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Show that (25)^n… (Class 10 Maths Basic SQP 2026-27, Q21B)

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MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 21(B)

From the official CBSE sample question paper for 2026-27, section B, question 21(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(B) · 2 marks · Very short answerReal Numbers

Show that will never end with digit zero for any natural number .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

When does a number end with the digit 0? Think about divisibility by 10.

Hint 2

Write 25 as a power of a prime and check whether 2 can ever be a factor.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. ½ mark

  2. So the prime factorisation of contains only the prime 5. By the Fundamental Theorem of Arithmetic, this factorisation is unique.

    ½ mark

  3. A number ends with digit 0 only if it is divisible by 10, that is, its prime factorisation must contain both 2 and 5. Here 2 is not a factor of .

    ½ mark

  4. Hence can never end with the digit zero for any natural number .

    ½ mark

Answer: has no factor 2, so it is not divisible by 10 and never ends in 0.

Where the marks are

  • Writes (½ mark)
  • States that the factorisation contains only 5 and is unique (½ mark)
  • States that ending in 0 needs both 2 and 5 as factors, and 2 is absent (½ mark)
  • Concludes that it never ends in 0 (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.