Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.

The following additional facts are known.

i. No composer who assigned item to Princess, assigned any item to Queen.
ii. No composer who assigned item to Rani, assigned any item to Samragni.
iii. The first performance was by Princess; this item was assigned by Badal.
iv. The last performance was by Rani; this item was assigned by Gagan.
v. The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.

Which of the following is true?

The correct option is 1.

Let's construct the sequence of the 8 performances step-by-step:

1. Since there are 4 dancers who each perform 2 items in the same sequence, the sequence of dancers repeats: 1st, 2nd, 3rd, 4th, then 5th, 6th, 7th, 8th.
- Princess performs 1st (and thus 5th).
- Rani performs last (8th, and thus 4th).
- Princess's 1st item is composed by Badal (Performance 1).
- Rani's 2nd item is composed by Gagan (Performance 8).

2. Let the gap in terms of performances between the two items composed by Badal, Gagan, and Dyu be $x$. Therefore, if one item is at position $p$, the other is at position $p+x+1$.
- Badal is at Performance 1, so Badal's second item is at $2+x$.
- Gagan is at Performance 8, so Gagan's first item is at $7-x$.
- Ashman's items are consecutive, so they must occupy a adjacent pair of slots (e.g., positions 4 and 5).

3. Testing values of $x$:
- If $x=4$, then Badal is at 1 and 6, and Gagan is at 3 and 8.
- This leaves Dyu at 2 and 7 (which has a gap of 4 slots: 3, 4, 5, 6). This fits perfectly.
- The consecutive slots left for Ashman are 4 and 5.

4. The resulting sequence of composers is:
1. Badal
2. Dyu
3. Gagan
4. Ashman
5. Ashman
6. Badal
7. Dyu
8. Gagan

Thus, the second performance was composed by Dyu, which makes Statement 1 true.