Answer

Correct Option: (ii) The choice of path is nondeterministic (and equivalently (iii); if “All of the mentioned” is offered, (iv) is also defensible)

Explanation

Deterministic FA: $\delta: Q \times \Sigma \rightarrow Q$ — exactly one next state for each $(q,a)$.

Nondeterministic FA: $\delta: Q \times \Sigma \rightarrow 2^{Q}$ — a set of possible next states. The machine may:

• be in several states simultaneously (subset view), or
• guess a path.

So “non-deterministic” means:

• Next state is not uniquely determined → (iii)
• Choice of computation path is nondeterministic → (ii)

The “result” (accept/reject) is determined (exists some accepting path ⇔ accept), so (i) “result undetermined” is misleading.

In many textbooks the canonical answer is (ii) Choice of path is nondeterministic (or (iii)). If option (iv) “All of the mentioned” lumps (ii)+(iii), some keys mark (iv) as correct.

Formal

$N = (Q,\Sigma,\delta,q_0,F)$, $\delta(q,a) = \{p_1,p_2,\dots\}$. On input $w$, $N$ accepts iff there exists a path $q_0 \xrightarrow{w} f\in F$.

Final Answer

NFA is nondeterministic because the next state / path is not uniquely determined → Option (ii) (and (iii)).