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Mathematics — CBSE Class 10 board question

Q1. [1]
In question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): $4^n$ ends with digit 0 for some natural number $n$. Reason (R): For a number '$x$' having 2 and 5 as its prime factors, $x^n$ always ends with digit 0 for every natural number $n$.
  1. (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
  2. (b) Both, Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of 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
2025 30/4/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer

(d) Assertion (A) is false but Reason (R) is true.

Since $4^n = 2^{2n}$, its only prime factor is 2, never 5. So $4^n$ never ends with 0 — Assertion is false. Reason is true: if $x$ has both 2 and 5 as prime factors, then $x^n$ is divisible by 10, so it always ends with 0.

Source: Chapter 1, Section 1.2 (Example 1)

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Explanation

The textbook (Example 1, Section 1.2) explicitly states that $4^n = (2)^{2n}$ contains only the prime 2, so it can never end in 0. This makes Assertion (A) false. The Reason correctly states a general principle — a number with both 2 and 5 as factors will always produce a multiple of 10 when raised to any natural number power — so Reason (R) is true. When A is false and R is true, the answer is option (d).

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