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Recent questions and answers in Networks, Signals and Systems
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GATE2017 EC2: 32
Consider the circuit shown in the figure. The Thevenin equivalent resistance (in Ω) across PQ is _____________
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Nov 25, 2017
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Network Solution Methods
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gate2017ec2
theveninequation
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GATE2017 EC2: 35
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $h_1(t)=2\delta (t+2)3\delta (t+1)$ $h_2(t)=\delta (t2)$. If the input $x(t)$ is a unit step signal, then the energy of $y(t)$ is ____________
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Nov 25, 2017
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Continuoustime Signals
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gate2017ec2
impulseresponse
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3
GATE2017 EC2: 31
The switch in the circuit, shown in the figure, was open for a long time and is closed at $t=0$. The current $i(t)$ (in ampere) at $t=0.5$ seconds is ____________
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Nov 25, 2017
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Network Solution Methods
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gate2017ec2
nodalmeshanalysis
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GATE2017 EC2: 19
Consider the state space realization $\begin{bmatrix} \dot{x_1}(t)\\ \dot{x_2}(t) \end{bmatrix}=\begin{bmatrix} 0 &0 \\ 0&9 \end{bmatrix}\begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}+\begin{bmatrix} 0\\ 45 \end{bmatrix} u(t)$ , with the initial ... the unit step function. The value of $\lim_{t\rightarrow \infty }\left  \sqrt{x_1^2(t)+x_2^2(t)} \right $ is __________.
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Nov 23, 2017
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Continuoustime Signals
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gate2017ec2
discretetimesignals
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5
GATE2017 EC2: 6
A connection is made consisting of resistance A in series with a parallel combination of resistances $B$ and $C$. Three resistors of value $10 Ω, 5 Ω, 2 Ω$ are provided. Consider all possible permutations of the given resistors into the ... minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ___________.
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Nov 23, 2017
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nodalmeshanalysis
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6
GATE2017 EC2: 5
In the circuit shown, V is a sinusoidal voltage source. The current Ⅰ is in phase with voltage V. The ratio$\frac{amplitude of voltage across the capacitor}{amplitude of voltage across the resistor}$ is ___________.
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Nov 23, 2017
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Network Solution Methods
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gate2017ec2
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GATE2017 EC2: 8
The input x(t) and the output y(t) of a continuous –time system are related as $y(t)=\int_{tT}^{t}x(u) du.$ The system is linear and timevariant linear and timeinvariant nonlinear and timevariant nonlinear and timeinvariant
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Nov 23, 2017
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Continuoustime Signals
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gate2017ec2
ltisystems
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GATE2017 EC2: 7
An LTI system with unit sample response $h[n]=5\delta [n]7\delta [n1]+7\delta [n3]5\delta [n4]$ is a lowpass filter highpass filter bandpass filter bandstop filter
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Nov 23, 2017
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Continuoustime Signals
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gate2017ec2
ltisystems
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9
GATE2017 EC1: 52
A continous time signal $x(t)=4cos(200\pi t)+8cos(400\pi t)$, where $t$ is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $h(t)=\left\{\begin{matrix} \frac{2sin(300\pi t)}{\pi t},\: t\neq 0\\ 600,\: t=0 \end{matrix}\right.$ Let $y(t)$ be the output of this filter. The maximum value of $\left  y(t)) \right $ is _________.
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Nov 17, 2017
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Continuoustime Signals
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lti
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10
GATE2017 EC1: 35
The figure shows an RLC circuit excited by the sinusoidal voltage $100cos(3t) Volts$, where $t$ is in seconds. The ratio $\frac{amplitude\,of\,V_{2}}{amplitude\,of\,V{1}}$ is______.
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Nov 17, 2017
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gate2017ec1
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11
GATE2017 EC1: 33
Let h[n] be the impulse response of a discretetime linear time invariant(LTI) filter. The impulse response is given by $h[0]=\frac{1}{3};\,h[1]=\frac{1}{3};\,h[2]=\frac{1}{3}$; and $h[n]=0$ for $n<0$ and $n>2$. Let $H(ω)$ be ... normalized angular frequency in radians. Given that $H(ω_{0})=0$ and $0< ω_{0}<π$, the value of $ω_{0}$ (in radians) is equal to__________.
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Nov 17, 2017
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Continuoustime Signals
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gate2017ec1
dtft
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12
GATE2017 EC1: 32
Two discretetime signals $x[n]$ and $h[n]$ are both nonzero 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__________.
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Nov 17, 2017
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Continuoustime Signals
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13
GATE2017 EC1: 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 $x(3t)$: I.The complex Fourier ... which 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
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Nov 17, 2017
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Continuoustime Signals
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fourierseries
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14
GATE2017 EC1: 9
A periodic signal $x(t)$ has a trigonometric Fourier series expansion $x\left ( t \right )= a_{0}+\sum_{n=1}^{ \infty }\left ( a_{n}cosn\omega _{0}t+b_{n}sinn\omega _{0}t \right )$ If $x(t)= x(t)=x(t\frac{\Pi }{\omega _{0}})$ ... $n$ odd $a_n$ are zero for $n$ even and $b_n$ are zero for $n$ odd $a_n$ are zero for $n$ odd and $b_n$ are zero for $n$ even
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Nov 17, 2017
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Continuoustime Signals
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gate2017ec1
fourierseries
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15
GATE2017 EC1: 6
Consider a single input single output discretetime system with $x\left [ n \right ]$ as input and $y\left [ n \right ]$ ... is true about the system? It is causal and stable It is causal but not stable It is not causal but stable It is neither causal nor stable
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Nov 17, 2017
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Continuoustime Signals
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lti
systems
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16
GATE2017 EC1: 5
Consider the following statements for continuoustime linear time invariant (LTI) systems. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. There is no causal and BIBO stable with a pole in the right half of ... the following is correct? Both I and II are true Both I and II are not true Only I is true Only II is true
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Nov 17, 2017
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lti
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17
GATE2017 EC1: 12
In the circuit shown, the positive angular frequency $\omega$ (in radians per second) at which the magnitude of the phase differnce between the voltages $V_1$ and $V_2$ equals $\omega \frac{\pi }{4}$ radians, is_________
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Nov 17, 2017
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Network Solution Methods
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gate2017ec1
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