GATE EC 2019 Question Paper (09-Feb-2019) (Shift 1)

Which one of the following functions is analytic over the entire complex plane?

The families of curves represented by the solution of the equation

$\frac{dy}{dx}=-{\left(\frac{x}{y}\right)}^n$

for n = −1 and n = +1, respectively, are

Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If $P\left(z\right)=H\left(z\right)H\left(\frac{1}{z}\right)$ has a zero at $z=\frac{1}{2}+\frac{1}{2}j$, and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?

Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).

Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?

Let Y(s) be the unit-step response of a causal system having a transfer function

$G\left(s\right)=\frac{3-s}{\left(s+1\right)\left(s+3\right)}$

that is, $Y\left(s\right)=\frac{G\left(s\right)}{s}$ . The forced response of the system is