Question

Assertion (A): If 'e' is a product of odd primes and 'n' is a natural number, then the $e^n$ can end with zero.

Reasoning (R): Any number with 2 and 5 as prime factors then, by the fundamental theorem of arithmetic, that number ends with zero.

• A. Both A and R are true, and R is the correct reason for A.
• B. Both A and R are true, and R is not the correct reason for A.
• C. A is true, but R is false.
• D. A is false, but R is true

Answer 1

Answer: (D)

d. A is false, but R is true

Answer 2

Assertion (A):

• $e$ is defined as a product of odd primes, so it does not include the prime 2.

• A number ending in 0 must be divisible by both 2 and 5 (i.e., it must have at least one 2 and one 5 as factors).

• Therefore, no power $e^n$ (which remains odd) can end with 0.

• Conclusion: Assertion (A) is false.

Reason (R):

• It is true that any number having both 2 and 5 in its prime factorization will have a factor of 10, and hence, will end with 0 in base 10.

• Conclusion: Reason (R) is true.

Since (A) is false and (R) is true, the correct answer is d.