Sequence is $0-2-3-1-0$
From the given sequence, we have state table as
$${\begin{array}{c|c|c|c}
\bf{Q_2}& \bf{Q_1}& \bf{Q_2^+}&\bf{ Q_1^+}\\\hline
0&0&1&0 \\\hline 0&1&0&0 \\ \hline 1&0&1&1 \\ \hline 1&1&0&1 \\
\end{array}}$$
Now we have present state and next state, use excitation table of $T$ flip-flop
$${\begin{array}{c|c|c|c}
\bf{Q_2}& \bf{Q_1}& \bf{Q_2^+}&\bf{ Q_1^+} & \bf{T_2} & \bf{T_1}\\\hline
0&0&1&0 & 1&0\\\hline 0&1&0&0&0&1 \\ \hline 1&0&1&1&0&1 \\ \hline 1&1&0&1&1&0 \\
\end{array}}$$
From state table, $T_2=Q_2 \odot Q_1$, and $T_1 = Q_2 \oplus Q_1 $
$X=T_1 = Q_2 \oplus Q_1 $
Correct Answer: $D$