The question requires understanding the statement in the context of the Indian Constitution's Preamble. Let's break it down step-by-step:

1. Assertion (A): The assertion states, "The preamble to the constitution of India clearly indicates the ideals set before the Nation." This statement is true. The Preamble of the Indian Constitution does serve as an introductory statement that outlines the guiding principles and philosophy upon which the Constitution is based. It highlights fundamental values such as Justice, Liberty, Equality, and Fraternity.
2. Reason (R): The reason given is, "The ideals set before the Nation are Justice, Equity, Fraternity of the individual and unity and integrity of the Nation." While the reason appears to refer to the values in the Preamble, it has an incorrect mention of 'Equity' instead of 'Equality,' which is actually the term used in the Preamble. Furthermore, the Preamble also includes Liberty, which is not mentioned in the Reason. Therefore, the statement in the reason is incorrect.

Option Analysis:

• Both (A) and (R) are true and (R) is the correct explanation of (A): This is false since (R) is not completely true.
• Both (A) and (R) are true but (R) is not the correct explanation of (A): This is false as (R) contains incorrect detail about the Preamble.
• (A) is true but (R) is false: This is the correct option. The assertion is right, but the reason is not a factual representation of the Preamble's ideals.
• (A) is false but (R) is true: This is incorrect as (A) is a correct statement.

The correct answer is (A) is true but (R) is false.

Conclusion: The Preamble to the Indian Constitution accurately sets the ideals for the nation, but the Reason provided in the question offers incorrect details, making (A) true but (R) false.