Correct Answer - Option 2 : The second performance was composed by Dyu.
EXPLANATION:
From the information given in the question, there are a total of 8 dance items.
As per the question, the 1st performance was by Princess and it was composed by Badal and the last performance was by Rani and which was composed by Gagan. No dancer performed its 2nd item before the performance of the 1st item by all the other dancers. The dancers performed their 2nd item in the same sequence as theirs1st.
∴ The 4th and the 5th performances are by Rani and Princess respectively.
Items assigned by Ashman were consecutively numbered because the 1st four performances were by four different composers and it is only possible when Ashman composed the 4th and the 5th performances.
If the 6th performance was composed by Badal, then the 7th would have been composed by Dyu. As per the question number of performances between items assigned by the remaining composers is the same. In that case, performances two, three, and four would have been composed by Badal, Dyu, and Gagan respectively.
If Dyu composed the 6th performance then the 7th has to be composed by Badal. Considering that case, the number of performances between items assigned by Badal is 5.
∴ The number of items assigned by Dyu should also be 5 which is not possible.
So, the 2nd, 3rd, 6th, and 7th performances were composed by Dyu, Gagan. Badal and Dyu respectively.
Since no composer who assigned music to Princess is assigned music to Queen, the 6th performance cannot be by Queen.
∴ The 6th and 7th performances will be by Samragni and Queen respectively. Since the sequence is the same for their 1st items as well, the 2nd and 3rd performances will be by Samragni and Queen respectively.
∴ The overall sequence will be as follows:
Sequence
|
Dancer
|
Music Composer
|
1
|
Princess
|
Badal
|
2
|
Samragni
|
Dyu
|
3
|
Queen
|
Gagan
|
4
|
Rani
|
Ashman
|
5
|
Princess
|
Ashman
|
6
|
Samragni
|
Badal
|
7
|
Queen
|
Dyu
|
8
|
Rani
|
Gagan
|
∴ The second performance was composed by Dyu