Question

Assertion (A): The number \(4^n\) cannot end with the digit 0, where \(n\) is a natural number.
Reason (R): A number ends with 0 if its prime factorization contains both 2 and 5.

• A. Both A and R are correct and R is the correct explanation of A.
• B. Both A and R are correct but R is not the correct explanation of A.
• C. A is correct but R is incorrect.
• D. Both A and R are incorrect.

Hint:

A number ends with 0 only if its prime factorization includes both 2 and 5, but this is not the explanation for why \( 4^n \) cannot end in 0.

Answer 1

The Correct Option is C

- Assertion (A): The number \(4^n\) cannot end with the digit 0, where \(n\) is a natural number. This is correct because \(4^n\) always results in a number that ends with 4, and therefore cannot end in 0. - Reason (R): A number ends with 0 if its prime factorization contains both 2 and 5. This is also correct because a number will end with 0 if its prime factorization contains both 2 and 5. However, the assertion does not directly explain the reason as \(4^n\) cannot end with a 0 because of its structure and the absence of the factor 5, not because of the prime factorization rule of numbers that end in 0.
Step 2: Conclusion.
Therefore, the correct answer is (C) A is correct but R is incorrect. Final Answer:} A is correct but R is incorrect.