The input $$ - 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If the initial value of the output is -2, then the value of the output at steady state is _____.

Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the following three statements.

S1: The system is stable.
S2: $${{h\left( {t + 1} \right)} \over {h\left( t \right)}}$$ is independent of t for t > 0.
S3: A non-casual system with the same transfer function is stable.

For the above system,

The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with the region of convergence $$\left| z \right| > 2$$. Then, $$x\left[ 2 \right]$$ is ____________________.

Let $$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \right)$$ be sampled at $$20\,\,\,Hz$$ and reconstructed using an ideal low-pass filter with cut-off frequency of $$20\,\,\,Hz$$. The frequency/frequencies present in the reconstructed signal is/are.