The circuit shown in the figure uses matched transistors with a thermal voltage $${V_T} = 25\,mV.$$ The base currents of the transistors are negligible. The value of the resistance $$R$$ in $$k\Omega $$ that is required to provide $$1\,\,\,\mu A$$ bias current for the differential amplifier block shown is ____________.

The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

For a system having transfer function $$G\left( s \right) = {{ - s + 1} \over {s + 1}},$$ a unit step input is applied at time $$t=0.$$ The value of the response of the system at $$t=1.5$$ sec (round off to three decimal places) is __________.

Let a causal $$LTI$$ system be characterized by the following differential equation, with initial rest condition
$${{{d^2}y} \over {d{t^2}}} + 7{{dy} \over {dt}} + 10y\left( t \right) = 4x\left( t \right) + 5{{dx\left( t \right)} \over {dt}}\,\,$$

Where, $$x(t)$$ and $$y(t)$$ are the input and output respectively. The impulse response of the system is ($$u(t)$$ is the unit step function)