GATE EE 2018 Question Paper (10-Feb-2018) (Shift 2)

A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the figure. Assume i(0) = 0, v(0) = 0. Which one of the following circular loci represents the plot of i(t) versus v(t)?

The equivalent impedance Z${}_{eq}$ for the infinite ladder circuit shown in the figure is

Consider a system governed by the following equations

$\frac{d{x}_1\left(t\right)}{dt}=x_2\left(t\right)-x_1\left(t\right)$

$\frac{d{x}_2\left(t\right)}{dt}=x_1\left(t\right)-x_2\left(t\right)$

The initial conditions are such that $x_1\left(0\right)<x_2\left(0\right)<\infty .$ Let $x_{1f}=\underset{t\to \infty }{\lim }{x}_1\left(t\right)$ and $x_{2f}=\underset{t\to \infty }{\lim }{x}_2\left(t\right)$. Which one of the following is true?

The number of roots of the polynomial, s⁷ + s⁶ + 7s⁵ + 14s⁴ + 31s³ + 73s² + 25s + 200, in the open left half of the complex plane is

If C is a circle |z| = 4 and $f\left(z\right)=\frac{z^2}{{\left(z^2-3z+2\right)}^2}$, then $\oint f\left(z\right)dz$ is