Recent questions tagged gate2017-ec-1

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GATE ECE 2017 Set 1 | GA Question: 10
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at $25$ m intervals in this plot. The path from $P$ to $Q$ is best described by Up-Down-Up-Down Down-Up-Down-Up Down-Up-Down Up-Down-Up

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at $25$ ...

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Lakshman Bhaiya asked May 31, 2019

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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...

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GATE ECE 2017 Set 1 | Question: 52
A continuous time signal $x(t)=4 \cos(200\pi t)+8 \cos(400\pi t)$, where $t$ is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $h(t)=\begin{cases} \frac{2 \sin (300\pi t)}{\pi t},& t\neq 0 \\ 600, & t=0. \end{cases}$ Let $y(t)$ be the output of this filter. The maximum value of $ \mid y(t) \mid $ is _________.

A continuous time signal $x(t)=4 \cos(200\pi t)+8 \cos(400\pi t)$, where $t$ is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response...

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GATE ECE 2017 Set 1 | Question: 54
The expression for an electric field in free space is , $\textbf{E}=E_{0}( \hat{x}+\hat{y}+j2 \hat{z} )e^{-j( \omega t-kx+ky)}$ where $x,y,z$ represent the special coordinates, $t$ represents time, and ... normal to the $z$-axis represents an elliptically polarized plane wave propagating along the $x - y$ plane represents a linearly polarized plane wave

The expression for an electric field in free space is , $\textbf{E}=E_{0}( \hat{x}+\hat{y}+j2 \hat{z} )e^{-j( \omega t-kx+ky)}$ where $x,y,z$ represent the special coordi...

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GATE ECE 2017 Set 1 | Question: 49
The Nyquist plot of the transfer function $G(s)=\frac{K}{(s^{2}+2s+2)(s+2)}$ does not encircle the point $(-1+j0)$ for $K=10$ but does encircle the point $(-1+j0)$ for $K=100$. Then the closed loop system (having unity gain feedback) is stable ... $K=10$ and unstable for $K=100$ unstable for $K=10$ and stable for $K=100$ stable for $K=10$ and unstable for $K=100$

The Nyquist plot of the transfer function$$G(s)=\frac{K}{(s^{2}+2s+2)(s+2)}$$does not encircle the point $(-1+j0)$ for $K=10$ but does encircle the point $(-1+j0)$ for $K...

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GATE ECE 2017 Set 1 | Question: 50
In binary frequency shift keying (FSK), the given signal waveforms are $u_{0}(t)=5\, \cos(20000\pi t)\, ;0\leq t\leq T \text{, and } \\ u_{1}(t)=5\, \cos(22000\pi t)\, ;0 \leq t \leq T,$ where $T$ is the bit-duration interval and $t$ is in seconds ... (in milliseconds) required to have $u_{0}(t)$ and $u_{1}(t)$ uncorrelated is $0.25$ ms $0.5$ ms $0.75$ ms $1.0$ ms

In binary frequency shift keying (FSK), the given signal waveforms are $$u_{0}(t)=5\, \cos(20000\pi t)\, ;0\leq t\leq T \text{, and } \\ u_{1}(t)=5\, \cos(22000\pi t)\, ;...

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GATE ECE 2017 Set 1 | Question: 51
Let $X(t)$ be a wide sense stationary random process with the power spectral density $S_{X}(f)$ as shown in Figure (a), where $f$ is in Hertz$(Hz)$. The random process $X(t)$ ... Select the correct option: only I is true only II and III are true only I and II are true only I and III are true

Let $X(t)$ be a wide sense stationary random process with the power spectral density $S_{X}(f)$ as shown in Figure (a), where $f$ is in Hertz$(Hz)$. The random process $X...

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GATE ECE 2017 Set 1 | Question: 53
An optical fiber is kept along the $\hat{z}$ direction. The refractive indices for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are $n_{x}=1.5000$ and $n_{y}=1.5001$, ... is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters,is______________.

An optical fiber is kept along the $\hat{z}$ direction. The refractive indices for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are $n_{x}=1....

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GATE ECE 2017 Set 1 | Question: 55
A half wavelength dipole is kept in the $x-y$ plane and oriented along $45^{\circ}$ from the $x$-axis. Determine the direction of null in the radiation pattern for $0\leq \phi \leq \pi$. Here the angle $\theta (0\leq \theta \leq \pi )$ is measured from the $z$-axis and ... $\theta =45^{o},\phi =90^{o}$ $\theta =90^{o},\phi =135^{o}$ $\theta =45^{o},\phi =135^{o}$

A half wavelength dipole is kept in the $x-y$ plane and oriented along $45^{\circ}$ from the $x$-axis. Determine the direction of null in the radiation pattern for $0\leq...

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GATE ECE 2017 Set 1 | Question: 44
A $4$-bit shift register circuit configured for right-shift operation, i.e. $D_{in}\rightarrow A,A\rightarrow B,B\rightarrow C,C\rightarrow D$, is shown. If the present state of the shift register is $ABCD=1101$, the number of clock cycles required to reach the state $ABCD=1111$ is _________.

A $4$-bit shift register circuit configured for right-shift operation, i.e. $D_{in}\rightarrow A,A\rightarrow B,B\rightarrow C,C\rightarrow D$, is shown. If the present s...

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GATE ECE 2017 Set 1 | Question: 46
A finite state machine (FSM) is implemented using the D flip-flop A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are $Q_{A}Q_{B}=00,01,10$ and $11$. Assume that $X_{IN}$ is held at a constant logic ... states if $X_{IN}=0$ only two or four possible states if $X_{IN}=1$ only two or four possible states if $X_{IN}=0$

A finite state machine (FSM) is implemented using the D flip-flop A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are $Q_{A}Q_...

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GATE ECE 2017 Set 1 | Question: 45
The following FIVE instructions were executed on an $8085$ microprocessor. MVI A, $33$H MVI B, $78$H ADD B CMA ANI $32$H The Accumulator value immediately after the execution of the fifth instruction is $00H$ $10H$ $11H$ $32H$

The following FIVE instructions were executed on an $8085$ microprocessor.MVI A, $33$HMVI B, $78$HADD BCMAANI $32$HThe Accumulator value immediately after the execution o...

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GATE ECE 2017 Set 1 | Question: 43
Which one of the following gives the simplified sum of products expression for the Boolean function $F=m_{0}+m_{2}+m_{3}+m_{5}$, where $m_{0},m_{2},m_{3}$ and $m_{5}$ are minterms corresponding to the inputs $A,B$ and $C$ with $A$ as the $MSB$ and ... $\overline{A} BC+\overline{A} \: \overline{C}+A \overline{B}C$

Which one of the following gives the simplified sum of products expression for the Boolean function $F=m_{0}+m_{2}+m_{3}+m_{5}$, where $m_{0},m_{2},m_{3}$ and $m_{5}$ are...

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GATE ECE 2017 Set 1 | Question: 37
As shown , a uniformly doped Silicon bar of length $L=0.1\mu m$ with a donor concentration $N_{D}=10^{16}cm^{-3}$ is illuminated at $x=0$ ... that goes to $0$ at $x=L$, the magnitude of the diffusion current density at $x=L/2$, in $A/cm^{2}$, is ___________.

As shown , a uniformly doped Silicon bar of length $L=0.1\mu m$ with a donor concentration $N_{D}=10^{16}cm^{-3}$ is illuminated at $x=0$ such that electron and hole pair...

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GATE ECE 2017 Set 1 | Question: 36
The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of $n=1 \times 10^{16} cm^{3}$ and electronic charge $q=1.6 \times 10 ^{-19}C$. If a bias ... a $1 µm$ region of this semiconductor, the resulting current density in this region, in $kA/cm^{2} $, is _____.

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of $n=1 \times 1...

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GATE ECE 2017 Set 1 | Question: 47
A linear time invariant (LTI) system with the transfer function $G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}-3s+2)}$ is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for $0< K < \infty$ ... $K>1.5$ $1<K<1.5$ $0<K<1$ no positive value of $K$

A linear time invariant (LTI) system with the transfer function $$G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}-3s+2)}$$is connected in unity feedback configuration as shown in the fi...

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GATE ECE 2017 Set 1 | Question: 41
For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal. Given that $V_{T}=25mV,V_{BE}=0.7V$, and the BJT output resistance $r_{o}$ is practically infinite. Under these conditions, the midband voltage gain magnitude, $A_{v}=\mid v_{o}/v_{i} \mid $, V/V is ____________.

For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal. Given that $V_{T}=25mV,V...

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GATE ECE 2017 Set 1 | Question: 41
For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage $V_{tn}=1V$ and its transconductance parameter $\mu_{n}C_{ox}\big(\frac{W}{L}\big)=1 \: mA/V^{2}$.Neglect channel length modulation and body bias effects. Under these conditions, the drain current $I_{D}$ in $mA$ is ________.

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage $V_{tn}=1V$ and its transconductance parameter $\mu_{n}C_{ox}\big(\frac{W}{...

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GATE ECE 2017 Set 1 | Question: 39
In the figure shown, the $npn$ transistor acts as a switch. For the input $V_{in}(t)$ as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when $T$ is large. Assume collector-to-emitter ... $(\alpha)$ of the transistor for the switching should be __________.

In the figure shown, the $npn$ transistor acts as a switch.For the input $V_{in}(t)$ as shown in the figure, the transistor switches between the cut-off and saturation re...

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GATE ECE 2017 Set 1 | Question: 38
As shown, two Silicon (Si) abrupt $p-n$ junction diodes are fabricated with uniform donor doping concentrations of $ N_{D1}=10^{14} cm^{-3} $ and $N_{D2}=10^{16}cm^{-3}$ in the $n$-regions of the diodes, and uniform acceptor ... in potentials of the diodes, the ratio $C_{2}/C_{1}$ of their reverse bias capacitance for the same applied reverse bias, is _________.

As shown, two Silicon (Si) abrupt $p-n$ junction diodes are fabricated with uniform donor doping concentrations of $ N_{D1}=10^{14} cm^{-3} $ and $N_{D2}=10^{16}cm^{-3}$ ...

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GATE ECE 2017 Set 1 | Question: 42
The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, $A_{0}=10^{5}V/V$ and an open-loop cut-off frequency, $f_{c}=8Hz$. The voltage gain of the amplifier at $15$ kHz, in V/V, is____________.

The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, $A_{0}=10^{5}V/V$ and an o...

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GATE ECE 2017 Set 1 | Question: 28
Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,-1)$.The value of $I$ is ____________.

Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,-1)$.The value of...

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GATE ECE 2017 Set 1 | Question: 29
Which one of the following is the general solution of the first order differential equation $\frac{dy}{dx}=(x+y-1)^{2},$ where $x,y$ are real? $y=1+x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1+x+\tan(x+c)$, where $c$ is a constant $y=1-x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1-x+\tan(x+c)$, where $c$ is a constant

Which one of the following is the general solution of the first order differential equation $$\frac{dy}{dx}=(x+y-1)^{2},$$ where $x,y$ are real?$y=1+x+\tan^{-1}(x+c)$, wh...

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GATE ECE 2017 Set 1 | Question: 26
Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$. $1 + x + x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $ $1 + x +3 x^{2} + 7x^{3} $

Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than...

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GATE ECE 2017 Set 1 | Question: 9
A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true? Silicon atoms act as $p$-type dopants in Arsenic sites and ... Arsenic sites as well as Gallium sites Silicon atoms act as $n$-type dopants in Arsenic sites as well as Gallium sites

A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statem...

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GATE ECE 2017 Set 1 | Question: 31
Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is integer valued. Consider the following statements about $x(3t)$: The complex ... one of the following is correct? Only II and III are true Only I and III are true Only III is true Only I is true

Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is in...

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GATE ECE 2017 Set 1 | Question: 33
Let $h[n]$ ... radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.

Let $h[n]$ be the impulse response of a discrete-time linear time invariant(LTI) filter. The impulse response is given by $$h[0]=\frac{1}{3}; \, h =\frac{1}{3}; \, h =\fr...

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GATE ECE 2017 Set 1 | Question: 25
Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and ... factor of $2$ Decreases by a factor of $2$ Remains unchanged Decreases by a factor of $\sqrt{2}$

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of t...

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GATE ECE 2017 Set 1 | Question: 34
The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitude of }V{1}}$ is______.

The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitu...

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GATE ECE 2017 Set 1 | Question: 35
In the circuit shown, the voltage $V_{IN}(t)$ is described by: $V_{IN}(t)=\begin{cases} 0, & \text{for } t< 0 \\ 15 \text{Volts} & \text{for } t\geq 0 \end{cases}$ where $t$ is in seconds. The time (in seconds) at which the current $I$ in the circuit will reach the value $2$ Amperes is ___________.

In the circuit shown, the voltage $V_{IN}(t)$ is described by: $$V_{IN}(t)=\begin{cases} 0, & \text{for } t< 0 \\ 15 \text{Volts} & \text{for } t\geq 0 \end{cases}$$wher...

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GATE ECE 2017 Set 1 | Question: 20
Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

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GATE ECE 2017 Set 1 | Question: 32
Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that $x[0]=1, \: x[1]=2, \: x[2]=1, \: h[0]=1$ Let $y[n]$ be the linear convolution of $x[n]$ and $h[n]$. Given that $y[1]=3$ and $y[2]=4$, the value of the expression $(10y[3]+y[4])$ is__________.

Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that$$x[0]=1, \: x =2, \: x =1, \: h[0]=1$$ Let $y[n...

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GATE ECE 2017 Set 1 | Question: 15
In the latch circuit shown, the $NAND$ gates have non-zero, but unequal propagation delays. The present input condition is $P=Q=’0’$. If the input condition is changed simultaneously to $P=Q=’1’$, the outputs $X$ and $Y$ are, $X=’1’$, $Y=’1’$ either $X=’1’$, $Y=’0’$ or $X=’0’$, $Y=’1’$ either $X=’1’$, $Y=’1’$ or $X=’0’$, $Y=’0’$ $X=’0’$, $Y=’0’$

In the latch circuit shown, the $NAND$ gates have non-zero, but unequal propagation delays. The present input condition is $P=Q=’0’$. If the input condition is change...

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GATE ECE 2017 Set 1 | Question: 17
Consider the D-Latch shown in the figure, which is transparent when its clock input $CK$ is high and has zero propagation delay. In the figure , the clock signal $CLK$ has a $50 \%$ duty cycle and $CLK2$ is a one-fifth period delayed version of $CLK1$.The duty cycle at the output of the latch in percentage is _________.

Consider the D-Latch shown in the figure, which is transparent when its clock input $CK$ is high and has zero propagation delay. In the figure , the clock signal $CLK$ ha...

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GATE ECE 2017 Set 1 | Question: 30
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.

Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.

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GATE ECE 2017 Set 1 | Question: 19
Consider a stable system with transfer function,$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$, where $b_1, \dots ,b_p$ and $a_1, \dots ,a_q$ are real valued constants.The slope of the Bode log magnitude curve of $G(s)$ ... of values for $p$ and $q$ is $p=0$ and $q=3$ $p=1$ and $q=7$ $p=2$ and $q=3$ $p=3$ and $q=5$

Consider a stable system with transfer function,$$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$$, where $b_1, \dots ,b_p$ and $a_1, \dots ...

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GATE ECE 2017 Set 1 | Question: 18
The open loop transfer function $G(s)=\frac{(s+1)}{s^{p}(s+2)(s+3)}$ where $p$ is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is $6$ for unit ramp input, the parameter $p$ is__________.

The open loop transfer function $$G(s)=\frac{(s+1)}{s^{p}(s+2)(s+3)}$$ where $p$ is an integer, is connected in unity feedback configuration as shown in figure.Given that...

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GATE ECE 2017 Set 1 | Question: 15
A good transconductance amplifier should have high input resistance and low output resistance low input resistance and high output resistance high input and output resistances low input and output resistances

A good transconductance amplifier should havehigh input resistance and low output resistancelow input resistance and high output resistancehigh input and output resistanc...

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GATE ECE 2017 Set 1 | Question: 22
Which one of the following statements about differential pulse code modulation (DPCM) is true? The sum of message signal sample with its prediction is quantized The message signal sample is directly quantized, and its prediction is not ... signal sample and a random signal is quantized The difference of message signal sample with its prediction is quantized

Which one of the following statements about differential pulse code modulation (DPCM) is true?The sum of message signal sample with its prediction is quantizedThe message...

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GATE ECE 2017 Set 1 | Question: 23
In a digital communication system, the overall pulse shape $p(t)$ at the receiver before the sampler has the Fourier transform $P(f)$. If the symbols are transmitted at the rate of $2000$ symbols per second, for which of the following cases is the inter symbol interference zero?

In a digital communication system, the overall pulse shape $p(t)$ at the receiver before the sampler has the Fourier transform $P(f)$. If the symbols are transmitted at t...

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