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321

GATE ECE 2016 Set 3 | Question: 41
In the circuit shown in the figure , the channel length modulation of all transistors is non-zero $(\lambda\neq0)$. Also, all transistors operate in saturation and have negligible body effect .The ac small signal voltage gain ($V_o/V_{in}$ ... $-g_{m1}(r_{o1}\mid\mid \left (\frac{1}{gm3}\mid\mid r_{o3})\mid\mid r_{o2} \right )$

In the circuit shown in the figure , the channel length modulation of all transistors is non-zero $(\lambda\neq0)$. Also, all transistors operate in saturation and have n...

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322

GATE ECE 2013 | Question: 38
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. Then, for all values of $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$

Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. ...

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Milicevic3306 asked Mar 25, 2018

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323

GATE ECE 2018 | Question: 14
Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is $x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}$ The same function $x(t)$ can also ... $\sum _{k=-\infty}^{\infty } \mid b_{k} \mid$ is equal to $256$ $64$ $16$ $4$

Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is$$x\left ( t \right )=...

gatecse

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324

GATE ECE 2017 Set 1 | Question: 12
For the operational amplifier circuit shown, the output saturation voltage are $\pm 15 \:V$. The upper and lower threshold voltages for the circuit are,respectively, $+ 5 \: V$ and $– 5 V$ $+ 7 \: V$ and $– 3 \: V$ $+ 3 \: V$ and $- 7 \: V$ $+ 3 \: V$ and $– 3 \: V$

For the operational amplifier circuit shown, the output saturation voltage are $\pm 15 \:V$. The upper and lower threshold voltages for the circuit are,respectively,$+ 5 ...

admin

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admin asked Nov 17, 2017

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325

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).

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 ...

Arjun

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Arjun asked Feb 15, 2022

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326

GATE ECE 2019 | GA Question: 9
Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the hour hand moved by $210$ degrees on the clock. $Q$ stopped working when ... paying the consultants, the client shall have USD _______ remaining in the budget. $000.00$ $166.67$ $300.00$ $433.33$

Two design consultants, $P$ and $Q,$ started working from $8$ AM for a client. The client budgeted a total of USD $3000$ for the consultants. $P$ stopped working when the...

Arjun

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Arjun asked Feb 12, 2019

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327

GATE ECE 2004 | Question: 89
A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non magnetic, dielectric material with $\varepsilon>\varepsilon_{0}$. Maxima and minima are observed when the electric field is measured in front of the slab. The maximum electric ... $60 \; \pi \Omega$ $600 \; \pi \Omega$ $24 \; \pi \Omega$

A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non magnetic, dielectric material with $\varepsilon>\varepsilon_...

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admin asked Sep 25, 2022

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328

GATE ECE 2014 Set 1 | Question: 29
Consider the matrix ... $\alpha$ is a non-negative real number. The value of $\alpha$ for which $\text{det(P)} = 0$ is _______.

Consider the matrix $$J_{6} = \begin{bmatrix} 0&0 &0 &0 &0 &1 \\ 0& 0& 0& 0& 1&0 \\ 0& 0& 0& 1& 0&0 \\ 0&0 & 1& 0&0 &0 \\0 &1 &0 &0 &0 &0 \\1 &0 &0 &0 & 0& 0\end{bmatrix}...

Milicevic3306

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Milicevic3306 asked Mar 25, 2018

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329

GATE ECE 2011 | Question: 35
The system of equations $ \begin{aligned} &x+y+z=6 \\ &x+4 y+6 z=20 \\ &x+4 y+\lambda z=\mu \end{aligned} $ has NO solution for values of $\lambda$ and $\mu$ given by $\lambda=6, \mu=20$ $\lambda=6, \mu \neq 20$ $\lambda \neq 6, \mu=20$ $\lambda \neq 6, \mu \neq 20$

The system of equations $$ \begin{aligned} &x+y+z=6 \\ &x+4 y+6 z=20 \\ &x+4 y+\lambda z=\mu \end{aligned} $$ has NO solution for values of $\lambda$ and $\mu$ given by$\...

admin

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admin asked Sep 3, 2022

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330

GATE ECE 2021 | Question: 10
Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure. Assuming $\left | V_{\text{IN}} \right |\ll \left | V_{\text{CC}} \right |$ and $\left | V_{\text{REF}} \right |\ll \left | V_{\text{CC}} \right | $, the condition at which $V_{\text{OUT}}$ equals ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$

Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure.Assuming $\left | V_{\text{IN}} \right |\ll \left | V_{\text{CC}} \right |$ and $\left | V_{\text{RE...

Arjun

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Arjun asked Feb 19, 2021

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331

GATE ECE 2019 | Question: 24
In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{1}=R_{2}=50\: \Omega.$ The average value of $V_{L}$ is _______ volts (rounded off to $1$ decimal place).

In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{...

Arjun

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Arjun asked Feb 12, 2019

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332

GATE ECE 2022 | Question: 6
Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10} \; \text{cm}^{-3}.$ Electron and hole diffusion lengths are $2 \; \mu\text{m}$ ... $3.7 \times 10^{14} \; \text{cm}^{-3}$ $10^{3} \; \text{cm}^{-3}$

Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentrat...

Arjun

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Arjun asked Feb 15, 2022

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333

GATE ECE 2020 | Question: 4
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is $y=C_{1}e^{3x}+C_{2}e^{-3x}$ $y=(C_{1}+C_{2}x)e^{-3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=C_{1}e^{3x}$

The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is$y=C_{1}e^{3x}+C_{2}e^{-3x}$$y=(C_{1}+C_{2}x)e^{-3x}$$y=(C...

go_editor

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go_editor asked Feb 13, 2020

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334

GATE ECE 2016 Set 3 | Question: 44
For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are $2$ ns, $1.5$ ns and $1$ ns, respectively. If all the inputs $P, Q, R, S$ and $T$ are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is _________

For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are $2$ ns, $1.5$ ns and $1$ ns, respectively. If all the inputs $P, Q, R, S$ and...

Milicevic3306

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335

GATE ECE 2015 Set 3 | Question: 14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is a modulo-$5$ binary up counter a modulo-$6$ binary down counter a modulo-$5$ binary down counter a modulo-$6$ binary up counter

The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit isa...

Milicevic3306

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336

GATE ECE 2014 Set 4 | Question: 54
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \times \overrightarrow{F} \cdot \overrightarrow{ds}$ is __________.

Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \ti...

Milicevic3306

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Milicevic3306 asked Mar 26, 2018

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337

GATE ECE 2017 Set 2 | Question: 33
Consider an LTI system with magnitude response $\mid H(f) \mid=\begin{cases} 1-\frac{\mid f \mid}{20}, & \mid f \mid \leq 20 \\ 0,& \mid f \mid > 20 \end{cases}$ and phase response $\arg \{ H(f) \}= - 2f.$ If the input to the ... $y(t)$ is ____________

Consider an LTI system with magnitude response $$\mid H(f) \mid=\begin{cases} 1-\frac{\mid f \mid}{20}, & \mid f \mid \leq 20 \\ 0,& \mid f \mid 20 \end{cases}$$ and pha...

admin

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admin asked Nov 25, 2017

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338

GATE ECE 1997 | Question 1.1
The current $i_4$ in the circuit of the figure is equal to $12 \mathrm{~A}$ $-12 \mathrm{~A}$ $4 \mathrm{~A}$ None of these

The current $i_4$ in the circuit of the figure is equal to$12 \mathrm{~A}$$-12 \mathrm{~A}$$4 \mathrm{~A}$None of these

admin

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admin asked Oct 2, 2022

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339

GATE ECE 2022 | Question: 11
Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure. Note that the Nyquist contour has been ... of the closed-loop transfer function in the closed right-half of the complex plane is ________________. $0$ $1$ $2$ $3$

Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer func...

Arjun

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Arjun asked Feb 15, 2022

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340

GATE ECE 2016 Set 3 | Question: 45
For the circuit shown in the figure, the delay of the bubbled NAND gate is $2\:ns$ and that of the counter is assumed to be zero. If the clock (Clk) frequency is $1\:GHz$, then the counter behaves as a $\text{mod}-5\:\text{counter}$ $\text{mod}-6\:\text{counter}$ $\text{mod}-7\:\text{counter}$ $\text{mod}-8\:\text{counter}$

For the circuit shown in the figure, the delay of the bubbled NAND gate is $2\:ns$ and that of the counter is assumed to be zero. If the clock (Clk) frequency is $1\:GHz$...

Milicevic3306

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341

GATE ECE 2012 | Question: 53
An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. A hole of radius $b$ (b < a) ia now drilled along the length of the wire at a distance $d$ from the center of the wire as shown ... uniform and depends only on $d$ uniform and depends only on $b$ uniform and depends only on both $b$ and $d$ non uniform

An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$.A hole of radius $b$ (b < a) ia now drilled along the len...

Milicevic3306

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Milicevic3306 asked Mar 25, 2018

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342

GATE ECE 2023 | Question: 19
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) ...

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic(a) Continuous, aperiod...

admin

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admin asked May 20, 2023

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343

GATE ECE 2021 | Question: 7
The energy band diagram of a $\text{p-type}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in the figure. The valance band $E_{V}$ is sloped since doping is non-uniform along the bar. The difference ... bar is $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$

The energy band diagram of a $\text{p-type}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in th...

Arjun

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Arjun asked Feb 19, 2021

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344

GATE ECE 2020 | Question: 6
A single crystal intrinsic semiconductor is at a temperature of $300$ $\text{K}$ with effective density of states for holes twice that of electrons. The thermal voltage is $26$ mV. The intrinsic Fermi level is shifted from mid-bandgap energy level by $18.02 \: meV$ $9.01 \: meV$ $13.45 \: meV$ $26.90 \: meV$

A single crystal intrinsic semiconductor is at a temperature of $300$ $\text{K}$ with effective density of states for holes twice that of electrons. The thermal voltage i...

go_editor

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go_editor asked Feb 13, 2020

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345

GATE ECE 2013 | Question: 45
There are four chips each of $1024\:\text{bytes}$ connected to a $16\:\text{bit}$ address bus as shown in the figure below. $RAMs\: 1, 2, 3$ and $4$ ... $0500H-08FFH, 1500H-18FFH, 3500H-38FFH, 5500H-58FFH$ $0800H-0BFFH, 1800H-1BFFH, 2800H-2BFFH, 3800H-3BFFH$

There are four chips each of $1024\:\text{bytes}$ connected to a $16\:\text{bit}$ address bus as shown in the figure below. $RAMs\: 1, 2, 3$ and $4$ respectively are mapp...

Milicevic3306

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346

GATE ECE 2012 | Question: 40
The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is $H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618\times10^2y)\:\cos(6.283\times10^{10}t-\beta z)$ The phase velocity $v_p$ of the wave inside the waveguide satisfies $v_p\gt c$ $v_p=c$ $0\lt v_p\lt c$ $v_p=0$

The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is$$H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618...

Milicevic3306

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347

GATE ECE 2017 Set 1 | Question: 48
Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane? Four left half plane(LHP) roots One right half plane(RHP) root,one LHP root and two roots on the imaginary axis Two RHP roots and two LHP roots All four roots are on the imaginary axis

Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane?Four left half plane(LHP) rootsOn...

admin

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admin asked Nov 17, 2017

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348

GATE ECE 2020 | Question: 7
Consider the recombination process via bulk traps in a forward biased $pn$ homojunction diode. The maximum recombination rate is $U_{\text{max}}$ ... bias. With all other parameters unchanged, $U_{\text{max}}$ increases if the thermal velocity of the carriers increases.

Consider the recombination process via bulk traps in a forward biased $pn$ homojunction diode. The maximum recombination rate is $U_{\text{max}}$. If the electron and the...

go_editor

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go_editor asked Feb 13, 2020

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349

GATE ECE 2016 Set 2 | Question: 43
In an $N$ bit flash ADC, the analog voltage is fed simultaneously to $2^{N}-1$ comparators. The output of the comparators is then encoded to a binary format using digital circuits. Assume that the analog voltage source $V_{in}$ ... maximum sampling rate? $1$ megasamples per second $6$ megasamples per second $64$ megasamples per second $256$ megasamples per second

In an $N$ bit flash ADC, the analog voltage is fed simultaneously to $2^{N}-1$ comparators. The output of the comparators is then encoded to a binary format using digita...

Milicevic3306

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350

GATE ECE 2007 | Question: 22
Consider the function $f(x)=x^{2}-x-2$. The maximum value of $f(x)$ in the closed interval $[-4,4]$ is $18$ $10$ $-2.25$ indeterminate

Consider the function $f(x)=x^{2}-x-2$. The maximum value of $f(x)$ in the closed interval $[-4,4]$ is$18$$10$$-2.25$indeterminate

admin

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admin asked Sep 19, 2022

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351

GATE ECE 2019 | Question: 29
It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form $x[n]= c_{1}exp\left(-\dfrac{j\pi n}{2}\right)+c_{2}\left(\dfrac{j\pi n}{2}\right),$ where $c_{1}$ and $c_{2}$ are arbitrary real numbers. The desired three-tap filter is ... $n$, when $x[n]$ is as given above ? $a=1,b=1$ $a=0,b=-1$ $a=-1,b=1$ $a=0,b=1$

It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form$$x[n]= c_{1}exp\left(-\dfrac{j\pi n}{2}\right)+c_{2}\left(\df...

Arjun

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Arjun asked Feb 12, 2019

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352

GATE ECE 2020 | Question: 43
For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A vertical infinitesimally small electric dipole $\left (\delta l \ll \lambda \right )$ ... field radiation pattern occurs at $\theta =60^{\circ}$, is $\lambda$ $0.5\lambda$ $0.25\lambda$ $0.75\lambda$

For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A...

go_editor

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go_editor asked Feb 13, 2020

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353

GATE ECE 2015 Set 1 | GA Question: 8
Fill in the missing value

Fill in the missing value

Milicevic3306

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354

GATE ECE 2018 | GA Question: 8
The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans. it has taken a toll on his own batting. ... ii) and (iii) only (iii) and (iv) only (ii) and (iv) only (i), (ii), (iii) and (iv)

The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior...

gatecse

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gatecse asked Feb 19, 2018

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355

GATE ECE 2018 | Question: 38
An op-amp based circuit is implemented as shown below. In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node $A$, connected to the negative input of the op-amp as indicated in the figure is ________.

An op-amp based circuit is implemented as shown below. In the above circuit, assume the op-amp to be ideal. The voltage (in volt...

gatecse

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gatecse asked Feb 19, 2018

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356

GATE ECE 2021 | Question: 3
Two continuous random variables $X$ and $Y$ are related as $Y=2X+3$ Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The variances are related as $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$

Two continuous random variables $X$ and $Y$ are related as$$Y=2X+3$$Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The vari...

Arjun

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Arjun asked Feb 19, 2021

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357

GATE ECE 2016 Set 3 | Question: 32
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 $i(t)$ (in ampere) at $t=0^+$ is _______

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...

Milicevic3306

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358

GATE ECE 2019 | Question: 40
In the circuits shown the threshold voltage of each $\text{nMOS}$ transistor is $0.6\:V.$ Ignoring the effect of channel length modulation and body bias. the values of $\text{Vout}1$ and $\text{Vout} 2,$ respectively, in volts, are $1.8$ and $1.2$ $2.4$ and $2.4$ $1.8$ and $2.4$ $2.4$ and $1.2$

In the circuits shown the threshold voltage of each $\text{nMOS}$ transistor is $0.6\:V.$ Ignoring the effect of channel length modulation and body bias. the values of $\...

Arjun

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Arjun asked Feb 12, 2019

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359

GATE ECE 2016 Set 3 | Question: 3
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 probability of getting “head” for the first time in the fifth toss is _______

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, ...

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360

GATE ECE 2015 Set 2 | Question: 19
By performing cascading and/or summing/differencing operations using transfer function blocks $G_{1}(s )$ and $G_{2}(s),$ one CANNOT realize a transfer function of the form $G_{1}(s)G_{2}(s) \\$ $\dfrac{G_{1}(s)}{G_{2}(s)} \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)} + G_{2}(s)\right) \\$ $G_{1}(s)\left(\dfrac{1}{G_{1}(s)} - G_{2}(s)\right)$

By performing cascading and/or summing/differencing operations using transfer function blocks $G_{1}(s )$ and $G_{2}(s),$ one CANNOT realize a transfer function of the f...

Milicevic3306

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Milicevic3306 asked Mar 27, 2018