Match the following:
List - $${\rm I}$$ (Circuit)

List - $${\rm II}$$ (Functions)
$$(P)$$$$\,\,\,\,\,$$ High-pass filter
$$(Q)$$$$\,\,\,\,\,$$ Amplifier
$$(R)$$$$\,\,\,\,\,$$ Comparator
$$(S)$$$$\,\,\,\,\,$$ Low-pass filter

One of the applications of current mirror is

A $$NPN$$ Si transistor is meant for low-current audio amplification. Match is following characteristic against their values.

The state-space representation of a system is given by $$\left[ {\matrix{ {\mathop {{X_1}}\limits^ \bullet } \cr {\mathop {{X_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 5} & 1 \cr { - 6} & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right].$$
Find the Laplace transform of the state transistion matrix. Find also the value of $${x_1}$$ at $$t=1$$ if $${x_1}\left( 0 \right) = 1$$ and $${x_2}\left( 0 \right) = 0.$$