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Mathematics — CBSE Class 10 board question

Q1. [1]
Assertion (A) : The number $5^n$ cannot end with the digit 0, where $n$ is a natural number. Reason (R) : Prime factorisation of 5 has only two factors, 1 and 5.
  1. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  2. (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  3. (c) Assertion (A) is true, but Reason (R) is false.
  4. (d) Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2023 30/5/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer

(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Explanation

A is true: $5^n = 5 \times 5 \times \ldots$ has only 5 as its prime factor; for a number to end in 0 it must be divisible by both 2 and 5, but 2 is absent from the prime factorisation of $5^n$, so it can never end in 0.

R is true: 1 and 5 are indeed the only factors of 5 (definition of a prime).

Why R does NOT explain A: The correct explanation uses the Fundamental Theorem of Arithmetic — $5^n$ lacks the prime factor 2, so it cannot be divisible by 10. The statement about 5 having only two factors (1 and 5) is a general property of primes and does not directly explain why $5^n$ cannot end in 0. Hence option (b).

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