The following sequence of operations is performed on stack: PUSH (10),PUSH (20),POP,PUSH (10),PUSH (20),POP,POP,POP,PUSH (20),POP The sequence of the value popped out is:

Find the maximum clock frequency at which the counter in Fig., can be operated. Assume that the propagation delay through each flip-flop and $$AND$$ gate is $$10$$ $$ns.$$ Also assume that the setup time for the $$JK$$ inputs of the flip-flops is negligible.

Find the minimum sum of products form of the logic function
$$f\left( {A,B,C,D} \right) = \sum d \left( {3,11,12,14} \right)$$
Where $$m$$ and $$d$$ denote the minterms and don't cares respectively.

The maximum number of possible edges in an undirected graph with a vertices and $$k$$ components is _________ .