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2921
GATE ECE 2018 | Question: 22
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value of $k$ for which the equation $Ax=0$ has infinitely many solutions is _________.
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value o...
gatecse
1.6k
points
98
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
numerical-answers
linear-algebra
system-of-equations
+
–
0
votes
0
answers
2922
GATE ECE 2018 | Question: 23
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
gatecse
1.6k
points
154
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
probability
random-variable
variance
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0
votes
0
answers
2923
GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
gatecse
1.6k
points
179
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
taylor-series
+
–
0
votes
0
answers
2924
GATE ECE 2018 | Question: 25
The $\text{ABCD}$ matrix for a two-port network is defined by: $\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2}\\ -I_{2} \end{bmatrix}$ The parameter $\text{B}$ for the given two-port network (in ohms, correct to two decimal places) is _________.
The $\text{ABCD}$ matrix for a two-port network is defined by:$$\begin{bmatrix} V_{1}\\ I_{1} \end{bmatrix}=\begin{bmatrix} A &B \\ C& D \end{bmatrix}\begin{bmatrix} V_{2...
gatecse
1.6k
points
217
views
gatecse
asked
Feb 19, 2018
Network Solution Methods
gate2018-ec
numerical-answers
two-port-network
network-solution-methods
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–
0
votes
0
answers
2925
GATE ECE 2018 | Question: 26
The circuit shown in the figure is used to provide regulated voltage $(5 V)$ across the $1\: k\Omega$ resistor. Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a minimum required Zener current, $I_{Z min}=2\:mA$ to its ... $10\:mW$ $100\:\Omega$ and $40\:mW$ $100\:\Omega$ and $10\:mW$ $186\:\Omega$ and $40\:mW$
The circuit shown in the figure is used to provide regulated voltage $(5 V)$ across the $1\: k\Omega$ resistor. Assume that the Zener diode has a constant reverse breakdo...
gatecse
1.6k
points
114
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
electronic-devices
zener-diode
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–
0
votes
0
answers
2926
GATE ECE 2018 | Question: 27
Let $c\left ( t \right )=A_{c} \cos \left ( 2\pi f_{c}t\right )$ and $m\left ( t \right )=\cos \left ( 2\pi f_{m}t\right )$. It is given that $f_{c}>> 5f_{m}.$ The signal $c\left ( t \right )+m\left ( t \right )$ is applied to ... wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then $a/b$ is $0.25$ $0.5$ $1$ $2$
Let $c\left ( t \right )=A_{c} \cos \left ( 2\pi f_{c}t\right )$ and $m\left ( t \right )=\cos \left ( 2\pi f_{m}t\right )$. It is given that $f_{c}> 5f_{m}.$ The signal ...
gatecse
1.6k
points
106
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
communications
amplitude-modulation
+
–
0
votes
0
answers
2927
GATE ECE 2018 | Question: 10
The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circuit, Q: Short Circuit, R: Matched Load}$ $\text{P: Open Circuit, Q: Matched Load, R: Short Circuit}$ $\text{P: Short Circuit, Q: Matched Load, R: Open Circuit}$ $\text{P: Short Circuit, Q: Open Circuit, R: Matched Load}$
The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent: $\text{P: Open Circu...
gatecse
1.6k
points
148
views
gatecse
asked
Feb 19, 2018
Electromagnetics
gate2018-ec
electromagnetics
impedance
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–
0
votes
0
answers
2928
GATE ECE 2018 | Question: 11
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements: $S1: M $ has $4$ linearly independent eigenvectors. $S2: M$ has $4$ distinct eigenvalues. $S3: M$ is non-singular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements:$S1: M $ has $4$ linearly independent eigenvectors.$S2: M$ has $4$ distinct eigenvalues. $S...
gatecse
1.6k
points
116
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
2929
GATE ECE 2018 | Question: 12
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and $y = 2$, then the relation between $a$ and $b$ is $a=\dfrac{b}{4}$ $a=\dfrac{b}{2}$ $a=2b$ $a=4b$
Let $f\left ( x,y \right )=\dfrac{ax^{2}+by^{2}}{xy},$ where $a$ and $b$ are constants. If $\dfrac{\partial f}{\partial x}=\dfrac{\partial f}{\partial y}$ at $x = 1$ and ...
gatecse
1.6k
points
107
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
2930
GATE ECE 2018 | Question: 13
A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE? It has two more poles at $0.5\angle 30^{\circ}$ and ... response is two-sided. It has constant phase response over all frequencies. It has constant phase response over the entire $\text{z-plane}$.
A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE?It...
gatecse
1.6k
points
146
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
continuous-time-signals
impulse-response
+
–
0
votes
0
answers
2931
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$$x\left ( t \right )=...
gatecse
1.6k
points
232
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
2
answers
2932
GATE ECE 2018 | Question: 15
Consider the following amplitude modulated signal: $s\left ( t \right )=\cos\left ( 2000\:\pi t \right )+4\cos\left ( 2400\:\pi t \right )+ \cos\left ( 2800\:\pi t \right ).$The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is _________.
Consider the following amplitude modulated signal:$$s\left ( t \right )=\cos\left ( 2000\:\pi t \right )+4\cos\left ( 2400\:\pi t \right )+ \cos\left ( 2800\:\pi t \right...
gatecse
1.6k
points
274
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
numerical-answers
communications
amplitude-modulation
+
–
0
votes
0
answers
2933
GATE ECE 2018 | Question: 16
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at least $2$. The maximum number of codewords such a code can contain is __________.
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at le...
gatecse
1.6k
points
149
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
numerical-answers
communications
hamming-codes
+
–
0
votes
0
answers
2934
GATE ECE 2018 | Question: 17
A binary source generates symbols $X\in \left \{ -1,1 \right \}$ which are transmitted over a noisy channel.The probability of transmitting $X=1$ is $0.5.$ Input to the threshold detector is $R=X+N$ ... is shown below. If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.
A binary source generates symbols $X\in \left \{ -1,1 \right \}$ which are transmitted over a noisy channel.The probability of transmitting $X=1$ is $0.5.$ Input to the t...
gatecse
1.6k
points
134
views
gatecse
asked
Feb 19, 2018
Communications
gate2018-ec
numerical-answers
probability-density-function
communications
+
–
0
votes
0
answers
2935
GATE ECE 2018 | Question: 18
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to $0.6\:\mu m$ is __________.
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two...
gatecse
1.6k
points
127
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
numerical-answers
electronic-devices
p-n-junction
+
–
0
votes
0
answers
2936
GATE ECE 2018 | Question: 1
Two identical $\text{nMOS}$ transistors $M_{1}$ and $M_{2}$ are connected as shown below. The circuit is used as an amplifier with the input connected between $\text{G and S}$ terminals and the output taken between $D\: \text{and}\: S$ terminals. $V_{bias}$ and $V_{D}$ are ... $g_{m}\approx g_{m1} \:\:\text{and}\:\: r_{o}\approx r_{o2}$
Two identical $\text{nMOS}$ transistors $M_{1}$ and $M_{2}$ are connected as shown below. The circuit is used as an amplifier with the input connected between $\text{G an...
gatecse
1.6k
points
173
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
analog-circuits
nmos-transistor
amplifier
+
–
0
votes
0
answers
2937
GATE ECE 2018 | Question: 2
In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is $2.5\: volts$. At the input, unit step voltage is applied, i.e. $v_{IN}\left ( t \right ) = u\left ( t \right )\:volts$. Also, at $t = 0$, the voltage across each of the ... zero. The time $t$, in milliseconds, at which the output voltage $v_{OUT}$ crosses $-10\: V$ is $2.5$ $5$ $7.5$ $10$
In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is $2.5\: volts$. At the input, unit step voltage is applied, i.e. $v_{IN}\left ( t \right ...
gatecse
1.6k
points
173
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
electronic-devices
zener-diode
+
–
0
votes
0
answers
2938
GATE ECE 2018 | Question: 3
A good transimpedance amplifier has low input impedance and high output impedance high input impedance and high output impedance high input impedance and low output impedance low input impedance and low output impedance
A good transimpedance amplifier haslow input impedance and high output impedancehigh input impedance and high output impedancehigh input impedance and low output impedanc...
gatecse
1.6k
points
130
views
gatecse
asked
Feb 19, 2018
Electromagnetics
gate2018-ec
electromagnetics
impedance
+
–
0
votes
0
answers
2939
GATE ECE 2018 | Question: 4
Let the input be $u$ and the output be $y$ ... $y=au+b,b\neq 0$ $y=au$
Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:$\d...
gatecse
1.6k
points
123
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
1
answer
2940
GATE ECE 2018 | Question: 5
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability od feedback controllers. Identify which of the following statements is FALSE: Both the criteria provide information relative to the ... criterion. The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability od feedback controllers. Identify which of the foll...
gatecse
1.6k
points
340
views
gatecse
asked
Feb 19, 2018
Control Systems
gate2018-ec
control-systems
nyquist
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–
0
votes
0
answers
2941
GATE ECE 2018 | Question: 6
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is $0$ $1$ $2$ $3$
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)...
gatecse
1.6k
points
114
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
calculus
derivatives
+
–
0
votes
0
answers
2942
GATE ECE 2018 | Question: 7
In a $\text{p-n}$ junction diode at equilibrium, which one of the following statements is NOT TRUE? The hole and electron diffusion current components are in the same direction. The hole and electron drift current components are in the same ... an average, holes and electrons drift in opposite direction. On an average, electrons drift and diffuse in the same direction.
In a $\text{p-n}$ junction diode at equilibrium, which one of the following statements is NOT TRUE?The hole and electron diffusion current components are in the same dire...
gatecse
1.6k
points
155
views
gatecse
asked
Feb 19, 2018
Electronic Devices
gate2018-ec
electronic-devices
diffusion-current
p-n-junction
+
–
0
votes
0
answers
2943
GATE ECE 2018 | Question: 8
The logic function $f(X, Y)$ realized by the given circuit is NOR AND NAND XOR
The logic function $f(X, Y)$ realized by the given circuit is NORANDNANDXOR
gatecse
1.6k
points
199
views
gatecse
asked
Feb 19, 2018
Digital Circuits
gate2018-ec
digital-circuits
combinational-circuits
logic-gates
+
–
2
votes
1
answer
2944
GATE ECE 2018 | Question: 9
A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by $F=\overline{A}\:.\overline{B}\:.\overline{C}+\overline{A}\:.B\:.\overline{C}+A\:.\overline{B}\:.\overline{C}$ ...
A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by$$F=\overline{A}\:.\overline{B}\:.\overline{C}...
gatecse
1.6k
points
448
views
gatecse
asked
Feb 19, 2018
Digital Circuits
gate2018-ec
digital-circuits
boolean-algebra
+
–
0
votes
0
answers
2945
GATE ECE 2017 Set 2 | Question: 51
A modulating signal given by $x(t)=5\sin (4\pi 10^3t -10\pi \cos 2\pi 10^3t)V$ is fed to a phase modulator with phase deviation constant $k_p=5$ rad/V. If the carrier frequency is $20$ kHz, the instantaneous frequency(in kHz) at $t=0.5$ ms is ____________
A modulating signal given by $x(t)=5\sin (4\pi 10^3t -10\pi \cos 2\pi 10^3t)V$ is fed to a phase modulator with phase deviation constant $k_p=5$ rad/V. If the carrier f...
admin
46.4k
points
118
views
admin
asked
Nov 25, 2017
Communications
gate2017-ec-2
numerical-answers
communications
+
–
0
votes
0
answers
2946
GATE ECE 2017 Set 2 | Question: 52
Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. The channel is lossless noiseless useless deterministic
Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure.The channel islosslessnoiselessuselessdeterministic
admin
46.4k
points
298
views
admin
asked
Nov 25, 2017
Communications
gate2017-ec-2
channel-capacity-theorem
communications
+
–
0
votes
0
answers
2947
GATE ECE 2017 Set 2 | Question: 53
An electron $(q_1)$ is moving in free space with velocity $10^5$ m/s towards a stationary electron $(q_2)$ far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is ____________$\times 10^{-8}$ ... $e=-1.6\times 10^{-19}$ C, and permittivity $\varepsilon _0=(1/36\pi)\times 10^{-9}$ F/m]
An electron $(q_1)$ is moving in free space with velocity $10^5$ m/s towards a stationary electron $(q_2)$ far away. The closest distance that this moving electron gets t...
admin
46.4k
points
215
views
admin
asked
Nov 25, 2017
Electronic Devices
gate2017-ec-2
numerical-answers
electronic-devices
+
–
0
votes
0
answers
2948
GATE ECE 2017 Set 2 | Question: 54
Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02 $ cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $TE_{10}$ mode with the operating frequency at least $25 \%$ ... $6.55 \: GHz \leq f \leq 13.1 \: GHz$ $1.64 \: GHz \leq f \leq 10.24 \: GHz$
Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02 $ cm are designed for radar applications. It is desired that these waveguides operate onl...
admin
46.4k
points
213
views
admin
asked
Nov 25, 2017
Electromagnetics
gate2017-ec-2
waveguides
electromagnetics
+
–
0
votes
0
answers
2949
GATE ECE 2017 Set 2 | Question: 55
The permittivity of water at optical frequencies is $1.75 \varepsilon _0$. It is found that an isotropic light source at a distance $d$ under water forms an illuminated circular area of radius $5$ m, as shown in the figure. The critical angle is $\theta _c$. The value of $d$ (in meter) is _______________
The permittivity of water at optical frequencies is $1.75 \varepsilon _0$. It is found that an isotropic light source at a distance $d$ under water forms an illuminated c...
admin
46.4k
points
240
views
admin
asked
Nov 25, 2017
Electromagnetics
gate2017-ec-2
numerical-answers
electromagnetics
+
–
0
votes
0
answers
2950
GATE ECE 2017 Set 2 | Question: 40
Assuming that transistors $M_1$ and $M_2$ are identical and have a threshold voltage of $1$ V, the state of transistors $M_1$ and $M_2$ are respectively Saturation, Saturation Linear, Linear Linear, Saturation Saturation, Linear
Assuming that transistors $M_1$ and $M_2$ are identical and have a threshold voltage of $1$ V, the state of transistors $M_1$ and $M_2$ are respectivelySaturation, Satura...
admin
46.4k
points
102
views
admin
asked
Nov 25, 2017
Analog Circuits
gate2017-ec-2
transistor
analog-circuits
+
–
0
votes
0
answers
2951
GATE ECE 2017 Set 2 | Question: 41
In the circuit shown, transistors $Q_1$ and $Q_2$ are biased at a collector current of $2.6$ mA. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of $26$ mV, the magnitude of voltage gain $V_0/V_s$ in the mid-band frequency range is __________(up to second decimal place).
In the circuit shown, transistors $Q_1$ and $Q_2$ are biased at a collector current of $2.6$ mA. Assuming that transistor current gains are sufficiently large to assume c...
admin
46.4k
points
165
views
admin
asked
Nov 25, 2017
Analog Circuits
gate2017-ec-2
bipolar-junction-transistor
numerical-answers
analog-circuits
+
–
0
votes
0
answers
2952
GATE ECE 2017 Set 2 | Question: 42
In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors $Q_1, Q_2, \dots ,Q_{32}$ are identical in all respects and have infinitely large values of common-emitter current gain $(\beta)$. The collector current $(Ic)$ ... is $0.7$ V and the thermal voltage $V_T = 26$ mV. The output voltage $V_{out}$ (in volts) is ______________
In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors $Q_1, Q_2, \dots ,Q_{32}$ are identical in all respects and have infinitely...
admin
46.4k
points
190
views
admin
asked
Nov 25, 2017
Analog Circuits
gate2017-ec-2
op-amps
numerical-answers
analog-circuits
+
–
0
votes
0
answers
2953
GATE ECE 2017 Set 2 | Question: 43
The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input 'In' and an output 'Out'. The initial state of the FSM is $S_0$. ... is $10101101001101$, starting with the left-most bit, then the number of times 'Out' will be $1$ is ____________
The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input 'In' and an output...
admin
46.4k
points
318
views
admin
asked
Nov 25, 2017
Number Representations
gate2017-ec-2
fsm
numerical-answers
digital-circuits
+
–
1
votes
2
answers
2954
GATE ECE 2017 Set 2 | Question: 44
Figure Ⅰ shows a $4$-bit ripple carry adder realized using full adders and Figure Ⅱ shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure Ⅱ are $20$ ns, $15$ ns and $10$ ns, respectively. Assume ... $Y_3Y_2Y_1Y_0=0100$ and $Z_0=1$. The output of the ripple carry adder will be stable at $t$ (in ns) = ___________
Figure Ⅰ shows a $4$-bit ripple carry adder realized using full adders and Figure Ⅱ shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and ...
admin
46.4k
points
3.3k
views
admin
asked
Nov 25, 2017
Number Representations
gate2017-ec-2
numerical-answers
digital-circuits
combinational-circuits
adder
+
–
1
votes
0
answers
2955
GATE ECE 2017 Set 2 | Question: 45
A programmable logic array (PLA) is shown in the figure. The Boolean function $F$ implemented is $\overline{P} \: \overline{Q}R+ \overline{P}QR+P \overline{Q} \: \overline{R}$ $(\overline{P}+\overline{Q}+R)(\overline{P}+Q+R)(P+\overline{Q}+\overline{R})$ ... $(\overline{P}+\overline{Q}+R)(\overline{P}+Q+R)(P+\overline{Q}+R)$
A programmable logic array (PLA) is shown in the figure. The Boolean function $F$ implemented is$\overline{P} \: \overline{Q}R+ \overline{P}QR+P \overline{Q} \: \overli...
admin
46.4k
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Digital Circuits
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2956
GATE ECE 2017 Set 2 | Question: 46
A unity feedback control system is characterized by the open-loop transfer function $G(s)=\frac{2(s+1)}{s^3+ks^2+2s+1}$ The value of $k$ for which the system oscillates at $2$ rad/s is ___________
A unity feedback control system is characterized by the open-loop transfer function $$G(s)=\frac{2(s+1)}{s^3+ks^2+2s+1}$$ The value of $k$ for which the system oscillates...
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Control Systems
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numerical-answers
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2957
GATE ECE 2017 Set 2 | Question: 47
A second-order LTI system is described by the following state equations, $ \begin{array}{ll} \frac{d}{dt}x_1(t)-x_2(t)=0 \\ \frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t) \end{array}$ where $x_1(t)$ and $x_2(t)$ are the two state variables and $r(t)$ denotes the input. The output $c(t)=x_1(t)$. The system is undamped (oscillatory) underdamped critically damped overdamped
A second-order LTI system is described by the following state equations, $$ \begin{array}{ll} \frac{d}{dt}x_1(t)-x_2(t)=0 \\ \frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t) \end{...
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Control Systems
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linear-time-invariant-systems
control-systems
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2958
GATE ECE 2017 Set 2 | Question: 48
A unity feedback control system is characterized by the open-loop transfer function $G(s)=\frac{10K(s+2)}{s^3+3s^2+10}$ The Nyquist path and the corresponding Nyquist plot of $G(s)$ are shown in the figures below. If $0 < K < 1$, then the number of poles of the closed-loop transfer function that lie in the right-half of the $s$-plane is $0$ $1$ $2$ $3$
A unity feedback control system is characterized by the open-loop transfer function $$G(s)=\frac{10K(s+2)}{s^3+3s^2+10}$$ The Nyquist path and the corresponding Nyquist p...
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Control Systems
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control-systems
nyquist
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2959
GATE ECE 2017 Set 2 | Question: 49
The signal $x(t)=\sin (14000\pi t)$, where $t$ is in seconds, is sampled at a rate of $9000$ samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response $H(f)$ ... $= 3$, frequencies $= 2,7,11$ Number $= 2$, frequencies $= 2,7$ Number $= 2$, frequencies $= 7,11$
The signal $x(t)=\sin (14000\pi t)$, where $t$ is in seconds, is sampled at a rate of $9000$ samples per second. The sampled signal is the input to an ideal lowpass filte...
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Continuous-time Signals
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continuous-time-signals
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2960
GATE ECE 2017 Set 2 | Question: 50
The unmodulated carrier power in an AM transmitter is $5$ kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is $50 \%$. If it is reduced to $40 \%$, then the maximum unmodulated carrier power (in kW) that can be used without overloading the transmitter is _________
The unmodulated carrier power in an AM transmitter is $5$ kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is $50 \%$...
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Communications
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amplitude-modulation
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