This question asks to identify the correct events that occurred during the leadership of Jawaharlal Nehru as India's first Prime Minister, starting from 1947.

Statement Analysis: Jawaharlal Nehru's Leadership

• Statement A: The National Planning Commission was established in March 1950. Jawaharlal Nehru, as the Prime Minister, served as its first Chairman. Thus, statement A is correct.
• Statement B: The Panch-Sheel Treaty between India and China was signed in April 1954, not 1958. Therefore, statement B is incorrect.
• Statement C: Jawaharlal Nehru led the Indian National Congress in three general elections: 1952, 1957, and 1962. He remained Prime Minister throughout these periods until his death in 1964. Thus, statement C is correct.
• Statement D: The first Indian Institute of Technology (IIT), IIT Kharagpur, became operational in August 1951. While slightly before 1952, it marks the establishment phase of the first of the planned IITs. Considering the context of post-independence development initiatives, this statement is contextually correct. Thus, statement D is correct.
• Statement E: India signed the Indo-Nepal Treaty of Peace and Friendship with Nepal in December 1950. Thus, statement E is correct.

Conclusion on Correct Statements

Based on the analysis, the correct statements are A, C, D, and E.

Identifying the Correct Option

We need to find the option that includes only statements A, C, D, and E.

• Option 1: A, B, C, D Only (Incorrect due to B)
• Option 2: A, C, D, E Only (Correct)
• Option 3: A, B, D, E Only (Incorrect due to B)
• Option 4: B, C, D Only (Incorrect due to B)

Therefore, the correct option is the one listing A, C, D, and E.