Recent questions tagged numerical-answers

0 votes

1 answer

1

GATE ECE 2022 | Question: 21
The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in $17$ of her matches, the bowler has taken $5$ wickets each. The median number of wickets taken by the bowler in a match is _______________ (rounded off to one decimal place).

Arjun asked in Analytical Aptitude Feb 15, 2022

by Arjun

6.0k points

385 views

0 votes

0 answers

2

GATE ECE 2022 | Question: 22
A simple closed path $C$ in the complex plane is shown in the figure. If $\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$ where $i = \sqrt{-1},$ then the value of $A$ is _________ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

111 views

0 votes

0 answers

3

GATE ECE 2022 | Question: 23
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}(t),$ then $\displaystyle \lim_{t \rightarrow \infty} y(t) =$ ______________ (rounded off to one decimal place).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

67 views

0 votes

0 answers

4

GATE ECE 2022 | Question: 24
An ideal $\text{MOS}$ capacitor (p-type semiconductor) is shown in the figure. The $\text{MOS}$ capacitor is under strong inversion with $V_{G} = 2 \; \text{V}.$ The corresponding inversion charge density $(Q_{IN})$ is $2.2 \; \mu \text{C /cm}^{2}.$ ... $Q_{IN}$ is ______________ $\mu \text{C/cm}^{2}$ (rounded off to one decimal place).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

106 views

0 votes

0 answers

5

GATE ECE 2022 | Question: 25
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the raw (uncoded) data rate is ____________ mega-bits per second (rounded off to one decimal place).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

78 views

0 votes

0 answers

6

GATE ECE 2022 | Question: 43
The value of the integral $ \iint_{D} 3(x^{2} + y^{2})dxdy,$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

31 views

0 votes

0 answers

7

GATE ECE 2022 | Question: 44
A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance $R$ is connected across Port $2.$ As $R$ is varied, the measured voltage ... by the load shown in $\text{Fig.(c)},$ the current $I_{2}$ is ___________ $\text{mA}$ (rounded off to one decimal place).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

18 views

0 votes

0 answers

8

GATE ECE 2022 | Question: 45
For a vector $\overline{x} = \left[ x [0], x[1], \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\overline{x}) = \left[ X [0], X[1], \dots, X[7] \right],$ ... $\overline{y} = DFT (DFT(\overline{x})),$ then the value of $y[0]$ is _____________ (rounded off to one decimal place).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

20 views

0 votes

0 answers

9

GATE ECE 2022 | Question: 46
A $p-$type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at $x = \pm 2l_{n},$ where $l_{n} = 10 ^{-4} \; \text{cm}$ is the diffusion length of ... photo-generated electrons at $x = + 2l_{n}$ is ______________ $\text{mA/cm}^{2}$ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

27 views

0 votes

0 answers

10

GATE ECE 2022 | Question: 47
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{out}}}{\partial V_{\text{in}}}$ is ____________ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

25 views

0 votes

0 answers

11

GATE ECE 2022 | Question: 48
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

21 views

0 votes

0 answers

12

GATE ECE 2022 | Question: 49
Consider the circuit shown with an ideal long channel $n \text{MOSFET}$ (enhancement-mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with $V_{GG}$ and $V_{DD}$ such that it acts as a linear amplifier ... $\dfrac{v_{A}}{v_{B}}$ is _____________ (rounded off to one decimal place).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

25 views

0 votes

0 answers

13

GATE ECE 2022 | Question: 50
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and $d(t),$ ... $e (\infty),$ due to a unit step disturbance $d(t),$ is __________ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

35 views

0 votes

0 answers

14

GATE ECE 2022 | Question: 51
The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked. The parameter $\alpha$ lies in the interval $[0.25, 1].$ The value of $\alpha$ for which the capacity of this channel is maximized, is ___________ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

35 views

0 votes

0 answers

15

GATE ECE 2022 | Question: 52
Consider communication over a memoryless binary symmetric channel using a $(7, 4)$ Hamming code. Each transmitted bit is received correctly with probability $(1 - \in),$ and flipped with probability $\in.$ For each codeword transmission, the ... the probability that a transmitted codeword is decoded correctly is ___________(rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

28 views

0 votes

0 answers

16

GATE ECE 2022 | Question: 53
Consider a channel over which either symbol $x_{A}$ or symbol $x_{B}$ is transmitted. Let the output of the channel $Y$ be the input to a maximum likelihood $\text{(ML)}$ detector at the receiver. The conditional probability density ... the standard unit step function. The probability of symbol error for this system is _____________ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

27 views

0 votes

0 answers

17

GATE ECE 2022 | Question: 54
Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, $f(x),$ as shown in the figure. Consider a $1$ bit quantizer that maps positive samples to value $\alpha$ and others to ... error, then $(\alpha^{\ast} - \beta^{\ast}) = $____________ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

92 views

0 votes

0 answers

18

GATE ECE 2022 | Question: 55
In an electrostatic field, the electric displacement density vector, $\overrightarrow{D},$ is given by $\overrightarrow{D} (x, y, z) = (x^{3} \overrightarrow{i} + y^{3} \overrightarrow{j} + xy^{2} \overrightarrow{k}) \; \text{C/m}^{2},$ where ... $R$ is _____________ $\text{C}$ (rounded off to two decimal places).

Arjun asked in Others Feb 15, 2022

by Arjun

6.0k points

25 views

0 votes

0 answers

19

GATE ECE 2021 | Question: 16
If the vectors $(1.0,\:-1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________

Arjun asked in Vector Analysis Feb 20, 2021

by Arjun

6.0k points

171 views

0 votes

0 answers

20

GATE ECE 2021 | Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4y-c_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ in a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x},\:a_{y}$ and $a_{z}$. If the field $F$ is irrotational (conservative), then the constant $c_{1}$ (in integer) is _________________

Arjun asked in Vector Analysis Feb 20, 2021

by Arjun

6.0k points

144 views

0 votes

0 answers

21

GATE ECE 2021 | Question: 18
Consider the circuit shown in the figure. The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

150 views

0 votes

0 answers

22

GATE ECE 2021 | Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

154 views

0 votes

0 answers

23

GATE ECE 2021 | Question: 20
An $8$-bit unipolar (all analog output values are positive) digital-to-analog converter $\text{(DAC)}$ has a full-scale voltage range from $0\; V$ to $7.68\:V$. If the digital input code is $10010110$ (the leftmost bit is $\text{MSB}$), then the analog output voltage of the $\text{DAC}$ (rounded off to one decimal place) is ___________ $V$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

116 views

0 votes

0 answers

24

GATE ECE 2021 | Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a wide-sense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

121 views

0 votes

0 answers

25

GATE ECE 2021 | Question: 22
Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of $50\%$. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is ______________

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

122 views

0 votes

0 answers

26

GATE ECE 2021 | Question: 23
A speech signal, band limited to $4\:\text{kHz}$, is sampled at $1.25$ times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range $-5\:V$ to $+5\:V$, are ... transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _____ $\text{kHz}$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

166 views

0 votes

0 answers

27

GATE ECE 2021 | Question: 24
A $4\:kHz$ sinusoidal message signal having amplitude $4\:V$ is fed to a delta modulator ($DM$) operating at a sampling rate of $32\:\text{kHz}$. The minimum step size required to avoid slope overload noise in the $DM$ (rounded off to two decimal places) is _____ $V$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

110 views

0 votes

0 answers

28

GATE ECE 2021 | Question: 25
The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

160 views

0 votes

0 answers

29

GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & -3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________

Arjun asked in Linear Algebra Feb 20, 2021

by Arjun

6.0k points

119 views

0 votes

0 answers

30

GATE ECE 2021 | Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________

Arjun asked in Vector Analysis Feb 20, 2021

by Arjun

6.0k points

72 views

0 votes

0 answers

31

GATE ECE 2021 | Question: 38
In the circuit shown in the figure, the switch is closed at time $t=0$, while the capacitor is initially charged to $-5\:V$ (i.e., $v_{c}(0)=-5V$). The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is ________________ $\text{ms}$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

78 views

0 votes

0 answers

32

GATE ECE 2021 | Question: 39
The exponential Fourier series representation of a continuous-time periodic signal $x(t)$ is defined as $x\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _{0}t}$ where $\omega _0$ ... $x(t)$ (rounded off to one decimal place) is ______________

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

63 views

0 votes

0 answers

33

GATE ECE 2021 | Question: 40
For a unit step input $u[n]$, a discrete-time $\text{LTI}$ system produces an output signal $\left ( 2\delta \left [ n+1 \right ] +\delta \left [ n \right ]+\delta \left [ n-1 \right ]\right )$. Let $y[n]$ be the output of the system for an input $\left ( \left ( \dfrac{1}{2} \right )^n u\left [ n \right ]\right )$. The value of $y[0]$ is _________________

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

50 views

0 votes

0 answers

34

GATE ECE 2021 | Question: 41
Consider the signals $x\left [ n \right ]=2^{n-1}u\left [ -n+2 \right ]$ and $y\left [ n \right ]=2^{-n+2}u\left [ n+1 \right ]$, where $u[n]$ is the unit step sequence. Let $X(e^{jw})$ and $Y(e^{jw})$ be the discrete-time Fourier ... (rounded off to one decimal place) is ___________

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

41 views

0 votes

0 answers

35

GATE ECE 2021 | Question: 43
An asymmetrical periodic pulse train $v_{in}$ of $10\:V$ amplitude with on-time $T_{\text{ON}}=1\:ms$ and off-time $T_{\text{OFF}}=1\:\mu s$ is applied to the circuit shown in the figure. The diode $D_{1}$ is ideal. The difference between the maximum voltage and minimum voltage of the output waveform $v_{o}$ (in integer) is ______________ $V$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

138 views

0 votes

0 answers

36

GATE ECE 2021 | Question: 44
For the transistor $M_{1}$ in the circuit shown in the figure, $\mu_{n} C_{\text{ox}} = 100\:\mu A/V^{2}$ and $(W/L)=10$, where $\mu_{n}$ is the mobility of electron, $C_{\text{ox}}$ is the oxide capacitance ... $V$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

52 views

0 votes

0 answers

37

GATE ECE 2021 | Question: 45
A circuit with an ideal $\text{OPAMP}$ is shown in the figure. A pulse $V_{\text{IN}}$ of $20\:ms$ duration is applied to the input. The capacitors are initially uncharged. The output voltage $V_{\text{OUT}}$ of this circuit at $t=0^{+}$ (in integer) is ____________________ $V$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

42 views

0 votes

0 answers

38

GATE ECE 2021 | Question: 46
The propagation delay of the exclusive$-\text{OR}$ ($\text{XOR}$) gate in the circuit in the figure is $3\:ns$. The propagation delay of all the flip-flops is assumed to be zero. The clock ($\text{Clk}$ ... of triggering clock edges after which the flip-flop outputs $Q_{2}Q_{1}Q_{0}$ becomes $1\; 0\; 0$ (in integer) is

Arjun asked in Digital Circuits Feb 20, 2021

by Arjun

6.0k points

150 views

0 votes

0 answers

39

GATE ECE 2021 | Question: 47
The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time ... maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is _______________ $A$.

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

99 views

0 votes

0 answers

40

GATE ECE 2021 | Question: 48
A unity feedback system that uses proportional-integral ($\text{PI}$) control is shown in the figure. The stability of the overall system is controlled by tuning the $\text{PI}$ control parameters $K_{P}$ and $K_{I}$. The maximum ... as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is ___________________

Arjun asked in Others Feb 20, 2021

by Arjun

6.0k points

68 views