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 periodic signal $x(t)$ is

$$ x(t)=1+2 \cos 2 \pi t+2 \cos 4 \pi t+2 \cos 6 \pi t $$

If $T$ is the period of $x(t)$, then $\frac{1}{T} \int_0^T|x(t)|^2 d t=$________(round off to the nearest integer).

Let continuous-time signals $x_1(t)$ and $x_2(t)$ be

$x_1(t)=\left\{\begin{array}{cc}1, & t \in[0,1] \\ 2-t, & t \in[1,2] \\ 0, & \text { otherwise }\end{array}\right.$

and $x_2(t)=\left\{\begin{array}{cc}t, & t \in[0,1] \\ 2-t, & t \in[1,2] \\ 0, & \text { otherwise }\end{array}\right.$.

Consider the convolution

$y(t)=x_1(t) * x_2(t)$. Then $\int\limits_{-\infty}^{\infty} y(t) d t$ is :

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system $S$. The output is observed to be the continuous-time unit step signal $u(t)$. Which one of the following statements is true?