Assertion: Both `HCOOH (I)` and `CH_3 COOH (II)` give precipitate with aqueous `AgNO_3` solution soluble in `HNO_3`.
Reason: `HCOOH` gives positive Tollens test.

Options

A. If both `(A)` are `( R)` are true and `( R)` is the correct explanation of `(A)`.
B. If both `(A)` and `( R)` are true but `( R)` is not the correct explanation of `(A)`.
C. If `(A)` is true but `( R)` is false.
D. If `(A)` is false but `( R)` is true.

Explanation

To solve the question, we need to analyze the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that both formic acid (HCOOH) and acetic acid (CH3COOH) give a precipitate with aqueous AgNO3 solution that is soluble in HNO3.

- **Formic Acid (HCOOH)**: When formic acid reacts with AgNO3, it forms silver formate (AgCOO) as a precipitate. This precipitate is indeed soluble in nitric acid (HNO3).

- **Acetic Acid (CH3COOH)**: Similarly, acetic acid reacts with AgNO3 to form silver acetate (AgOOCCH3), which is also a precipitate that dissolves in nitric acid.

Thus, the assertion is correct.

### Step 2: Analyze the Reason
The reason states that formic acid gives a positive Tollens test.

- **Tollens Test**: This test is used to identify aldehydes, and formic acid is unique among carboxylic acids because it behaves like an aldehyde. It can reduce silver ions to metallic silver, giving a positive result in the Tollens test.

Since formic acid does indeed give a positive Tollens test, the reason is also correct.

### Step 3: Determine the Relationship
Now we need to determine if the reason correctly explains the assertion. The assertion discusses the behavior of both acids with AgNO3, while the reason only addresses formic acid's ability to give a positive Tollens test.

- The assertion is about the precipitate formation with AgNO3, which applies to both acids, while the reason focuses solely on formic acid's behavior in the Tollens test.

Thus, while both statements are correct, the reason does not explain the assertion.

### Conclusion
Both the assertion and the reason are correct, but the reason does not provide a correct explanation for the assertion. Therefore, the answer is:

**Option B**: Both A and R are correct, but R is not the correct explanation of A.

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