The number of roots on the equation $$2{s^4} + {s^3} + 3{s^2} + 5s + 7 = 0$$ that lie in the right half of $$S$$ plane is:

The open collector outputs of two$$2$$-inputs $$NAND$$ gates are connected to a common pull up resistor. If the input to the gates are $$P,Q$$ and $$R,S$$ respectively, the output is equal to

Match the following

$$(a)$$ Construct the truth table for the circuit given in Figure $${Q_1},{Q_2}$$ and $${Q_3}$$ are outputs and the clock pulses are the inputs. Unused $$JK$$ inputs are assumed to be at logic $$1.$$ All flip flops are reset at power $$ON$$.
$$(b)$$ Sketch the output waveforms at $${Q_1},{Q_2}$$ and $${Q_3}$$.
$$(c)$$ What function does this circuit perform.