
In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the…
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Question
$In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be$
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A. $4E and 0$ B. $4E and 1$ C. $4F and 0$ D. $4F and 1$
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$D_7$
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27
Q27MCQ1 markEasy
The logic functionality realized by the circuit shown below is [figure]
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Question
$NMOS pass transistor logic circuit with inputs $A$, $B$, $\bar{B}$ and output $Y$$
Your answer
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A. $OR$ B. $XOR$ C. $NAND$ D. $AND$
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$B$
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28
Q28MCQ1 markEasy
The minimum number of $2$ -input NAND gates required to implement a $2$ -input XOR gate is
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Question
$2$
Your answer
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A. $4$ B. $5$ C. $6$ D. $7$
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$Y = A \oplus B = A\bar{B} + \bar{A}B$
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29
Q29MCQ1 markMedium
The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain $G$ of the system is [figure]
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Question
$G$
Your answer
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A. $G = \frac{G_1 G_2}{1 + G_1 H_1}$ B. $G = \frac{G_1 G_2}{1 + G_1 G_2 + G_1 H_1}$ C. $G = \frac{G_1 G_2}{1 + G_1 G_2 H_1}$ D. $G = \frac{G_1 G_2}{1 + G_1 G_2 + G_1 G_2 H_1}$
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$G_1$
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30
Q30MCQ1 markEasy
For the unity feedback control system shown in the figure, the open-loop transfer function $G(s)$ is given as $G(s) = \frac{2}{s(s+1)}.$ The steady state error $e_{ss}$ due to a…
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Question
$G(s)$
Your answer
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A. $0$ B. $0.5$ C. $1.0$ D. $\infty$
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$G(s) = \frac{2}{s(s+1)}$
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31
Q31NAT1 markMedium
For a superheterodyne receiver, the intermediate frequency is $15\text{ MHz}$ and the local oscillator frequency is $3.5\text{ GHz}$ . If the frequency of the received signal is…
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Question
$15\text{ MHz}$
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$f_{IF} = 15\text{ MHz}$
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32
Q32NAT1 markMedium
An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities…
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Question
$p_1 = p_4 = 0.125$
Your answer
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$f_s$
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33
Q33MCQ1 markEasy
A binary baseband digital communication system employs the signal [figure] $p(t) = \begin{cases} \frac{1}{\sqrt{T_S}}, & 0 \leq t \leq T_S \\ 0, & \text{otherwise} \end{cases}$ …
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Question
$p(t) = \begin{cases} \frac{1}{\sqrt{T_S}}, & 0 \leq t \leq T_S \\ 0, & \text{otherwise} \end{cases}$
Your answer
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A.B.C.D.
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$p(t)$
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34
Q34MCQ1 markEasy
If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be
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Question
$If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be$
Your answer
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A. $right-handed circularly polarized$ B. $left-handed circularly polarized$ C. $45^0$ D. $horizontally polarized$
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$180^\circ$
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35
Q35MCQ1 markEasy
Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?
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Question
$Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?$
Your answer
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A. $\nabla \cdot \vec{B} = 0$ B. $\nabla \cdot \vec{D} = \rho_V$ C. $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$ D. $\nabla \times \vec{H} = \sigma \vec{E} + \frac{\partial \vec{D}}{\partial t}$
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$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$
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36
Q36MCQ2 marksMedium
The particular solution of the initial value problem given below is…
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Question
$\frac{d^2y}{dx^2} + 12\frac{dy}{dx} + 36y = 0 \text{ with } y(0) = 3 \text{ and } \left.\frac{dy}{dx}\right|_{x=0} = -36$
Your answer
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A. $(3 - 18x) e^{-6x}$ B. $(3 + 25x) e^{-6x}$ C. $(3 + 20x) e^{-6x}$ D. $(3 - 12x) e^{-6x}$
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$\frac{d^2y}{dx^2} + 12\frac{dy}{dx} + 36y = 0$
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37
Q37MCQ2 marksMedium
If the vectors $\mathbf{e}_1 = (1, 0, 2)$ , $\mathbf{e}_2 = (0, 1, 0)$ and $\mathbf{e}_3 = (-2, 0, 1)$ form an orthogonal basis of the three-dimensional real space $\mathbb{R}^3$ ,…
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Question
$\mathbf{e}_1 = (1, 0, 2)$
Your answer
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A. $\mathbf{u} = -\frac{2}{5}\mathbf{e}_1 - 3\mathbf{e}_2 - \frac{11}{5}\mathbf{e}_3$ B. $\mathbf{u} = -\frac{2}{5}\mathbf{e}_1 - 3\mathbf{e}_2 + \frac{11}{5}\mathbf{e}_3$ C. $\mathbf{u} = -\frac{2}{5}\mathbf{e}_1 + 3\mathbf{e}_2 + \frac{11}{5}\mathbf{e}_3$ D. $\mathbf{u} = -\frac{2}{5}\mathbf{e}_1 + 3\mathbf{e}_2 - \frac{11}{5}\mathbf{e}_3$
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$\{\mathbf{e}_1, \mathbf{e}_2, \mathbf{e}_3\}$
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38
Q38NAT2 marksMedium
A triangle in the $xy$ -plane is bounded by the straight lines $2x = 3y$ , $y = 0$ and $x = 3$ . The volume above the triangle and under the plane $x + y + z = 6$ is __________
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Question
$xy$
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$D$
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39
Q39MCQ2 marksMedium
The values of the integral $\frac{1}{2\pi j} \oint_c \frac{e^z}{z - 2} dz$ along a closed contour $c$ in anti-clockwise direction for (i) the point $z_0 = 2$ inside the contour…
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Question
$\frac{1}{2\pi j} \oint_c \frac{e^z}{z - 2} dz$
Your answer
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A. $(i) 2.72, (ii) 0$ B. $(i) 7.39, (ii) 0$ C. $(i) 0, (ii) 2.72$ D. $(i) 0, (ii) 7.39$
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$f(z)$
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40
Q40MCQ2 marksMedium
A signal $2 \cos \left( \frac{2\pi}{3} t \right) - \cos (\pi t)$ is the input to an LTI system with the transfer function $H(s) = e^s + e^{-s}.$ If $C_k$ denotes the $k^{th}$ …
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Question
$2 \cos \left( \frac{2\pi}{3} t \right) - \cos (\pi t)$
Your answer
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A. $0$ B. $1$ C. $2$ D. $3$
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$x(t) = 2 \cos\left(\frac{2\pi}{3}t\right) - \cos(\pi t)$
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41
Q41MCQ2 marksMedium
The ROC (region of convergence) of the $z$ -transform of a discrete-time signal is represented by the shaded region in the $z$ -plane. If the signal…
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Question
$z$
Your answer
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A.B.C.D.
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$x[n] = (2.0)^{|n|}$
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42
Q42NAT2 marksHard
Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\ \Omega$ resistor suddenly burns out, resulting in an open circuit. The current…
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Question
$t = 0$
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$t = 0^-$
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43
Q43NAT2 marksMedium
In the figure shown, the current $i$ (in ampere) is __________ [figure]
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$i$
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$i$
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44
Q44MCQ2 marksMedium
The z-parameter matrix $\begin{bmatrix} z_{11} & z_{12} \\ z_{21} & z_{22} \\ \end{bmatrix}$ for the two-port network shown is [figure]
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Question
$\begin{bmatrix} z_{11} & z_{12} \\ z_{21} & z_{22} \\ \end{bmatrix}$
Your answer
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A. $, [-2, 2]]]$ B. $, [2, 2]]]$ C. $, [6, 9]]]$ D. $, [6, 9]]]$
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$z_{11} = \frac{V_1}{I_1} \bigg|_{I_2=0}$
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45
Q45NAT2 marksHard
A continuous-time speech signal $x_a(t)$ is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size $N$ . The DFT of each block is to be…
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Question
$x_a(t)$
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$f_s = 8000$
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46
Q46MCQ2 marksMedium
The direct form structure of an FIR (finite impulse response) filter is shown in the figure. [figure]…
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Question
$is multiplied by 5 and also passed through two unit delays. The output of the second unit delay is multiplied by 5 and subtracted from the first product to give$
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A. $low-pass filter$ B. $high-pass filter$ C. $band-pass filter$ D. $band-stop filter$
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$y[n] = 5x[n] - 5x[n-2]$
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47
Q47NAT2 marksMedium
The injected excess electron concentration profile in the base region of an npn BJT, biased in the active region, is linear, as shown in the figure. If the area of the…
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Question
$0.001\text{ cm}^2$
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$I_C$
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48
Q48NAT2 marksMedium
Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator materials X (of thickness $t_1 = 1\text{ nm}$ and dielectric constant…
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Question
$t_1 = 1\text{ nm}$
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$C_I = \frac{\epsilon_0}{\frac{t_1}{\epsilon_1} + \frac{t_2}{\epsilon_2}}$
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49
Q49MCQ2 marksMedium
The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from 0 to 100…
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Question
$The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from 0 to 100 V, then breakdown occurs in$
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A. $D1 only$ B. $D2 only$ C. $both D1 and D2$ D. $none of D1 and D2$
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$Correct answer (A) D1 only Step-by-step solution In Figure II, the two Zener diodes D1 and D2 are connected in series with opposing orientations. 1. When the supply voltage is positive (0 to 100 V), D1 is reverse-biased and D2 is forward-biased. 2. From Figure I, the Zener breakdown voltage for D1 is 80 V and for D2 is 70 V. 3. As the supply voltage increases, D2 remains forward-biased (acting like a closed switch with a small forward drop). 4. D1 is in reverse bias and will enter Zener breakdown when the voltage across it reaches its breakdown threshold of 80 V. 5. Since the supply goes up to 100 V, D1 will definitely break down. D2, being forward-biased, does not undergo breakdown. Therefore, breakdown occurs in D1 only. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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50
Q50NAT2 marksMedium
For the circuit shown in the figure, $R_1 = R_2 = R_3 = 1\ \Omega$ , $L = 1\ \mu\text{H}$ and $C = 1\ \mu\text{F}$ . If the input $V_{\text{in}} = \cos(10^6 t)$ , then the overall…
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Question
$R_1 = R_2 = R_3 = 1\ \Omega$
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$\omega = 10^6\ \text{rad/s}$
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51
Q51MCQ2 marksMedium
In the circuit shown in the figure, the channel length modulation of all transistors is non-zero ( $\lambda \neq 0$ ). Also, all transistors operate in saturation and have…
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Question
$\lambda \neq 0$
Your answer
Choose one option, then check your answer.
A. $-g_{m1}(r_{o1}||r_{o2}|| r_{o3})$ B. $-g_{m1}(r_{o1}|| \frac{1}{g_{m3}} || r_{o3})$ C. $-g_{m1} (r_{o1}|| ( \frac{1}{g_{m2}} ||r_{o2}) || r_{o3})$ D. $-g_{m1}(r_{o1}|| ( \frac{1}{g_{m3}} ||r_{o3}) || r_{o2})$
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$M_1$
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52
Q52NAT2 marksHard
In the circuit shown in the figure, transistor M1 is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming the channel…
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Question
$g_m = 0.01$
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$g_m = 0.01$
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53
Q53MCQ2 marksMedium
Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is [figure]
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Question
$Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is$
Your answer
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A. $P\bar{Q}S\bar{X} + P\bar{Q}\bar{S}X + Q\bar{R}S\bar{X} + Q\bar{R}\bar{S}X$ B. $\bar{Q}S\bar{X} + \bar{Q}\bar{S}X$ C. $Q\bar{S}X + Q\bar{S}\bar{X}$ D. $Q\bar{S} + \bar{Q}S$
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$\bar{Q}S\bar{X}$
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54
Q54NAT2 marksMedium
For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are $2\text{ ns}$ , $1.5\text{ ns}$ and $1\text{ ns}$ , respectively. If all the inputs…
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Question
$2\text{ ns}$
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$Y$
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55
Q55MCQ2 marksHard
For the circuit shown in the figure, the delay of the bubbled NAND gate is $2\text{ ns}$ and that of the counter is assumed to be zero. [figure] If the clock (Clk) frequency is…
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$2\text{ ns}$
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A. $mod-5 counter$ B. $mod-6 counter$ C. $mod-7 counter$ D. $mod-8 counter$
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$1\text{ GHz}$
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56
Q56MCQ2 marksMedium
The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as | | | | |---|---|---| | $s^3$ | 1 | $(2K + 3)$ | | $s^2$ …
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$s^3$
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A. $-2.0 < K < 0.5$ B. $0 < K < 0.5$ C. $0 < K < \infty$ D. $0.5 < K < \infty$
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$s^3$
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57
Q57MCQ2 marksMedium
A second-order linear time-invariant system is described by the following state equations $\frac{d}{dt}x_1(t) + 2x_1(t) = 3u(t)$ $\frac{d}{dt}x_2(t) + x_2(t) = u(t)$ where…
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$\frac{d}{dt}x_1(t) + 2x_1(t) = 3u(t)$
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A. $controllable but not observable$ B. $observable but not controllable$ C. $both controllable and observable$ D. $neither controllable nor observable$
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$\dot{x} = Ax + Bu$
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58
Q58NAT2 marksMedium
The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as…
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$G(s) = \frac{K(s+2)}{s^2 + 2s + 2} \text{ and } H(s) = 1,$
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$1 + G(s)H(s) = 0$
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59
Q59MCQ2 marksMedium
A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$ , then the autocorrelation…
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$X(t)$
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A. $2R_X(\tau) + R_X(\tau - T_0) + R_X(\tau + T_0)$ B. $2R_X(\tau) - R_X(\tau - T_0) - R_X(\tau + T_0)$ C. $2R_X(\tau) + 2R_X(\tau - 2T_0)$ D. $2R_X(\tau) - 2R_X(\tau - 2T_0)$
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$Y(t)$
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60
Q60NAT2 marksHard
A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0$ kHz and two-sided noise power spectral density $\frac{\eta}{2} = 2.5 \times 10^{-5}$ …
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$4.0$
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$B = 4$
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61
Q61NAT2 marksMedium
The bit error probability of a memoryless binary symmetric channel is $10^{-5}$ . If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be…
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$10^{-5}$
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$p = 10^{-5}$
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62
Q62NAT2 marksMedium
Consider an air-filled rectangular waveguide with dimensions $a = 2.286\text{ cm}$ and $b = 1.016\text{ cm}$ . At $10\text{ GHz}$ operating frequency, the value of the propagation…
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$a = 2.286\text{ cm}$
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$TE_{10}$
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63
Q63MCQ2 marksMedium
Consider an air-filled rectangular waveguide with dimensions $a = 2.286\text{ cm}$ and $b = 1.016\text{ cm}$ . The increasing order of the cut-off frequencies for different modes is
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Question
$a = 2.286\text{ cm}$
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A. $TE_{01} < TE_{10} < TE_{11} < TE_{20}$ B. $TE_{20} < TE_{11} < TE_{10} < TE_{01}$ C. $TE_{10} < TE_{20} < TE_{01} < TE_{11}$ D. $TE_{10} < TE_{11} < TE_{20} < TE_{01}$
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$f_{c,mn} = \frac{c}{2} \sqrt{(\frac{m}{a})^2 + (\frac{n}{b})^2}$
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64
Q64NAT2 marksHard
A radar operating at $5\text{ GHz}$ uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and…
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$5\text{ GHz}$
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$P_r$
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65
Q65MCQ2 marksMedium
Consider the charge profile shown in the figure. The resultant potential distribution is best described by [figure]
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$Charge density profile $\rho(x)$ vs $x$$
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A.B.C.D.
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$\rho(x)$
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RS\PQ	00	10
00	0	0
01	1	1
11	1	1
10	0	0

RS\PQ	01	11
00	1	1
01	0	0
11	0	0
10	0	1


$s^3$	1	$(2K + 3)$
$s^2$	$2K$	4


$s^3$	1	$2K + 3$
$s^2$	$2K$	4
$s^1$	$\frac{2K(2K+3) - 1(4)}{2K}$	0
$s^0$	4

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