$$R(A,B,C,D)$$ is a relation. Which of the following does not have a lossless-join, dependency preserving $$BCNF$$ decomposition?

Consider the circuit given below with initial state $${Q_0} = 1,\,\,{Q_1} = {Q_2} = 0.$$ The state of the circuit is given by the value of $$4{Q_2} + 2{Q_1} + {Q_{0.}}$$

Which one of the following is correct state sequence of the circuit?

Consider the following circuit with initial state $${Q_0} = {Q_1} = 0.$$ The $$D$$ Flip-Flops are positive edge triggered and have set up times $$20$$ nanosecond and hold times $$0.$$

Consider the following timing diagram of $$X$$ and $$C;$$ the clock period of $$C>40$$ nanosecond which one is the correct plot of $$Y?$$

Consider the circuit shown below. The output of a $$2:1$$ Mux is given by the function $$(ac+bc)$$

Which of the following is true?