Step 1: Evaluate Assertion [As].
Assertion [As] states: "The Planning Commission of India mainly work to formulate the five year and annual plans of the country."
This statement is True. The primary function of the Planning Commission, established in 1950, was indeed to formulate Five-Year Plans and annual plans for the economic development of India.
Step 2: Evaluate Reason [R].
Reason [R] states: "The planning Commission is a Constitutional body."
This statement is False. A Constitutional body is one whose existence and powers are derived directly from the Constitution of India (e.g., Election Commission, Union Public Service Commission). The Planning Commission was an extra-constitutional or non-statutory body, set up by a Cabinet Resolution (an executive order) and not by an Act of Parliament or the Constitution itself. It was replaced by NITI Aayog in 2015.
Step 3: Choose the correct alternative based on the evaluation of [As] and [R].
Assertion [As] is True.
Reason [R] is False.
Comparing this with the given options:
(1). Both [As] and [R] are true, and [R] is the correct explanation of [As]. (Incorrect, as [R] is false)
(2). Both [As] and [R] are true, but [R] is not the correct explanation of [As]. (Incorrect, as [R] is false)
(3). [As] is true, but [R] is false. (Correct)
(4). [As] is false, but [R] is true. (Incorrect, as [As] is true and [R] is false)
The final answer is $\boxed{\text{C}}$.