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44
​​​​​To obtain the Boolean function $\text{F(X, Y)}=\text{X} \bar{\text{Y}}+\bar{\text{X}}$, the inputs $\text{PQRS}$ in the figure should be$1010$$1110$$0110$$...
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46
In the given circuit, the diodes are ideal. The current $\text{I}$ through the diode $\text{D} 1$ in milliamperes is __________(rounded off to two decimal places).
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47
Two passive two-port networks $\mathbf{P}$ and $\mathbf{Q}$ are connected as shown in the figure. The impedance matrix of network $\mathbf{P}$ is $Z_{\mathbf{P}}=\left[\b...
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48
Let $X(\omega)$ be the Fourier transform of the signal\[x(t)=e^{-t^{4}} \cos t, \quad-\infty < t < \infty.\]The value of the derivative of $X(\omega)$ at $\omega=0$ is (r...
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49
Consider the complex function $f(z)=\cos z+e^{z^{2}}$. The coefficient of $z^{5}$ in the Taylor series expansion of $f(z)$ about the origin is __________ (rounded off to ...
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59
​​​​For the three-bus lossless power network shown in the figure, the voltage magnitudes at all the buses are equal to $1$ per unit (pu), and the differences of t...