GATE EE 2024 Question Paper (11-Feb-2024) (Shift-2)

Consider the standard second-order system of the form $\frac{{\omega }_n^2}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}$ with the poles $p$ and $p^{\ast }$ having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below:
System 1: ${\omega }_n=3$ rad/sec and $\theta =60^{\circ }$
System 2: ${\omega }_n=1$ rad/sec and $\theta =70^{\circ }$
Which one of the following statements is correct?

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are same?

The table lists two instrument transformers and their features:The correct matching of the two columns is

Simplified form of the Boolean function
$F(P,Q,R,S)=\bar{P}\bar{Q}+\bar{P}QS+P\bar{Q}\bar{R}\bar{S}+P\bar{Q}R\bar{S}$
is

In the circuit, the present value of Z is 1. Neglecting the delay in the combinatorial circuit, the values of S and Z, respectively, after the application of the clock will be