An active filter consisting of an op-amp, resistor $${R_1},\,\,{R_2},\,\,{R_3}$$ and two capacitors of value $$C$$ each, has a transfer function
$$T\left( s \right) = {{{{ - s} \over {\left( {{R_1}C} \right)}}} \over {{s^2} + {{2s} \over {\left( {{R_3}C} \right)}} + {1 \over {\left( {R{R_3}{C^2}} \right)}}}}$$
where, $$R = {R_1}||{R_2}$$
If $${R_1} = 2k\Omega ,{R_2} = 2/3\,k\Omega ,\,\,{R_3} = 200\,k\Omega $$ and $$C = 0.1\,\,\mu F,$$ determine the center frequency $${\omega _0},$$ gain $${A_0}$$ and the $$Q$$ of the filter.

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

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

For the differential amplifier circuit shown in Figure, determine the differential gain, the common-mode gain and the common mode rejection ratio.

In the following circuit the output $$'V'$$ follows an equation of the form
$${{{d^2}V} \over {d{t^2}}} + a.{{dV} \over {dt}} + bV = f\left( t \right).$$
Find $$a,b$$ and $$f(t)$$