Let $x_C(t)$ be any continuous-time periodic signal with period $T$. It is sampled uniformly with a sampling period $T_s$ where $T_s \neq T$, resulting in the discrete sequence $x[n]=x_c\left(n T_s\right)$, where $n$ is an integer. Which one of the following statements is correct about $x[n]$ ?

Consider a continuous-time signal

$$ x(t)=-t^2\{u(t+4)-u(t-4)\} $$

where $u(t)$ is the continuous-time unit step function. Let $\delta(t)$ be the continuous-time unit impulse function. The value of

$$ \int_{-\infty}^{\infty} x(t) \delta(t+3) d t $$

is

A continuous-time system that is initially at rest is described by

$${{dy(t)} \over {dt}} + 3y(t) = 2x(t)$$,

where $$x(t)$$ is the input voltage and $$y(t)$$ is the output voltage. The impulse response of the system is

Consider the system with following input-output relation $$y\left[n\right]=\left(1+\left(-1\right)^n\right)x\left[n\right]$$ where, x[n] is the input and y[n] is the output. The system is