Explanation:

- The Panchatantra is a legendary collection of short stories.

This introduction sets the context for discussing the origin and purpose of the text.

- (1)______ composed in the 2nd century BC...

This part suggests that the text was created at a particular time.

- (2)______ to be written by Vishnu Sharma...

Here, the sentence needs a word that conveys an understanding or belief regarding the authorship.

- Option 1: established

Usually implies something is well-recognized or confirmed, not just believed.

- Option 2: believed

This word indicates that there is a general thought or understanding about the authorship, even if not definitively proven.

- Option 3: alleged

Often used when someone is accused, typically with negative connotations, not suitable for authorship of an ancient text.

- Option 4: designed

Refers to something that was deliberately planned or created, not fitting here regarding authorship.

The correct fill for blank number 2 is "believed".

Your answer is Option:2 - believed.