Lord Mountbatten is the correct answer for the brainchild behind the Balkan Plan for fragmentation of India. The plan was proposed during the partition of India in 1947 and aimed to divide the country along religious lines, creating separate Hindu and Muslim nations.

Explanation:

1. The Balkan Plan:
The Balkan Plan was a proposal put forward by Lord Mountbatten, the last Viceroy of India, during the partition negotiations in 1947. It was named after the Balkan Peninsula, which experienced numerous conflicts and fragmentation in the early 20th century.

2. Lord Mountbatten's Role:
Lord Louis Mountbatten was appointed as the Viceroy of India in March 1947. He was tasked with overseeing the transfer of power from British rule to Indian hands. Mountbatten played a key role in shaping the partition of India and the creation of Pakistan.

3. Partition and the Two-Nation Theory:
The partition of India was based on the Two-Nation Theory, which argued that Hindus and Muslims are two separate nations and cannot coexist in a single country. This theory was put forward by Muhammad Ali Jinnah, the leader of the All India Muslim League.

4. The Balkan Plan Objective:
Lord Mountbatten's Balkan Plan aimed to avoid a united India and proposed the partition of the country along religious lines. It suggested the creation of separate Hindu and Muslim nations, with the Muslim-majority areas forming Pakistan.

5. Implementation of the Plan:
The Balkan Plan was implemented through the Indian Independence Act of 1947, which divided British India into two dominions - India and Pakistan. The partition led to widespread violence, mass migrations, and communal riots, resulting in the deaths of hundreds of thousands of people.

6. Criticism and Controversy:
The Balkan Plan has been criticized for its hasty implementation and the resulting violence and displacement. Many argue that the partition could have been handled better, with more consideration given to the religious and cultural diversity of the Indian subcontinent.

In conclusion, the Balkan Plan for the fragmentation of India was the brainchild of Lord Mountbatten, who proposed the partition of the country along religious lines. The plan aimed to create separate Hindu and Muslim nations, resulting in the formation of India and Pakistan. However, the partition process was marred by violence and communal unrest.