PYQs Based test 6: Signals & Systems

Let f(x) be a real, periodic function satisfying f(-x) = -f(x). The general form of its Fourier series representation would be

The value of $\underset{-\infty }{\overset{+\infty }{\int }}{e}^{-t}\delta \left(2t-2\right)dt$, where $\delta \left(t\right)$ is the Dirac delta function, is

Let $X\left(s\right)=\frac{3s+5}{s^2+10s+21}$ be the Laplace Transform of a signal x(t). Then x(0⁺) is

A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

The solution for the differential equation

$\frac{d^{2}x}{d{t}^2}=-9x$

With initial conditions $x\left(0\right)=1and\frac{dx}{dt}{|}_{t=0}=1$, is