Assertion (A): A number N when divided by 15 gives the remainder 2 Then the remainder is same when N is divided by 5.
Reason (R):`sqrt(3)` is an irrational number.

Options

A. Both A and R are true and R is the correct explanation for A .
B. Both A and Rare true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the given question, we need to analyze both the Assertion (A) and the Reason (R) provided.

### Step-by-step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that a number \( N \) when divided by 15 gives a remainder of 2. This can be expressed mathematically as:
\[ N = 15k + 2 \]
where \( k \) is some integer (the quotient).

2. **Dividing by 5**:
- We need to check what happens when \( N \) is divided by 5. We can substitute the expression for \( N \) into the division by 5:
\[ N = 15k + 2 = (3 \times 5)k + 2 \]
- When we divide \( N \) by 5, we can focus on the remainder:
\[ N \mod 5 = (15k + 2) \mod 5 \]
- Since \( 15k \) is a multiple of 5, it will give a remainder of 0 when divided by 5. Therefore:
\[ N \mod 5 = 0 + 2 = 2 \]

3. **Conclusion for Assertion (A)**:
- Thus, when \( N \) is divided by 5, the remainder is indeed 2. Therefore, Assertion (A) is true.

4. **Understanding the Reason (R)**:
- The reason states that \( \sqrt{3} \) is an irrational number. This is a known fact in mathematics. It does not directly relate to the assertion about \( N \).

5. **Conclusion for Reason (R)**:
- While Reason (R) is true, it does not provide a logical explanation for Assertion (A).

6. **Final Evaluation**:
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation for Assertion (A).

### Final Answer:
- Both Assertion (A) and Reason (R) are true, but R is not the correct explanation for A.

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