The Laplace Transform of the signal $x(t)=u(t-2) *(t u(t))$ is given by which of the following expressions?

["*" represents convolution operator]

Two analog signals $x_1(t)$ and $x_2(t)$ ( $t$ in second), are sampled at a rate $F_s=40 \mathrm{~Hz}$, where $x_1(t)=\cos (20 \pi t), t \geq 0$, and $x_2(t)=\cos (100 \pi t), t \geq 0$.

The first ten samples (starting from $t=0$ ) are considered for the analysis.

Which of the following statements is TRUE?

The response of a discrete time system $\mathrm{y}[\mathrm{n}]$ obeys the following relation:

$$ y[n]=\frac{5}{6} y[n-1]-\frac{1}{6} y[n-2]+x[n] . $$

The input to the system is $x[n]=\delta[n]-\frac{1}{3} \delta[n-1]$.

Which of the following options is TRUE for $y[n]$ ?

The continuous time signal $x(t)$ is real, periodic with period $T$ and satisfies the Dirichlet conditions.

The Fourier series representation of $x(t)=\sum_{n=-\infty}^{\infty} a_n e^{j\left(\frac{2 \pi n t}{T}\right)}$ and $x(t)$ satisfies the following:

$$ x\left(t-\frac{T}{2}\right)=-x(t) $$

For any integer $m$, which of the following options is correct?