GATE IN 2022 Question Paper (06-Feb-2022) (Shift 2)

The input 𝑥(𝑡) to a system is related to its output 𝑦(𝑡) as

$\frac{\mathrm{dy}(\mathrm{t})}{\mathrm{dt}}+\mathrm{y}(\mathrm{t})=3x(\mathrm{t}-3)\mathrm{u}(\mathrm{t}-3)$

Here 𝑢(𝑡) represents a unit-step function.

The transfer function of this system is ________

A pneumatic nozzle-flapper system is conventionally used to convert ________

A periodic function 𝑓(𝑥), with period 2, is defined as

$\mathrm{f}(\mathrm{x})=\{\begin{array}{cc}-1-x& -1\le x<0\\ 1-x& 0<x\le 1\end{array}$

The Fourier series of this function contains ________

The output of a system 𝑦(𝑡) is related to its input 𝑥(𝑡) according to the relation 𝑦(𝑡) = 𝑥(𝑡) sin(2𝜋𝑡). This system is _______

A unity-gain negative-feedback control system has a loop-gain 𝐿(𝑠) given by

$\mathrm{L}(\mathrm{s})=\frac{6}{\mathrm{s}(\mathrm{s}-5)}$

The closed-loop system is ________