The correct answer is B, C and E only.

To understand why this is the correct choice, let us analyze each of the given pairs individually:

[A] Kalidasa – Amoghvarsha: Incorrect
Kalidasa was one of the greatest Sanskrit poets and dramatists of ancient India, famous for works like Abhijnanashakuntalam, Meghaduta, and Raghuvaṃsa. Amoghvarsha (Amoghavarsha I) was a famous emperor of the Rashtrakuta dynasty who was a patron of literature and wrote the Kavirajamarga (in Kannada) and Prashnottara Ratnamalika. They are not associated as author and work in this manner.

[B] Bhavabhuti – Uttararamcharita: Correct
Bhavabhuti was an 8th-century Sanskrit scholar and playwright. His play Uttararamacharita (The Later Story of Rama) depicts the later life of Rama, focusing on the abandonment of Sita and their eventual reunion.

[C] Bhasa – Urubhanga: Correct
Bhasa is one of the earliest known Sanskrit dramatists. His play Urubhanga (The Shattering of the Thigh) is a unique tragedy in Sanskrit literature that focuses on the character of Duryodhana during and after his final duel with Bhima in the Mahabharata war.

[D] Rajashekhara – Rajatarangini: Incorrect
Rajashekhara was an eminent Sanskrit poet, dramatist, and critic, known for works like Kavyamimamsa and Karpuramanjari. On the other hand, the Rajatarangini (a historical chronicle of the kings of Kashmir) was written by Kalhana in the 12th century, not by Rajashekhara.

[E] Somadeva – Kathasaritsagara: Correct
Somadeva was an 11th-century Kashmiri writer who compiled the Kathasaritsagara (Ocean of the Streams of Stories), a famous collection of Indian legends, fairy tales, and folk stories.

Therefore, the correctly matched pairs are B, C, and E.