Option 1: Finance Commission is not an extra-constitutional and non-statutory body. It is a constitutional body established under Article 280 of the Constitution.

Option 2: Planning Commission is the correct answer. It is an extra-constitutional and non-statutory body. It was established in 1950 by a government resolution, not through an act of Parliament. The Planning Commission was responsible for formulating Five-Year Plans and advising the government on economic and social issues.

Option 3: Union Public Service Commission (UPSC) is a constitutional body mentioned in Article 315 of the Constitution. It is responsible for the recruitment and appointment of civil servants in the central government.

Option 4: Election Commission is also a constitutional body mentioned in Article 324 of the Constitution. It is responsible for conducting free and fair elections in the country.

In summary, the correct answer is option 2: Planning Commission, as it is the only extra-constitutional and non-statutory body among the options provided.