0 votes
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121
The $S$-parameters of a two-port network is given as$$[S]=\left[\begin{array}{ll}S_{11} & S_{12} \\S_{21} & S_{22}\end{array}\right]$$with reference to $Z_0$. Two lossles...
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125
Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t...
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126
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128
The switch $\mathrm{S}_{1}$ was closed and $\mathrm{S}_{2}$ was open for a long time. At $t=0$, switch $\mathrm{S}_{1}$ is opened and $\mathrm{S}_{2}$ is closed, simultan...
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130
The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are
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132
2 votes
1 answer
135
Assuming that all flip-flops are in reset condition initially, the count sequence observed at $\text{Q}_\text{A}$ in the circuit shown is$0010111 \ldots$$0001011 \ldots$$...
1 votes
1 answer
136
The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by$G(s) H(s)=k \frac{s(s+1)}{(s+2)(s+3)}$$G(s) H(s)=k...
1 votes
1 answer
137
If the unit step response of a network is $\left(1-e^{-\alpha t}\right)$, then its unit impulse response is$\alpha e^{-\alpha t}$$\alpha^{-1} e^{-\alpha t}$$\left(1-\alph...
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1 answer
138
The given figure shows a ripple counter using positive edge triggered flip-flops. If the present state of the counter is $Q_{2} \; Q_{1} \; Q_{0}=011$, then its next stat...
2 votes
1 answer
140
The logic function implemented by the circuit below is (ground implies a logic $\text{“0”})$$\text{F=AND(P,Q})$$\text{F=OR(P,Q})$$\text{F=XNOR(P,Q})$$\text{F=XOR(P,Q}...
2 votes
1 answer
141
Match the logic gates in Column A with their equivalents in Column B.$\text{P-2, Q-4, R-1, S-3}$$\text{P-4, Q-2, R-1, S-3}$$\text{P-2, Q-4, R-3, S-1}$$\text{P-4, Q-2, R-3...
2 votes
1 answer
142
2 votes
1 answer
143
0 votes
1 answer
144
In the modulo-$6$ ripple counter shown in the given figure, the output of the $2$-input gate is used to clear the J-K flip-flops.The $2$-input gate isa NAND gatea NOR gat...
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147
Let\[\mathcal{P}=\left\{(x, y): x+y \geq 1,2 x+y \geq 2, x+2 y \geq 2,(x-1)^{2}+(y-1)^{2} \leq 1\right\} .\]Compute\[\min _{(x, y) \in \mathcal{P}} 2 x+3 y\]$2$$3$$4$$6$N...
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148
$\begin{array}{rlr}a^*=\max_{x, y} & x^2+y^2-8 x+7 \\ \text { s.t. } & \qquad x^2+y^2 \leq 1 \\ & \qquad \qquad y \geq 0\end{array}$Then $a^{\star}$ is$16$$14$$12$$10$Non...
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152
Let $X$ be a random variable which takes values $1$ and $-1$ with probability $1 / 2$ each. Suppose $Y=X+N$, where $N$ is a random variable independent of $X$ with the fo...
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157
An ant in the plane travels in a spiral such that its position $(x(t), y(t))$ at time $t \geq 0$ is $\left(e^{t} \cos t, e^{t} \sin t\right)$. At time $t=1$, find the rea...
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158