a$)$ Please design an inverting amplifier with an op amp which has a gain of $15.$ The amplifier shall have a $3-$dB frequency of $10$ kHz $($the capacitor of the operational amplifier shall be placed in the feedback loop of the operational amplifier$)$

b$)$ If the resistors have a tolerance of $+-1\%,$ what will be the minimum and maximum gain of the operational amplifier?

c$)$ If the capacitor of the operational amplifier has a tolerance of $+-10\%$ and if the resistors have a tolerance of $+-1\%,$ what will be the minimum and maximum $3-$dB frequency of the operational amplifier?

d$)$ A $12-$bit analog$-$to$-$digital converter $($ADC$)$ is connected to the operational amplifier given in a$).$ What will be the ADC digital output signal in LSBs $($Least Significant Bit$)?$

e$)$ If the ADC has a total error of $+-5$ LSBs$.$ What is the minimum and maximum ADC output signal in LSBs and in Volts?

The input voltage of the operational amplifier is V$\_("$in $")=15$mV $($frequency is $0$ Hz $).$ ADC reference voltage is $5\mathrm{.}0$ V $.$