Identify the correct statements from the following:

(A) As long as MP>AP, the average Product (AP) can rise even when the Marginal Product (MP) is falling.
(B) The law of variable proportions operates only if the factor ratio happens to change.
(C) Total Product (TP) must increase no matter if there are increasing or decreasing returns to a factor.
(D) Marginal Product (MP) = Average Product (AP), when AP is maximum.

Choose the correct answer from the options given below:

(A), (B), (C) and (D)

The correct answer is Option (3) → (A), (B), (C) and (D)

(A) As long as MP>AP, the average Product (AP) can rise even when the Marginal Product (MP) is falling. (Correct). This is a standard rule of production theory — as long as MP is greater than AP, AP will keep increasing, even if MP itself is declining.
(B) The law of variable proportions operates only if the factor ratio happens to change. (Correct). This law assumes that one factor (say, labour) changes while others (like land or capital) are held fixed, so the input ratio changes.
(C) Total Product (TP) must increase no matter if there are increasing or decreasing returns to a factor. Incorrect. Total Product (TP) increases during both increasing and decreasing returns to a factor. However, TP starts to fall when Marginal Product (MP) becomes negative. If MP is negative, it means the additional unit of variable input is actually reducing total output, causing TP to decrease. So, TP does not always increase; it only increases as long as MP is positive.
(D) Marginal Product (MP) = Average Product (AP), when AP is maximum. (Correct). This is a key point in the relationship between marginal and average curves. The marginal curve intersects the average curve at the average curve's maximum point.

Note: The given answer answer is as per NTA. However, there appears to be a mistake in the naswer by NTA as explained above.