Consider the following circuit involving three Dtypes flip-flops used in a certain type of Counter configuration.

If all the flip-flops were reset to $$0$$ at power on, what is the total number of distinct outputs (states) represented by $$PQR$$ generated by the counter?

If the difference between the expectation of the square of a random variable $$\left( {E\left[ {{X^2}} \right]} \right)$$ and the square of the expectation of the random variable $${\left( {E\left[ X \right]} \right)^2}$$ is denoted by R then

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is probability that the two cards are selected with the number on the first card is one higher than the number on the second card.

Which one of the following options is correct given three positive integers $$x, y$$ and $$z$$, and a predicate
$$P\left( x \right) = \neg \left( {x = 1} \right) \wedge \forall y\left( {\exists z\left( {x = y * z} \right) \Rightarrow \left( {y = x} \right) \vee \left( {y = 1} \right)} \right)$$