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.
Since the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:
The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Also, the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.
Then Ashman can only compose for the following performances.
Hence Dyu will compose for the following performances:
From (i) No composer who assigned item to Princess, assigned any item to Queen.
From (ii) No composer who assigned item to Rani, assigned any item to Samragni.
Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for Queen 1st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.
Hence, the complete table is as follows:
Option A: Samragni did not perform in any item composed by Ashman. This statement is true.
Option B: Princess did not perform in any item composed by Dyu. This is also true.
Option C: Rani did not perform in any item composed by Badal. This statement is true.
Option D: Queen did not perform in any item composed by Gagan. This statement is false.
Hence D is the answer.
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